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• Andrei Constantin: "Domain Wall Dynamics in the String Landscape" (advisor: Helling)
• Korbinian Paul: ""1D disordered systems with interaction" (advisor: Yevtushenko)
• Nitin Rughoonauth: "One-Loop Correction to the Potential in D3/D7-Inflation" (advisor: Haack)
• Sebastian Novak: "Defects in c = 1 conformal field theories" (advisor: Brunner)
• Lasma Alberte: " On Diffeomorphism Invariance and Black Hole Quantization " (advisor: Mukhanov)
• Alexander Pritzel: "On the Origin of Species by Means of Large Gauge Groups" (advisor: Dvali)
• Jegors Korovins: " Holographic Renormalization for Fermions in Real Time " (advisor: Erdmenger)
• Pablo Dominguez: "Time dependent Wegner-Brockett Flow for ?nite systems" (advisor: Kehrein)
• Andreas Deser: " D-brane Instantons and Flavour Physics " (advisor: Lüst)
• Daniel Plencner: "D-Branes in Topological Landau-Ginzburg Models" (advisor: Brunner)
• Matthias Drews: "Disk amplitudes of open an closed string moduli" (advisor: Lüst)
• Jarno van der Kolk: " Time Evolution of Matrix Product Operators in the Heisenberg Picture " (advisor: Schollwöck)
• Niklas Boers: " Derivation of Mean Field Equations for Classical Systems " (advisor: Dürr)
• Juri Smirnov: " Gauge Invaraint Cosmological Backreaction " (advisor: Hofmann)
• Pascal Reisert: "Tame Harmonic Bundles on Punctured Riemann Surfaces" (advisor: Schottenloher)
• Robert Schneider " Non-Perturbative Approach to Pure Yang-Mills Theory in 2+1 Dimensions " (advisor: Hofmann)
• Felix Rennecke " Strings in Background Fields and Nonassociative Geometry " (advisor: Blumenhagen)
• Martin Vogel "Eigenvalue Statistics for Random Block Operators" (advisor: Müller)
• Despoina Katsimpouri "Holographic Superconductors" (advisor: Haack)
• Elco Bakker "Detailed Analysis of Transcriptional Regulation in Yeast: Quantifying Gene Regulation Functions Using DTA Data" (advisor: Gerland)
• Sebastian Seehars "Symmetric Extensions in Entanglement Theory and Quantum Cryptography" (advisor: Christandl)
• Tiago Ramalho "Maximising positional information of morphogen gradients in the Drosophila embryo" (advisor: Gerland)
• Johannes Huster " A_oo-Structures in Lagrangian Floer Cohomology and String Field Theory " (advisor: Cieliebak)
• Sven Prüfer "Mirzakhani's Recursion Relations and Witten's Conjecture" (advisor: Cieliebak)
• Vytautas Matulevicius "Maxwell's Equations as Mean Field Equations" (advisor: Pickl)
• Vasil Bratanov " Landau and Van Kampen Spectra in Discrete Kinetic Plasma Systems " (advisor: Jenko)
• Johannes Knebel "Evolution of Cooperation in Bacterial Biofilms" (advisor: Frey)
• Carsten Klaus "D-branes and orientifolds in Landau-Ginzburg models and rational conformal field theories" (advisor: Brunner)
• João da Gama Batista "Coordination Game on Stepping-Stone Model" (advisor: Frey)
• Jan Sbierski "Strict Weyl Quantisation and the von Neumann Condition" (advisor: Schottenloher)
• Christoph Sträter "Quantum Integrability and its Application to the Dicke Model" (advisor: von Delft)
• André Franca "Classicalization, Declassicalization and Vainshtein" (advisor: Dvali)
• Karl Wienand "Cooperation in Changing Environments" (advisor: Frey)
• André Betz "T-Duality Covariant Formulations Of Supergravities: Double Field Theory and Generalized Geometry" (advisor: Lüst)
• Constantin Sluka "On Quasilocalization by Modified Kinetic Terms" (advisor: Dvali)
• Ingo Homrighausen " Fluctuation Effects in Chemical Reactions with Anomalous Diffusion " (advisor: Frey)
• Leonhard Horstmeyer "BPS Equations from the (2,0) Nonlinear Sigma Model" (advisor: Groot-Nibbelink)
• Tehseen Rug "Strong Coupling in Cascading DGP" (advisor: Dvali)
• Rui Coelho "On the Exactness of Powers of a Kähler Form" (advisor: Kotschick)
• Gino Knodel "On Alternative Mechanisms For Genrating Scale-Invariant Primordial Perturbations" (advisor: Dvali)
• Peter Uebele "Mirror Symmetry of P^1 x P^1 and Tropical Geometry" (advisor: Cieliebak)
• Marius Christopher Lemm "Localization Results For The Quantum XY Model In A Locally Varying External Field" (advisor: Warzel)
• Michael Handrek "On the Maximal Excess Charge of the Chandrasekhar-Coulomb Hamiltonian in 2 Dimensions" (advisor: Siedentop)
• Maximilian Imgrund " On the Two Stream Instability in Pulsar Magnetospheres " (external advisor)
• Anatolij Gelimson "Two Nonequilibrium Models in Biology --- Surface Active Colloids and the Dilemma of Cooperation" (advisor: Frey)
• Matthias Schlaffer "Analysis of e+ e- -> W+ W- within an Electroweak Effective Lagrangian at NLO" (advisor: Buchalla)
• Francesco Alaimo "On the Effects of Spin Orbit Interaction on the Conductance through a Quantum Dot in the Presence of Kondo Correlations" (advisor: von Delft)
• Cora Uhlemann "Cosmological Perturbation Theory in an Anisotropic Universe" (advisor: Hofmann)
• Henry David Gareau Hanson "Stability of Kasner Spacetimes" (advisor: Hofmann)
• Arvid Kingl "Localization in Disordered Bosonic Insulators with Strong Short-Range Interaction" (advisor: Yevtushenko)
• Valentina Ros "On the Lifshitz tails phenomenon for the Density of States of Anderson Hamiltonians on Trees" (advisor: Warzel)
• Benedikt Ziebarth "Ab-initio Study of Lithium Titanate as Mixed Conductor for Solid State Batteries" (external advisor)
• Sungmin Hwang "Vacuum Persistence in Massive Gravity" (advisor: Hofmann)
• Rudi Michael Rahn "Corrections to e+ e- ->  W+ W- scattering in electroweak chiral effective theory" (advisor: Buchalla)
• Paula Ida Reichert "Can a Parabolic Evolution of the Entropy of the Universe provide the Foundation for the Second Law of Thermodynamics?" (advisor: Dürr)
• Malte Lehmann "Optimal Timing Strategies for Induction of Sugar Utilization Systems" (advisor: Gerland)
• Mario Rainer Flory " Dynamical Black Holes in Topologically Massive Gravity " (advisor: Sachs)
• Jan Priel "On the Cobordism Hypothesis" (advisor: Schottenloher)
• Sebastian Gottwald "Semiclassical quantum dynamics via the method fo Stationary Phase for a rigorous approach to Feynman Path Integrals" (advisor: Erdös)
• Franz Martin Thoma "A Quantum Field Theoretical Detector Model for Probing the Unruh Effect" (advisor: Hofmann)
• Dennis Hank Schimmel "(Quasi-)Localization of Gauge Fields" (advisor: Dvali)
• Marc Nikolaus Max von Reutern "Simulations of Cilia on a Sphere" (advisor: Frey)
• Stefan Wiedenmann "Segal's Axioms of a Conformal Field Theory" (advisor: Schottenloher)
• Harishchandra Ramadas "Cutoff For The Noisy Voter Model" (advisor: Gantert)
• Marin Georgiev Bukov "Bose-Fermi Mixtures: A Mean-Field Study" (advisor: Pollet)
• Anupam Prasad Vedurmudi "Mechanical Processing in the ICE Model" (advisor: van Hemmen)
• Christoph Fischbacher "On the Spectrum of the XXZ Spin Chain" (advisor: Müller)
• Emanuel Reithmann "Correlations at the Edge of Lattice Gases --- How Tip-Tracking Proteins Influence Microtubule Dynamics" (advisor: Frey)
• Florian Kurz "On the Renormalization of a doubled worldsheet theory" (advisor: Groot Nibbelink)
• Thomas Bilitewski "Superconductivity in two dimensional Bose-Fermi-Mixtures: A Dynamical-Cluster- Approximation Study" (advisor: Pollet)
• Andreas Kapfer "Chern-Simons Terms and the Effective Action of F-Theory with U(1)-Factors" (advisor: Grimm)
• Emmanuel Gebhard Klinger "Quantum and Discrete Trees" (advisor: Warzel)
• Tobias Ried " Jordan Wigner Transformations and Quantum Spin Systems on Graphs " (advisor: Warzel)
• Katja Miller "Random Walks on Percolation Clusters with Carrying Capacities" (advisor: Gantert)
• Alexander Hach "Anderson Localization on Erd\H os-Rényi Random Graphs" (advisor: Müller/Warzel)
• Benedikt Sebastian Staffler "Lifshitz Tails For Random Band Matrices" (advisor: Müller)
• Eliska Greplová "Quantum Information With Fermionic Gaussian States" (advisor: Cirac)
• Benedikt Rehle "Scaling Limits of Biased Random Walks on Galton-Watson Trees with Leaves" (advisor: Gantert)
• Martin Peter Idel "On the structure of positive maps" (advisor: Wolf)
• Benedikt Mark Richter "The D-string - D-term string equivalence conjecture" (advisor: Dvali)
• Silke Bergeler "Active Turing Systems" (advisor: Frey)
• Peter Labus "Black Holes viewed as Bose-Einstein Condensates of Gravitons" (advisor: Dvali)
• Martin Krebs "Localized Wavefunctions on Magnetized Orbifolds" (advisor: Ratz)
• Brian Joseph Padden "The Mathematical Heart of the Unruh Effect" (advisor: Helling)
• Maximilian Jeblick "Mean-field Dynamics of a Tracer Particle in a Fermi Sea" (advisor: Pickl)
• Nikolai Leopold "Hypersurface Bohm models for Photons" (advisor: Dürr)
• David Müller "A minimax principle for eigenvalues in spectral gaps with an application to Dirac operators with singular potentials" (advisor: Siedentop)
• Patrik Ingo Omland "Characteristic Hypersurfaces and Constraint Theory" (advisor: Hofmann)
• Stefano Duca "Emergence of Cooperation in Structured Populations: Groups Splitting and the Role of Stochasticity" (advisor: Frey)
• Javier Enrique Cuesta Rueda "On a non-commutative version of the Darmois-Skitovich theorem" (advisor: Wolf)
• Ernest C. Yeung "Quantum super-A-Polynomials" (advisor: Sulkowsi)
• Markus Josef Dierigl " Towards a Topological Theory for Domain Walls in (Super-)Yang-Mills Theories " (advisor: Dvali)
• Markus Alexander Ebert "Monojet Distributions at the LHC as a Diagnostic Tool for Dark Matter Couplings" (advisor: Beneke)
• Pavel Hájek "On Manifolds with Corners" (advisor: Cieliebak)
• Michael Roland Wolff "The PCR using laser-heated nanoparticles" (advisor: Gerland)
• Christian Schmid "Lie Algebroids and Non-Geometry in String Theory" (advisor: Blumenhagen)
• Mauro Miguel Monsalve Mercado "Geometric Structures on Type IIB Supergravity Backgrounds and Implications for their FIeld Theory Duals" (advisor: Erdmenger)
• Stanislav Schmidt "Gauge Fields and Topology: Theory and Application" (advisor: Dvali)
• Roberto Oliveri "Gravitational Shockwaves on BTZ Black Holes" (advisor: Sachs)
• Nils-Oliver Linden "Open and Reduced Wilson Chains for Quantum Impurity Models" (advisor: Pollet)
• Flavio Carlos Montiel Montoya "Bound states of symmetry defects in topological Landau-Ginzburg models" (advisor: Brunner)
• Paco Giudice "On the Parametrization of Inflation" (advisor: Mukhanov)
• Christian Heinrich Behrens "Ground State Phase Diagram of the three-dimensional Bose-Hubbard model with anisotropic hopping" (advisor: Pollet)
• Vanessa Paulisch "Quantum Information Assisted by One-Dimensional Waveguides" (advisor: Cirac)
• Severin Lüst "Consistent Truncations and SU(2)-Structure Compactifications" (advisor: Grimm)
• Johannes Ruhl "Non-Colliding Markov Chains" (advisor: Wachtel)
• Han Yu " Randomness, a point of view in dynamical systems with applications statistical physics and number theory " (advisor: Pickl)
• Johannes Michael Hauschild "Detecting Phase Transitions in Anisotropic Heisenberg Models with the Stochastic Series Expansion" (advisor: Heidrich-Meisner)
• Thomas Frerix "Quaternionic Shape Analysis" (advisor: Cremers)
• Kevin Jägering "Majorana Fermions in Superconducting Quantum Wires" (advisor: von Delft)
• Lukas Weidinger "Longer-ranged interactions in quantum point contacts" (advisor: von Delft)
• Simon Adrian Weidinger "Magnon-Magnon interactions and Higgs mode in quantum antiferromagnets in Raman scattering" (advisor: Zwerger)
• Manuel Hubert Wickmann "On the Martin Boundary of the Galton-Watson Process" (advisor: Wachtel)
• Mykhaylo Panchenko "Nonperturbative Aspects of Quantum Field Theory" (advisor: Dvali)
• Matthias Reiter "From Single Cell Migration to Collective Motion: A Computational Model for Tissue Dynamics" (advisor: Frey)
• Anton Samojlow "Non-binding of strongly coupled many-polarons in dimensions two and three" (advisor: Sørensen)
• Maximilian Alfred Girlich "Simulating Continious Quantum Systems by Mean Field Fluctuations" (advisor: Keyl)
• Paul Pfeiffer "Quantum Memristors" (advisor: Solano/von Delft)
• Dominik Schröder "Phase transitions in the density of states of quantum spin glasses" (advisor: Erdös)
• Sebastian Zell "A corpuscular picture of gravitational scattering" (advisor: Dvali)
• Felix Maria Kempf "Interaction of Dislocation Pairs in a Flocking Model at High Density" (advisor: Frey)
• Dimitri Pimenov "Fermi-Edge Polaritons with Finite Hole Mass" (advisor: von Delft)
• Simone Anna Elvira Rademacher "Energy Levels of Dipoles in Graphene" (advisor: Siedentop)
• Toni Scharle "The Local Boundedness of Gradients of Solutions to Elliptic and Parabolic phi-Laplacian Systems" (advisor: Diening)
• Bernhard Lohner "Reaction-Diffusion Systems with Conservation of Mass" (advisor: Frey)
• Valenti Vall Camell "Branes, Monodromies and Non-Geometric Backgrounds" (advisor: Lüst)
• Nina Kudryashova "Post-Inflation Stability of the GEF Mechanism" (advisor: Dvali)
• Moritz Binder "Minimally Entangled Typical Thermal States for the evaluation of finite-temperature correlation and response functions" (advisor: Schollwöck)
• Isabella Ruth Krämer "Studies of totally asymmetric simple exclusion processes in different diffusive environments" (advisor: Frey)
• Patrick Wilke "Molecular Transport in Cylindrical Geometries - Geometric Frustration in Periodically Intersecting Totally Asymmetric Simple Exclusion Processes" (advisor: Frey)
• Lukas Nickel "On Relativistic Interactions in Quantum Theories" (advisor: Dürr)
• Florian Stecker "The Moduli Space of Higher Rank Higgs Bundles" (advisor: Weiß)
• Laurent Beauregard "On a statistical mechanical approach to self-gravitating systems" (advisor: Hofmann)
• Adrian Dietlein "Absence of Anderson orthogonality for localised Anderson models" (advisor: Müller)
• Andreas Bluhm "On the Area Law for the Entropy of Entanglement for Gapped Systems" (advisor: Bachmann)
• Sebastian Walter Greiner "Mirror Symmetry of Calabi-Yau Four-Folds with non-trivial Cohomology of odd Degrees" (advisor: Grimm)
• Bernhard Pfirsch "A Semiclassical Approximation to the Quantum Propagator for Weyl-Quantized Subquadratic Hamiltonians" (advisor: Sørensen)
• Benjamin Spreng "Quantum quenches with bosonic ladders in artificial gauge fields" (advisor: Pollet)
• Felix Hänle "Second Quantization of Liénard-Wiechert Fields" (advisor: Deckert)
• Andreas Christian Swoboda "Coulomb-Volkov Corrections in the Context of Time-dependent Surface Flux Methods" (advisor: Scrinzi)
• Robin Schlenga "On the Physical Origin of the Lamb Shift" (advisor: Dürr)
• Shan Wei "Poroelasticity and the Biot Consolidation Model" (advisor: extern)
• Florian Werner Johann Wolf "Flux-Scaling Scenarios for Moduli Stabilization in String Theory and Axion Monodromy Inflation" (advisor: Blumenhagen)
• Maximilian Paul Bode "Corpuscular Skyrmions" (advisor: Dvali)
• Fridtjof Brauns "A New Pattern Formation Mechanism in Budding Yeast" (advisor: Frey)
• Alexis Kassiteridis "From parton model to bound states" (advisor: Hofmann)
• Nils Prigge "Schoen surfaces from a topological perspective" (advisor: Kotschick)
• Abhishek Khanna "Scale vs Conformal Invariance in Field Theories" (advisor: Sachs)
• Nina Anne Renate Miekley "Holographic entanglement entropy: temperature and flavour contributions" (advisor: Erdmenger)
• Leila Mirzagholi "On the Recently Proposed Mimetic Dark Matter and its Modifications" (advisor: Mukhanov)
• Markus Hartmut Nöth "The Unruh-effect without observer" (advisor: Dürr)
• Philipp Moritz Geiger "Condensation and Coexistence in the Antisymmetric Lotka-Volterra Equation" (advisor: Frey)
• Anna Sophie Hackenbroich "Inverse-square t-J-V models as parent Hamiltonians for lattice Halperin states" (advisor: Cirac)
• Johannes Ehrmaier "Mechanisms of solar water splitting: Photodetachment of H-atoms from Heterocyclic Organic Radicals" (advisor: Domcke)
• Jan Mölter "On Anderson orthogonality within the interacting and non-interacting Luttinger-Sy model" (advisor: Müller)
• Mykhaylo Kogan "Application of the Generalized Auxuliary Current Description to de Sitter space-time" (advisor: Hofmann)
• Yuta Sekiguchi "Type IIB Calabi-Yau Orientifolds, Non-geometric fluxes, and Moduli Stabilization --- A Flux-Scaling Scenario and Its Phenomenology" (advisor: Blumenhagen)
• Gytis Kulaitis "Comparing Different Mathematical Definitions of 2D CFT" (advisor: Schottenloher)
• Dominik Hangleiter "Certification of Quantum Simulations" (advisor: Eisert)
• Yigit Yargic "Two-Loop Gauge Unification in Intersecting D7-Brane Models with Left-Right Symmetry" (advisor: Blumenhagen)
• Christoph Kehle "Interpolation of Hartree-Fock- and Müller Functional: Investigation of Continuity and Existence of a Minimiser" (advisor: Siedentop)
• Aaron Schaal "Derivation and Meaning of the Newton-Schrödinger Equation" (advisor: Dürr)
• Nelvis Fornasin "Equivariant cohomology and localization" (advisor: Görtsches)
• Florian Bernd Johannes Dorsch "Energy Levels of Dipoles generated by Point-Charges in Graphene" (advisor: Siedentop)
• Matteo Parisi "Symmetries of the Tree Amplituhedron" (advisor: Ferro)
• Joost Simon Wit "The Balck Hole N-Portrait: Quantum Computing in Critical Bose-Einstein Systems" (advisor: Dvali)
• Ruth Schulte "Boundary Effects on Alloy-Type Anderson Schrödinger Operators: Spectral Shift Functions and Entanglement Entropy" (advisor: Müller)
• Oksana Iarygina "Corpuscular Effects and Scattering on Coherent States" (advisor: Dvali)
• Lea Boßmann "On the Dipole Approximation" (advisor: Dürr)
• Leonard Stimpfle "Kähler and Sasaki Manifolds of Cohomogeneity One" (advisor: Görtsches)
• Fabian Bernd Kugler "Fermi Edge Singularity and the Functional Renormalization Group" (advisor: von Delft)
• Daniel González Cuadra "Quantum Simulations of Abelian Lattice Gauge Theories with Ultracold Atoms" (advisor: Cirac)
• Martin Vogrin "Superconformal interfaces in two dimensions and their g-function" (advisor: Mayr)
• Kilian Mayer "Higher derivatives in M-theory and type IIA compactifications on Calabi-Yau threefolds" (advisor: Grimm)
• David Licht "Decay of Black Holes as Bound States and Hawking Radiation" (advisor: Hofmann)
• Philip Betzler "T-duality and Mirror Symmetry" (advisor: Lüst)
• Johannes Frank König "keV Sterile Neutrino Dark Matter from Singlet Scalar Decays" (advisor: Raffelt)
• Margret Hildegard Heinze "Controllability of the Jaynes-Cummings-Hubbard model" (advisor: Keyl)
• Andreas Bauer "Symmetries and excitations in the quantum double models --- a tensor network approach" (advisor: Schuch)
• Abhiram Mamandur Kidambi "Aspects of black holes in Chern-Simons (Super)-Gravity and AdS/CFT" (advisor: Erdmenger)
• Carlo Cascio "Emission in Photonic Crystals" (advisor: Schollwöck)
• Tailin Li "One-Loop Einstein-Hilbert term in minimally supersymmetric type IIB T^6/Z_N orientifolds" (advisor: Haack)
• Juan Sebastian Cruz Avendano "Scattering of a Particle and a Black Hole described as a Bound State" (advisor: Dvali)
• Pavel Kos "Quantum Spin Liquid Ground States of the Heisenberg-Kitaev Model on the Triangular Lattice" (advisor: Punk)
• Marin Ferara " Introduction to Resurgence of Quartic Scalar Theory " (advisor: Sachs)
• Mareike Elena Bojer "Study of the totally asymmetric simple exclusion process on a lenth changing lane in a diffusive environment" (advisor: Frey)
• Wonyl Choi "On the Mathematical Represenation of Linguistic Structure" (advisor: Panagiotou)
• Hannes Herrmann "Finding Stationary States by Interacting Quantum Worlds" (advisor: Deckert)
• Ismail Achmed-Zade "Stringy T^3-fibrations, T-folds and Mirror symmetry" (advisor: Lüst)
• Ga-Ram Jeong "Stabilization of vacuum bubbles with weakly interacting medium fields" (advisor: Dvali)
• Ottavia Balducci " Graviton Quantum Tree Graphs " (advisor: Hofmann)
• Andreas Wegscheider "The eikonal approximation for scattering of a test particle on an N particle state" (advisor: Hofmann)
• Leo Johannes Martin Stenzel " A DMRG study of the Fermi-Hubbard model in hybrid space " (advisor: Schollwöck)
• Oriol Servera Sirés "Periodic orbits in high-dimensional Lotka-Volterra networks" (advisor: Frey)
• Simon Bürger " LSZ Reduction in QFT and Lattice Systems " (advisor: Dybalski)
• Dmytro Bondarenko " Tree tensor network approximations to conformal field theories " (advisor: König)
• Aris Konstantinos Papaioannou "Magnetic Monopoles in Gauge Theories" (advisor: Hamilton)
• Stephen Brennan "Surface gravity in dynamical spherically symmetric spacetimes" (advisor: Sachs)
• Michael Volpp " Running of Radiative Neutrino Masses --- A Study Of The Zee-Babu Model " (advisor: Raffelt)
• Alessandro Giacomo Bottero " Analysis of a two species TASEP as a model for heterogeneous transport on microtubules " (advisor: Frey)
• Hannah Julia Ochner "On Singularities in Bohmian Quantum Gravity" (advisor: Dürr )
• Spyridon Dimoudis "The Helffer-Sjörstrand Formula and Random Schrödinger Operators" (advisor: Müller)
• Daniel Steffens "Implications of Unitarity on the Structure of Scattering Amplitudes in Higher Spin Theories" (advisor: Sachs)
• Martin Philip Dupont "On the Practical Applications of Information Field Dynamics" (advisor: Enßlin)
• Laura Hui-Shin Shou "Stability of the Hall Conductance" (advisor: Warzel)
• Thomas Steingasser  "A field theoretic Approach to solitonic Moduli and its Connection with Spacetime Geometry" (advisor: Hofmann)
• Ludwig Fürst " On the Quantization of the Hall Conductance for Many-Body Interactions on a Torus " (advisor: Bachmann)
• Filip Kozarski "Analysis of the extended Harper-Hofstadter-Mott model using reciprocal cluster mean field theory" (advisor: Pollet)
• Simon-Raphael Fischer "Existence of Thin Shell Wormholes Using Non-Linear Distributional Geometry'' (advisor: Hamilton)
• Francesco Battistel "General Quantum Error Correction for MERA Codes" (advisor: König)
• Ilya Kull " Classification of Matrix Product States with a Local (Gauge) Symmetry " (advisor: Cirac)
• Alexander Tabler "Monodromy of q-difference equations in 3D supersymmetric gauge theories" (advisor: Mayr)
• Marcel Oliver Schaub "A Second Order Ground State Energy Expansion for the Dilute Bose Gas" (advisor: Sørensen)
• Konstantin Konrad Christoph Eder "Quantum Theory of Charged Black-Hole Horizons" (advisor: Sahlmann)
• Vivian Anthony Britto " A Mathematical Construction of an E_6 Grand Unified Theory " (advisor: Hamilton)
• Juraj Vrabel " Associative division algebras in field theories and non-commutative geometry " (advisor: Jurco)
• Daniel Konstantin Thung "Invariant Geometric Structures and Chern Numbers of G_2 Flag Manifolds" (advisor: Kotschick)
• Pablo Sala de Torres Solanot " A time-dependent Gaussian variational description of Lattice Gauge Theories " (advisor: Cirac)
• Julian Bender "Digital quantum simulation of lattice gauge theory" (advisor: Cirac)
• Leopold Karl Kellers " Making Use of Quantum Trajectories for Numerical Purposes " (advisor: Deckert)
• Siddhant Das "Arrival Time Distributions of spin-1/2 Particles" (advisor: Dürr)
• Francesco Romano "Early-warning signs for critical transitions in stochastic differential equations" (advisor: Kühn)
• Grzegorz Aleksander Gradziuk "Scaling behaviour of cycling frequencies in active biological assemblies" (advisor: Frey)
• Federico Roccati " Novel simulation techniques for a sterile neutrino seach with KATRIN " (advisor: Mertens)
• Andrea Morelato "Salter manifolds and inequivalent symplectic structures" (advisor: Kotschick)
• Korbinian Pöppel "Complex Patterns And Their Transitions In A Mass Conserving Reaction-Diffusion-System" (advisor: Frey)
• Nils Fritiof Persson " The No-Ghost Theorem of the BRST Quantised Bosonic String " (advisor: Helling)
• Johannes Feldmeier "Spectral Functions and Exact Solutions in a Quantum Dimer Model for Pseudogap Metals" (advisor: Punk)
• Daniel Wolfgang Issing " The Quantum Determinant of the Elliptic Quantum Algebra $ \cal A _ q.p (\hat gl _N)$ " (advisor: extern)
• Matthias Maximilian Englbrecht "Robust Preparation of Logical Basis States in Planar Codes" (advisor: König)
• Georgios Lioutas " Probing Skyrmion black holes " (advisor: Hofmann)
• Daniel Weiss " Spectral Theory of Inductive Limit C*-Algebras and Application to Loop Quantum Gravity " (advisor: Hofmann)
• Johannes Sedlmeir " The Vlasoc equation for multiple particle types " (advisor: Pickl)
• Max Christian Bollmann "A Web of Theories: Relating Scattering Amplitudes via Transmutation Operators" (advisor: Ferro)
• Simon Maximilian Weinzierl " Buildings, Amalgams and Reductive Linear Algebraic Groups " (advisor: Morel)
• Nina-Maria Gottschling "Gamma convergence of the Levy-Lieb density functional to the Thomas-Fermi functional" (advisor: Nam)
• Franz Xaver Sax "On Classical Mechanics and Quantum Mechanics on Shape Space" (advisor: Dürr)
• Benedikt Wegener " The problem of equivalence of different gauges in External Current QED " (advisor: Dybaslksi)
• Christoph Herbert Lienhard "Hamiltonian Monte Carlo Sampling for Fields" (advisor: Ensslin)
• Llorenç Espinosa-Portalés " On the emergence of Bekenstein entropy from spherical symmetry and quantum criticality " (advisor: Dvali)
• Matteo Scandi " Quantifying Dissipation via Thermodynamic Length " (advisor: Cirac)
• Kilian Adriano Lieret "Construction of Angular Observables Sensitive to New Physics in $\bar B\to D^*\tau^-\bar\nu_\tau$ Decays and Measurements of Differential Cross Sections of $\bar B\to D^*\ell^- \bar\nu_\ell$ Decays with Hadronic Tagging at Belle" (advisor: Kuhr)
• Jan-Niklas Toelstede "Renormalization of SMEFT operators by Super-Heat-Kernel Expansion" (advisor: Buchalla)
• Otari Sakhelashvili "On topological structure of QCD vacuum and Chiral symmetry breaking" (advisor: Dvali)
• Lukas Rauber " Quantum Compression and Fixed Points of Schwarz Maps " (advisor: Wolf)
• Marco Orts "Geometric Particle-in-Cell Methods for Magnetohydrodynamics" (advisor: Gerland)
• Jonas Vincent Bucher " A Survey of Low-Rank Methods with Applications in Computational Physics and Spectra of Fully-Correlated Helium " (advisor: Scrinzi)
• Albertus Johannes Jacobus Maria de Klerk " Energy Conservation in Open Quantum Systems " (advisor: Schollwöck)
• Maximilian Emanuel Kurthen " Baysian Causal Inference " (advisor: Ensslin)
• Sascha Lill "Existence of Multi-Time Dynamics in a Quantum Field Theory Model" (advisor: Tomulka)
• Yannick Michael Herbert Couzinié " Sublinearly reinforced Pólya urns on graphs of bounded degree " (advisor: Heydenreich)
• Roberto Caroli " Cosmological aspects of Mimetic Gravity " (advisor: Sachs)
• Pantelis Fragkos "Monodromy Defects in Linear Sigma Models" (advisor: Brunner)
• Robert Salzmann "Derivation of the 3D energy-critical non-linear Schrödinger equation and Bogoliubov excitations for Bose gases" (advisor: Nam)
• Matthias Michael Zipper "Effects of dimension-six operators of the Standard Model on top quark mass determination at a future lepton collider" (advisor: Beneke)
• Michael Zantedeschi " The parameter space of locked inflation and corrections to modulated reheating " (advisor: Dvali)
• David Alexander Wierichs " Thermalization of a Cavity Mode in the Presence of a Dye Molecule " (advisor: Schollwöck)
• Max Snijders "Automatic Probabilistic Modelling of Dynamical Systems Based on Global Geometry and Topology of Data" (advisor: extern)
• Dennis Gallenmüller "Hyperkähler quotients and their application to the moduli space of weak solutions to Nahm's equations" (advisor: Swoboda)
• Fabian Engelniederhammer "Symplectic Embedding of Poly-Cylinders" (advisor: Vogel)
• Tobias Benjamin Russ "On Singularity Resolution in Asymptotically Free Mimetic Gravity" (advisor: Mukhanov)
• Alexander Alfred Wierzba "Parametrodynamics" (advisor: Schuller)
• Evangelos Giantsos "N=2 Superconformal Interfaces" (advisor: Brunner)
• Benedikt Remlein "Non-equilibrium criticality in isostatic spring-networks" (advisor: Broedersz)
• Anamaria Hell "The massless limit of interacting Proca theory" (advisor: Mukhanov)
• Brin Verheijden "Two-Species Quantum Dimer Models on the Triangular Lattice" (advisor: Punk)
• Austris Akmentins "Optimal initialization of a quantum dot" (advisor: von Delft)
• Patrick Angus Hager "Smooth Interface Geometries and Unitarity in Curved Space-Times" (advisor: Hofmann)
• Markus Hasenöhrl "Interaction-Free Discrimination of Quantum Channels" (advisor: Wolf)
• Max Bramberger "Two Level System in a Bath of Morse Oscillators" (advisor: Schollwöck)
• Khoirul Faiq Muzakka "Electroweak Chiral Lagrangian with Two Scalars and SO(6)/SO(5) Composite Higgs Model" (advisor: Buchalla)
• Patrick Schnell "Dynamical structure factor of a chiral spin liquid" (advisor: Pollmann)
• Jan Michael Mandrysch " The necessity of indefinite metric Hilbert spaces in covariant gauge formulations of QED " (advisor: Dybalski)
• Gabriel Torregrosa Cortés "Effects of coloured noise in systems out of equilibrium" (advisor: )
• Johanna Christina Mayer "Two species of Self-Propelled Particles Interacting in a Snowdrift Game Scenario" (advisor: Frey)
• Oliver Benedikt Zier "The physics of the interstellar medium" (advisor: extern)
• Maximilian Heinz Ruep "On Self-Adjointness of Noether Charges in Algebraic Quantum Field Theory" (advisor: Dybalski)
• Michael Hofstetter "Maximum of the Ginzburg-Landau $\nabla$-interface model" (advisor: extern)
• Llibert Aresté Saló "Eigenspectrum of Fubini-Lipatov instanton solutions" (advisor: )
• Daniel Panea Lichtig "Testing Swampland Conjectures and the Emergence Proposal in a two-parameter Calabi-Yau model" (advisor: Lüst)
• Seyed Pouria Mazloumi "All multiplicity Einstein Yang-Mills amplitudes relations" (advisor: Stieberger)
• Martin Enriquez Rojo " Swampland Conjectures for N=1 Orientifolds " (advisor: Plauschinn/Lüst)
• Arman Korajac "Exploring Drell-Yan tails at the Large Hadron Collider" (advisor: Weiler)
• Eyup Samet Balkan "The Matsusaka-Ran Criterion" (advisor: Schneider)
• Leonardo García Heveling "On the double complex of bi-Lagrangian structures" (advisor: Kotschick)
• Zhiyuan Wei "Directional superradiant generation of strongly-entangled photonic states" (advisor: Cirac)
• Borislav Polovnikov "Fluctuations and Criticality in Reaction-Diffusion Systems" (advisor: Broedersz)
• Julian Johannes Freigang "Yang Mills Theory From String Field Theory" (advisor: Sachs)
• Christian Koke "The Segal-Bargmann Space As The Infinite Radius Limit Of Geometrically Quantized Two-Spheres" (advisor: Hofmann)
• Aleksander \L ukasz Strzelczyk "Towards Classification of the Indecomposable Summands of Motives over Number Fields" (advisor: Semenov)
• Lukas Mikio Nakamura "Non-regidity Results for non-Legendrian and C^0-limits of Legendrian Submanifolds" (advisor: Vogel)
• Teresa Dimitra Karanikolaou " Continuous Tensor Network States " (advisor: Cirac)
• José Diogo de Figueiredo e Simão " On the Causal Structure of Quantum Space-Time " (advisor: Hofmann)
• Yoobin Jeong "Embedding and Projection maps in Quantum Geometry" (advisor: Oriti)
• Simon Hirscher "Some details of the proof of the Positive-Mass Theorem in higher dimensions" (advisor: external)
• Sören Arlt "Dynamics of the Antisymmetric Lotka-Volterra Equation for 1D and 2D Systems" (advisor: Frey)
• Andriana Makridou "String Vacua and the Swampland" (advisor: Blumenhagen)
• Juan Sébastian Valbuena Bermúdez " Erasure of Topological Defects: Vortex Unwinding by Domain Wall Sweeping " (advisor: Dvali)
• Hrólfur Ásmundsson "String Field Theory Toy Models; Intermediate Field Decomposition and Effective Description" (advisor: Sachs)
• Henrik Weyer "Long-scale dynamics of mass-con\-ser\-ving reaction-diffusion models" (advisor: Frey)
• Richard Georg Swiderski "Critical Behaviour of Logistically Growing Auto-Chemotactic Cells: A Renormalisation Group Analysis" (advisor: Frey)
• Florian Raßhofer "A Renormalization Group Approach to the Critical Behavior of Dividing Chemotactic Cells" (advisor: Frey)
• Jasper van der Kolk "Renormalisation Group Analysis of Logistically Growing Auto-Chemotactic Bacteria" (advisor: Frey)
• Zhen Xu "Renormalons and Top Quark Observables with Jet Substructure" (advisor: Beneke)
• Felix Feist "The Zeno Effect in Quantum Arrival Times" (advisor: Pickl)
• Matej Logar "Importance of the recoil for the existence and properties of the atom-photon bound state" (advisor: Schollwöck)
• Georgios Papagoudis "Towards Bimetric Supergravity" (advisor: Lüst)
• Juan Antonio Guerrero Montero "Reaction-diffusion systems on dynamically evolving surfaces" (advisor: Frey)
• Juan Mauricio Valencia Villegas "Dynamical Features of UV-Completion by Classicalization" (advisor: Dvali)
• Simon Kuhn "Focusing instabilities and singularities in pp-wave spacetimes" (advisor: Sachs)
• Bláithín Power "Conformal symmetry predictions for on-shell scattering amplitudes" (advisor: Henn)
• Julia Brunkert "Effective theories for pseudogap metals" (advisor: Punk)
• Mathis Gerdes " Deep Learning Calabi-Yau Metrics " (advisor: Lüst)
• Lexin Ding " Fermionic Entanglement and Correlation " (advisor: Schilling)
• Davide De Biasio "Geometric Flow Equations, the Swampland Program and Schwarzschild-AdS Space-time" (advisor: Lüst)
• Joan Bernabeu Gómez "Axion Allignment During Inflation" (advisor: Dvali)
• Santiago Aguirre Lamus "Multiloop functional renormalization group in the Keldysh formalism --- A study of the single-impurity Anderson model" (advisor: von Delft)
• Anxiang Ge "Analytic Continuation of Correlators from the Matsubara to the Keldysh Formalism" (advisor: von Delft)
• Konstantinos Karampelas "D-Brane and O-Plane Einstein-Hilbert term Corrections in Type I String Theory" (advisor: Haack)
• Daniel González Cuadra "Higgs mechanisom as an alternative to confinement in Yang-Mills theories" (advisor: Cirac)
• Lukas Josef Anton Homeier "Analog quantum simulation and single hole doping of Z2 lattice gauge theories" (advisor: Schollwöck)
• Janni Harju "Statistical tools for interpreting single-cell contact data" (advisor: Brodersz)
• Angelo Brillante Romeo "Fidelity Estimates for Noisy Quantum Circuits with Haar-Random Gates" (advisor: König)
• Matteo Ciarchi "Noise Induced Patterns in Extended Systems" (advisor: Frey)
• Patricia Ribes Metidieri "Exploring Quantum Field Theory in Curved Space-times with Extended Information Networks" (advisor: Lüst)
• Matthias Carosi "Yang-Mills and Proca Theory from the spinning particle in the BRST formalism" (advisor: Sachs)
• Florian Pandler "Aspects of Top Quark Decay and Production in the SMEFT" (advisor: Buchalla)
• Wilhelm Kadow "Hole Dynamics in the t-J Model on the Triangular Lattice" (advisor: Knap)
• Merik Niemeyer "Geometrische Formalität von Drei-Mannigfaltigkeiten" (advisor: Kotschick)
• Ankit Shrestha "Constraining models of inflation with galaxy clustering" (advisor: Schmidt)
• Michael Reichert "Geometric Pattern Selection in Reaction-Diffusion Systems" (advisor: Frey)
• Panagiotis Rigatos "QCD factorization of the four lepton decay B^- \rightarrow \ell \bar \nu _ \ell \ell' \bar \ell'" (advisor: Beneke)
• Yilun Yang "Spectral Analysis of Quantum Many Body Systems with Tensor Network Algorithms" (advisor: Cirac)
• Valentin Leeb "Anomalous Quantum Oscillations in a Heterostructure of Graphene on a Proximate Quantum Spin Liquid" (advisor: Knolle)
• Rafael Álvarez-García "Periods and Moduli Stabilization near the Conifold" (advisor: Blumenhagen)
• Severin Angerpointner "Complex Reaction Networks --- A Study of the Formose Reaction" (advisor: Frey)
• Frederik Pfeiffer "Extended PAM in the context of SmB6 and Cold Atoms in optical lattices: a DMFT/DCA + NRG study" (advisor: von Delft)
• Charlotte Dietze "Dispersive Estimates for Nonlinear Schr\"odinger Equations with External Potentials" (advisor: Phan)
• Giacomo Contri "Limits of Approximately Thermal Evolution in Field Theories" (advisor: Dvali)
• Lukas Krumpeck "Phase Transitions in $ \cal N =(2,2)$ Gauged Linear Sigma Models with Defects" (advisor: Brunner)
• Flavio Rossetti "The Wave Equation in Cosmological Spacetimes" (advisor: Natário)
• Janik Kruse "The Nelson Model on Static Spacetimes" (advisor: Lampart)
• Johan Jacoby Klemmensen "On Classifying Solutions of the Kapustin-Witten Equations via Higgs Bundles" (advisor: Kotschick)
• Stefan Birnkammer " Confinement in Condensed Matter Systems --- Equilibrium and Non-Equilibrium" (advisor: Knap)
• Chun Yin Lam "Bogoliubov excitation spectrum for mean-field Bose gases with general interactions" (advisor: Phan)
• Kianusch Vahid Yousefnia "Bayesian approach to long-range correlations and multiplicity fluctuations in nucleus-nucleus collisions" (advisor: Ollitrault)
• Samuel Scalet "Computable R\'enyi Mutual Informations: Area Laws and Correlations" (advisor: Phan)
• Daesik Kim "Bosons in the Lowest Landau Level --– A Path Integral Approach to Electromagnetic Response" (advisor: Moroz)
• Martin Peev "Non-Commutative Regularity Structures" (advisor: Phan)
• Florian Michael Haberberger "Complete BEC for trapped Bosons with Neumann Boundary Conditions in the Gross-Pitaevskii Regime" (advisor: Hainzl)
• Loek van Rossem "The Shape of Vision: Decoding the Primary Visual Cortex with Homology" (advisor: Stemmler)
• Jonathan Lukas Korbinian König "Encircling Non-Hermitian Degeneracies" (advisor: Cirac)
• Dominik Haslehner "Spinors, Amplitudes and Unitarity: (Non-)Renormalization of Gravity from On-Shell Methods" (advisor: Weiler)
• Enric Solé-Farré "Instantons and Foliations: Moduli Spaces of Instantons on Foliated Manifolds" (advisor: Kotschick)
• Boris Betancourt Kamenetskaia "Boson Stars: Structure, Evolution and Detection. A Theoretical Proposal" (advisor: Ibarra)
• Paul Manuel Schindler "A Variational Method for the Quantum Sherrington Kirkpatrick Model" (advisor: Cirac)
• Silvia Gasparotto "Cosmic Birefringence from Axion Monodromy Potential" (advisor: Komatsu)
• Richard Maximilian Milbradt "Dual-, Ternary- and (\Delta+1)-Unitaries: A path to exact solutions of dynamics for multidimensional quantum lattices" (advisor: Mendl)
• Miaohan Long "2D Topological Quantum Field Theories" (advisor: Hensel)
• Anca-Victoria Preda "SO(10) Grand Unified Theory: from proton decay to LHC" (advisor: Dvali)
• Anja Stuhlfauth "Phenomenology of a light Higgs Triplet in SU(5)" (advisor: Dvali)
• Raúl Morral Yepes "String order in measurement-induced symmetry-protected topological phases" (advisor: Pollmann)
• Enya Hsiao "Unbounded Pontryagin numbers on nonnegatively curved spin manifolds" (advisor: Kotschick)
• Zhongda Zeng "Variational theory of Angulons and their rotational spectroscopy" (advisor: Cirac)
• Gabriel Schmid "On 3-Dimensional Quantum Gravity and Quasi-Local Holography in Spin Foam Models and Group Field Theory" (advisor: Oriti)
• Fabian Wagner "Towards a Canonical Form for Elliptic Feynman Integrals" (advisor: Henn)
• Simon Felix Langenscheidt "Superposed Random Spin Tensor Networks and their Holographic Properties" (advisor: Oriti)
• Paula Naomi Pilatus "Born Geometry" (advisor: Kotschick)
• Dorothea-Enrica von Criegern "The Liquid Drop Model: An Analysis of Non-Spherical Equilibrium Sets" (advisor: Sørensen)
• Gonzalo Fernández Casas "AdS_4 orientifold vacua, (in)stability of membranes and their Weak Gravity Conjecture" (advisor: Sachs)
• Andrii Dashko "Debye mass effects in the Dark Sector in the Early Universe" (advisor: Brambilla)
• Alexander Mayer "Topological Data Analysis of the Cosmic Web" (advisor: Weller)
• Sebastian Albrecht "Formulation of Batalin-Vilkovisky Field Theories as Homotopy Lie Algebras" (advisor: Sachs)
• Yahui Li "Hilbert Space Fragmentation in Open Quantum Systems" (advisor: Pollmann)
• Lukas Wangler "Motional Effects in Subwavelength Arrays of Atoms" (advisor: Cirac)
• Filippo De Luca "Pattern Formation of Active Filaments with Polar and Antipolar Interactions" (advisor: Frey)
• Sara Maggio "The role of high nucleon density on neutrino production in exploding Supernovae" (advisor: Weiler)
• Jonas Habel "Effects of Magnon-Magnon Interactions on Chiral Edge Modes in Topological Magnon Insulators" (advisor: Knolle)
• Denis Murphy "Metastable Vacuum Decay at Finite Temperature" (advisor: Garbrecht)
• Seyf Kaddachi "Inconsistencies in DKMM-refined KKLT placing it in the swampland" (advisor: Blumenhagen)
• Conall Vincent McCabe "Quantum Simulation of Lattice Quantum Electrodynamics using Rydberg Tweezer Arrays" (advisor: Grusdt)
• Dusan Novicic "Generalised Global Symmetries in Axion Electrodynamics" (advisor: L?st)
• Beatrice Nettuno "The Role of Diffusion and Temporary Immunization in the Classification of Absorbing Phase Transitions" (advisor: Frey)
• Christoph Metzl "Determining the Influence of Diffusion and Temporary Immunization of the Critical Behaviour of Absorbing Phase Transitions with Large Scale Stochastic Simulations" (advisor: Frey)
• Davide Toffenetti "The Effect of Temporary Immunization and Diffusion on the Critical Properties of Epidemics Models" (advisor: Frey)
• Deepak Aryal "Quotient Symmetry Protected Topological Phenomena" (advisor: Pollmann)
• Pit Bermes "Magnon Exitations in two-dimensional doped Anti-ferromagnets" (advisor: Grusdt)
• Aron Kerschbaumer "Quantum-Informed Optimization Algorithms" (advisor: Mendl)
• Arthur Kosmala "Ewald-based Long-Range Message Passing for Molecular Graphs" (advisor: Günnemann)
• Ralf Konietzka "Phase Space Analysis of the Local Interstellar Medium --- The Oscillation of the Radcliffe Wave" (advisor: Burkert)
• Xiyuan Gao "Spontaneous CP violation and Flavor Changing Neutral Currents in Minimal SO(10)" (advisor: Senjanovic)
• Yoon Yun Chan "The Absence of Phase Transitions And The Recursion Method" (advisor: Jansen)
• Michelangelo Tartaglia "Self-dual fields in 6D Supergravity" (advisor: Lüst)
• Julian Bösl "Excitations in Higher Moment Conserving Systems" (advisor: Knap)
• Loïc Honet "2-Group Symmetries in Quantum Field Theories: an Algebraic Approach" (advisor: extern)
• David García Heredia "Cosmological inhomogeneities from the Group Field Theory approach to Quantum Gravity" (advisor: Oriti)
• Marcin Stankiewicz "Cosmology-hydrodynamics correspondence via conformal symmetry" (advisor: Oriti)
• Martina Jung "Bose-Einstein condensation for hard-core bosons" (advisor: Schilling)
• Helene Lösl "Polarons in the triangular t-J Model" (advisor: Grusdt)
• Andreas Tsevas "Universal Mechanisms of Spontaneous Cell Polarization" (advisor: Frey)
• Jan Kochanowski "Static and Dynamic Properties of Quantum Spin Systems at Non-Zero T" (advisor: Cirac)
• Avedis Neehus "Dirac Fermions with Topological Mass Disorder" (advisor: Knolle)
• Antonia Eirini Paraskevopoulou "The Emergence Proposal with Multiple Moduli Fields" (advisor: Blumenhagen)
• Lukas Komisel "Metastable Discharges of False Vacua by Memory Burden" (advisor: Dvali)
• Jonas Peteranderl "Degenerate stability of the Caffarelli-Kohn-Nirenberg inequality along the Felli-Schneider curve" (advisor: Frank)
• Martin Link "Covariant Multipole Expansions in Non-Relativistic Effective Field Theories" (advisor: Beneke)
• Marc Machaczek "Neural Network Quantum States for Fracton Models" (advisor: Pollet)
• Benjamin Muntz "Moduli Stabilisation, Racetracks, and the Swampland Programme" (advisor: Blumenhagen)
• Nils Wagner "False Vacuum Decay Of Excited States From Finite-Time Instantons" (advisor: Gabrecht)
• Lukas Kienesberger " The Phase Dilemma and its Ramifications for Computational Complexity in Functional Theory " (advisor: Schilling)
• Josef Emanuel Seitz "Worldvolume Perspectives on Unstable D-brane Systems" (advisor: Dvali)

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Physics and Astronomy

Mathematical Physics

Mathematical physics is an interdisciplinary subject where theoretical physics and mathematics intersect. The University of Iowa has held an ongoing mathematical physics seminar for over forty years, in which faculty from both the mathematics and physics departments actively participate. Topics of interest include relativistic quantum mechanics, quantum field theory, general relativity, representation theory of groups and quantum groups, theory of dynamical systems, quantum information theory, phase transitions, quantum chaos, lattice gauge theory and C* algebras.

Our program in Mathematical Physics is one of the few in the U.S. that is fully interdisciplinary, combining both physicists and mathematicians in a working relationship. Every semester the mathematical physics seminar includes talks given by students, faculty and distinguished visitors, including a fields medalist.  Zoom has allowed us to include many talks by distinguished faculty from external institutions.  The seminar often features topical talks on subjects of interest to the participants.  Quantum information theory and machine learning were recently featured topics.

Students may work on interdisciplinary research topics involving mathematics and theoretical physics.  They can obtain a Ph.D. in the Department of Physics, Department of Mathematics, or through the University's Applied Mathematical and Computational Sciences program, in which a physicist and a mathematician jointly supervise the dissertation.  Students in mathematical physics often work closely with faculty in both the physics and mathematics departments. Several students have recently completed PhD dissertations in related areas of mathematical physics.

Faculty Specializing in this Area

Yannick Meurice, Ph.D.

Wayne N. Polyzou, Ph.D.

Vincent G.J. Rodgers, Ph.D.

Kory Stiffler, Ph.D.

Research staff in this area.

NOTICE: The University of Iowa Center for Advancement is an operational name for the State University of Iowa Foundation, an independent, Iowa nonprofit corporation organized as a 501(c)(3) tax-exempt, publicly supported charitable entity working to advance the University of Iowa. Please review its full disclosure statement.

My Students' Theses (and Other Papers)

• James Gilliam
• Laurel Langford
• Aaron Lauda
• Alissa Crans
• Valeria Michelle Carrión Álvarez
• Toby Bartels
• Jeffrey Morton
• Alex Hoffnung
• Chris Rogers
• John Huerta
• Christopher Walker
• Brendan Fong
• Jason Erbele
• Blake S. Pollard
• Brandon Coya
• Daniel Cicala
• Kenny Courser
• Joe Moeller
• Jade Edenstar Master
• Christian Williams
• James Gilliam, Lagrangian and Symplectic Techniques in Discrete Mechanics , Ph.D. thesis, U. C. Riverside, 1996. Available in PDF and Postscript .
• James Gilliam and John Baez, An algebraic approach to discrete mechanics, Letters in Mathematical Physics 31 (1994), 205–212. In PDF and Postscript .
• Laurel Langford, 2-Tangles as a Free Braided Monoidal 2-Category with Duals , Ph.D. thesis, U. C. Riverside, 1997. Available in Postscript .
• Laurel Langford and John Baez, 2-Tangles , Letters in Mathematical Physics 43 (1998), 187–197.
• Laurel Langford and John Baez, Higher-dimensional algebra IV: 2-tangles , Advances in Mathematics 180 (2003), 705–764.
• Aaron D. Lauda, Open-Closed Topological Quantum Field Theory and Tangle Homology , PhD thesis, Cambridge University, 2006. Available in Postscript .
• Aaron D. Lauda and John Baez, Higher-dimensional algebra V: 2-groups , Theory and Applications of Categories 12 (2004), 423–491
• Aaron D. Lauda and Eugenia Cheng, Higher-Dimensional Categories: an Illustrated Guide Book , to be published.
• Aaron D. Lauda, Frobenius algebras and ambidextrous adjunctions , Theory and Applications of Categories 16 (2006), 84–122.
• Aaron D. Lauda, Frobenius algebras and planar open string topological field theories .
• Aaron D. Lauda and Hendryk Pfeiffer, Open-closed strings: two-dimensional extended TQFTs and Frobenius algebras
• Alissa S. Crans, Lie 2-Algebras , Ph.D. thesis, U. C. Riverside, 2004. Available in PDF . Also available in a more user-friendly format on the arXiv .
• Alissa S. Crans and John Baez, Higher-dimensional algebra VI: Lie 2-algebras , Theory and Applications of Categories 12 (2004), 492–528.
• Alissa S. Crans, Higher linear algebra , transparencies for a lecture at the Institute of Mathematics and its Applications.
• Alissa S. Crans, John Baez, Danny Stevenson and Urs Schreiber, From loop groups to 2-groups , Homotopy, Homology and Applications , 9 (2007), 101–135.
• Alissa S. Crans, John Baez and Derek K. Wise, Exotic statistics for strings in 4d BF theory , Advances in Theoretical and Mathematical Physics 11 (2007), 707–749.
• Valeria Michelle Carrión Álvarez, Loop Quantization versus Fock Quantization of p-Form Electromagnetism on Static Spacetimes , Ph.D. thesis, U. C. Riverside, 2004. Available in PDF . Also available in a more user-friendly format on the arXiv .
• Valeria Michelle Carrión Álvarez, Variations on a theme of Gelfand and Naimark .
• Valeria Michelle Carrión Álvarez, Wilson loop dynamics without regularization , talk.
• Valeria Michelle Carrión Álvarez, Physics and analysis on noncompact manifolds , talk.
• Toby Bartels, Higher Gauge Theory: 2-Bundles , Ph.D. thesis, U. C. Riverside, 2006. Available in PDF . Also available in a more user-friendly format on the arXiv under the title Higher gauge theory I: 2-bundles .
• Toby Bartels and John Baez, dialog on Quaternionic functional analysis .
• Toby Bartels, Expository papers .
• Derek K. Wise, Topological Gauge Theory, Cartan Geometry, and Gravity , Ph.D. Thesis, U. C. Riverside, 2007. Available in PDF .
• Derek K. Wise, Lattice p-form electromagnetism and chain field theory , Classical and Quantum Gravity 23 (2006), 5129-5176.
• Derek K. Wise, John Baez and Alissa S. Crans, Exotic statistics for strings in 4d BF theory , Advances in Theoretical and Mathematical Physics 11 (2007), 707–749.
• Derek K. Wise, Symmetric space Cartan connections and gravity in three and four dimensions , SIGMA 5 (2009), 080.
• Derek K. Wise, MacDowell-Mansouri gravity and Cartan geometry , Classical and Quantum Gravity 27 (2010), 155010.
• Jeffrey Morton, Extended TQFT's and Quantum Gravity , Ph.D. thesis, U. C. Riverside, 2007. Available in PDF . Also available in a more user-friendly format on the arXiv .
• Jeffrey Morton, Categorified algebra and quantum mechanics , Theory and Applications of Categories 16 (2006), 785–854.
• Jeffrey Morton, Categorifying the quantum harmonic oscillator , talk at the International Category Theory Conference (CT06), White Point, Nova Scotia, 2006.
• Jeffrey Morton, Higher algebra, extended TQFTs, and 3d quantum gravity , talk at the Perimeter Institute, Waterloo, Canada, 2006.
• Jeffrey Morton, Double bicategories and double cospans , Journal of Homotopy and Related Structures 4 (2009), 389–428
• Jeffrey Morton, Extended TQFT, gauge theory, and 2-linearization .
• Alexander E. Hoffnung, Foundations of Categorified Representation Theory , Ph.D. Thesis, U. C. Riverside, 2010. Available in PDF .
• Alexander E. Hoffnung and John Baez, Convenient categories of smooth spaces , Transactions of the American Mathematical Society 363 (2011), 5789–5825.
• Alexander E. Hoffnung, John Baez and Christopher Rogers, Categorified symplectic geometry and the classical string , Communications in Mathematical Physics 293 (2010), 701–715.
• Alexander E. Hoffnung, John Baez and Christopher D. Walker, Higher-dimensional algebra VII: groupoidification , Theory and Applications of Categories 24 (2010), 489–553.
• Alexander E. Hoffnung, The Hecke bicategory .
• Alexander E. Hoffnung and Aaron D. Lauda, Nilpotency in type A cyclotomic quotients , Journal of Algebraic Combinatorics 32 (2010), 533.
• Christopher L. Rogers, Higher Symplectic Geometry , Ph.D. thesis, U. C. Riverside, 2011. Available in PDF .
• Christopher L. Rogers, John Baez and Alexander E. Hoffnung, Categorified symplectic geometry and the classical string , Commun. Math. Phys. 293 (2010), 701–715.
• Christopher L. Rogers and John Baez, Categorified symplectic geometry and the string Lie 2-algebra , Homotopy, Homology and Applications 12 (2010), 221–236.
• Christopher L. Rogers, L ∞ -algebras from multisymplectic geometry , Letters in Mathematical Physics 100 (2012), 29–50.
• Christopher L. Rogers, Domenico Fiorenza and Urs Schreiber, A higher Chern-Weil derivation of AKSZ sigma-models , International Journal of Geometric Methods in Modern Physics 10 (2013), 1250078.
• Christopher L. Rogers, 2-plectic geometry, Courant algebroids, and categorified prequantization , Journal of Symplectic Geometry 11 (2013), 53–91.
• Christopher L. Rogers, Domenico Fiorenza and Urs Schreiber, L ∞ -algebras of local observables from higher prequantum bundles, Homology, Homotopy and Applications 16 (2014), 107–142.
• John Huerta, Division Algebras, Supersymmetry and Higher Gauge Theory , Ph.D. thesis, U. C. Riverside, 2011. Available in PDF . Also available in a more user-friendly format on the arXiv .
• John Huerta and John Baez, Division algebras and supersymmetry I , in Superstrings, Geometry, Topology, and C*-Algebras , eds. Robert Doran, Greg Friedman and Jonathan Rosenberg, Proceedings of Symposia in Pure Mathematics 81 , AMS, Providence, Rhode Island, 2010, pp. 65–80.
• John Huerta and John Baez, Division algebras and supersymmetry II , Advances in Theoretical and Mathematical Physics 15 (2011), 1373–1410.
• John Huerta, Division algebras and supersymmetry III , Advances in Theoretical and Mathematical Physics 16 (2012), 1485–1589.
• John Huerta, Division algebras and supersymmetry IV .
• John Huerta, L ∞ superalgebras for superstring and M-theory , talk at the AMS special session on Topology, Geometry and Physics, November 2010.
• John Huerta, A categorified supergroup for string theory , talk at the Workshop and School on Higher Gauge Theory, TQFT and Quantum Gravity in Lisbon, February 2011.
• John Huerta and John Baez, The algebra of grand unified theories , with John Huerta, Bulletin of the American Mathematical Society 47 (2010), 483–552.
• John Huerta and John Baez, An invitation to higher gauge theory , General Relativity and Gravitation 43 (2011), 2335–2392
• John Huerta and John Baez, The strangest numbers in string theory , Scientific American , May 2011, 60–65.
• John Huerta and John Baez, G 2 and the rolling ball , Transactions of the American Mathematical Society 366 (2014), 5257–5293.
• Christopher D. Walker, A Categorification of Hall Algebras , Ph.D. thesis, U. C. Riverside, 2011. Available in PDF .
• Christopher D. Walker, John Baez and Alexander E. Hoffnung, Higher-dimensional algebra VII: groupoidification , Theory and Applications of Categories 24 (2010), 489–553.
• Christopher D. Walker, Hall algebras as Hopf objects .
• Christopher D. Walker, Groupoidified linear algebra , talk at Groupoidfest 2008.
• Christopher D. Walker, A categorification of Hall algebras , talk at the AMS Fall Western Section Meeting, November 2009.
• Mike Stay, Physics and Computation , Ph.D. thesis, Department of Computer Science, University of Auckland, 2015. Available in PDF .
• John Baez and Mike Stay, Physics, topology, logic and computation: a Rosetta Stone , in New Structures for Physics , ed. Bob Coecke, Lecture Notes in Physics 813 , Spinger, Berlin, 2011, 95–172.
• John Baez and Mike Stay, Algorithmic thermodynamics , Mathematical Structures in Computer Science 22 (2012), 771–787.
• Mike Stay and Jamie Vicary, Bicategorical semantics for nondeterministic computation , Proceedings of Mathematical Foundations of Programming Semantics 29 (2013), 345–359.
• Mike Stay, Compact closed bicategories , Theory and Applications of Categories 31 (2016), 755–798.
• Brendan Fong, The Algebra of Open and Interconnected Systems , Ph.D. thesis, University of Oxford, 2016. Available in PDF and on the arXiv .
• Brendan Fong, Causal theories: a categorical perspective on Bayesian networks .
• Brendan Fong and John Baez, A Noether theorem for Markov processes , Journal of Mathematical Physics 54 (2013), 013301.
• Brendan Fong and John Baez, Quantum techniques for studying equilibrium in reaction networks , Journal of Complex Networks 3 (2014), 22–34.
• Brendan Fong, Decorated cospans , Theory and Applications of Categories 30 (2015), 1096–1120. (Blog article here. )
• Brendan Fong and John Baez, A compositional framework for passive linear networks , Theory and Applications of Categories 33 (2018), 1158–1222. (Blog article here .)
• Brendan Fong, John Baez and Blake S. Pollard, A compositional framework for Markov processes , Journal of Mathematical Physics 57 (2016), 033301. (Blog article here .)
• Brendan Fong, Paolo Rapisarda and Paweł Sobociński, A categorical approach to open and interconnected dynamical systems , to appear in Proceedings of Logic in Computer Science 2016, LICS 16 .
• Brandon Coya and Brendan Fong, Corelations are the prop for extraspecial commutative Frobenius monoids , Theory and Applications of Categories 32 (2017), 380–395. (Blog article here .)
• Brendan Fong, Modelling interconnected systems with decorated corelations , talk at the Simons Institute for the Theory of Computing, December 6, 2016.
• Jason Erbele finished his Ph.D. thesis in 2016 and now teaches at Victor Valley College. He did his thesis on the use of symmetric monoidal categories, and specifically PROPs, to study control theory. He started by writing a paper with me that gives a presentation of the symmetric monoidal category of finite-dimensional vector spaces and linear relations. Starting from here, he constructed a symmetric monoidal category whose morphisms are the 'signal-flow' diagrams used in control theory. The all-important properties of 'observability' and 'controllability' of a linear time-invariant system can be nicely understood in this framework.
• Jason Michael Erbele, Categories in Control: Applied PROPs , Ph.D. thesis, U. C. Riverside, 2016. Available in PDF . Also available in a more user-friendly format on the arXiv .
• John Baez and Jason Erbele, Categories in control , Theory and Applications of Categories 30 (2015), 836–881. (Blog article here .)
• Jason Erbele, Categories in control , video of talk at QPL 2015 , University of Oxford, 2016.
• Blake S. Pollard finished his Ph.D. thesis in 2017. He did his thesis on open systems, particularly open versions of Markov processes and chemical reaction networks. He studied the change in relative entropy in open Markov processes, and nonequilibrium steady states for open Markov processes and reaction networks. He described a 'black-boxing' functor sending any such open system to the the relation between input and output concentrations and flows that holds in a steady state. He and I also worked with Metron Scientific Solutions on their Complex Adaptive System Composition and Design Environment project, funded by DARPA. In the last summer of his thesis work he did an internship with Siemens at Princeton working with Arquimedes Canedo on the project Next-Generation Engineering with Category Theory and Sheaves. Then he got a postdoc at NIST working with Eswaran Subrahanian and Spencer Breiner on an NSF-funded project called A Categorical Approach to Systems Modeling for Systems Engineering. He is now a Senior Scientist at CrossnoKaye, which builds advanced control systems for industrial cold storage facilities.
• Blake S. Pollard, Open Markov Processes and Reaction Networks , Ph.D. thesis, U. C. Riverside, 2017. Available in PDF . Also available in a more user-friendly format on the arXiv .
• Blake S. Pollard, Open Markov processes and reaction networks , thesis defense slides, June 1, 2017.
• Blake S. Pollard, A Second Law for open Markov processes , Open Systems and Information Dynamics 23 (2016), 1650006. (Blog article here .)
• Blake S. Pollard, John Baez and Brendan Fong, A compositional framework for Markov processes , Journal of Mathematical Physics 57 (2016), 033301. (Blog article here .)
• Blake S. Pollard, Open Markov processes: A compositional perspective on non-equilibrium steady states in biology , Entropy 18 (2016), 140. (Blog article here .)
• Blake S. Pollard and John Baez, A compositional framework for reaction networks , Reviews of Mathematical Physics 29 (2017), 1750028. (Blog article here .)
• Brandon Coya finished his thesis in 2018, and now teaches at Whittier College. He began his research by studying corelations with my student Brendan Fong. These are a way of describing electrical circuits made solely of ideal conductive wires. He then expanded his research by working with me and Franciscus Rebro on other electrical circuit diagrams, and then wrote a paper by himself on "bond graphs", another form of diagram used by engineers to describe not only electrical circuits but a large class of other systems.
• Brandon Coya, Circuits, Bond Graphs, and Signal-Flow Diagrams: A Categorical Perspective , Ph.D. thesis, U. C. Riverside, 2018. Available in PDF . Also available in a more user-friendly format on the arXiv .
• Brandon Coya, Circuits, bond graphs, and signal-flow diagrams: a categorical perspective , thesis defense slides, May 15, 2018.
• John Baez, Brandon Coya and Franciscus Rebro, Props in network theory . (Blog article here .)
• Brandon Coya, A compositional framework for bond graphs .
• Brandon Coya, Frobenius monoids, weak bimonoids, and corelations , talk at Applied Category Theory 2017, November 5, 2017. Video: part 1 and part 2 .
• Daniel Cicala finished his thesis in 2019 and now teaches at Southern Connecticut State University. His thesis was inspired by graph rewriting, with a strong focus on on 'open' graphs, which can be glued together to form larger graphs. But he worked at a high level of generality, considering not just graphs but objects in any topos. He developed two different approaches to rewriting open objects, both using the idea of structured cospans.
• Daniel Cicala, Rewriting Structured Cospans: A Syntax For Open Systems , Ph.D. thesis, U. C. Riverside, 2019. Available in PDF . Also available in a more user-friendly format on the arXiv .
• Daniel Cicala, Spans of cospans , Theory and Applications of Categories 33 (2018), 131–147.
• Daniel Cicala and Kenny Courser, Spans of cospans in a topos , Theory and Applications of Categories 33 (2018), 1–22.
• Daniel Cicala, Categorifying the ZX-calculus , in Proceedings 14th International Conference on Quantum Physics and Logic , eds. Bob Coecke and Aleks Kissinger.
• Daniel Cicala, Rewriting structured cospans .
• Kenny Courser finished his Ph.D. thesis in 2020. He did his thesis on double categories as a formalism for describing open systems. Most of his thesis is about 'structured cospans', a way to build double categories of networks — but a large chunk is about open Markov processes, which require some other techniques.
• Kenny Courser, Open Systems: A Double Categorical Perspective , Ph.D. thesis, U. C. Riverside, 2020. Available in PDF . Also available in a more user-friendly format on the arXiv . (Blog articles here. )
• Kenny Courser, A bicategory of decorated cospans , Theory and Applications of Categories 32 (2017), 995–1027.
• Kenny Courser and Daniel Cicala, Spans of cospans in a topos , Theory and Applications of Categories 33 (2018), 1–22.
• Kenny Courser and John Baez, Coarse-graining open Markov processes , Theory and Applications of Categories 33 (2018), 1223–1268. (Blog article here .)
• Kenny Courser and John Baez, Structured cospans , Theory and Applications of Categories 35 (2020), 1771–1822. (Blog article here .)
• Kenny Courser, Structured cospans , talk at the 4th Symposium on Compositional Structures, May 22, 2019.
• Kenny Courser, Coarse-graining open Markov processes , talk at Quantum Physics and Logic 2019, June 12, 2019.
• Joe Moeller finished his Ph.D. thesis in 2020. He did his thesis on network models and the monoidal Grothendieck construction. In 2021 he got a postdoc at NIST working with Eswaran Subrahanian and Spencer Breiner.
• Joe Moeller, The Grothendieck Construction in Categorical Network Theory , Ph.D. thesis, U. C. Riverside, 2020. Available in PDF . Also available in a more user-friendly format on the arXiv .
• Joe Moeller, John Baez, John Foley and Blake Pollard, Network models , Theory and Applications of Categories 35 (2020), 700–744.
• Joe Moeller and Christina Vasilakopoulou, Monoidal Grothendieck construction , Theory and Applications of Categories 35 (2020), 1159–1207.
• Joe Moeller, Noncommutative network models , Mathematical Structures in Computer Science 30 (2020), 14—32.
• Joe Moeller, John Baez and John Foley, Network models from Petri nets with catalysts , Mathematical Structures in Computer Science 30 (2020), 14–32.
• Joe Moeller, Monoidal Grothendieck construction , talk at the 4th Symposium on Compositional Structures, May 22, 2019.
• Joe Moeller, Network models from Petri nets with catalysts , talk at Quantum Physics and Logic 2019, June 12, 2019.
• Jade Edenstar Master finished her Ph.D. thesis in 2021 and now has a postdoc in computer and information sciences at the University of Strathclyde. She started by working with me on 'open' Petri nets, that is, Petri nets with some places specified as inputs and some as outputs. She then generalized these to Q-nets, which are specified by an arbitrary Lawvere theory Q: when this is the Lawvere theory for commutative monoids, we get Petri nets. She also worked on the 'algebraic path problem', a generalization of the shortest path problem from graphs to R-matrices, meaning matrices valued in an arbitrary quantale Q: when this is the booleans, such matrices are just graphs. She did her thesis on open Q-nets, open R-matrices, and their operational semantics.
• Jade Master, Composing Behaviors of Networks , Ph.D. thesis, U.C. Riverside, 2021. Available in PDF. Also available in a more user-friendly format on the arXiv .
• John Baez and Jade Master, Open Petri nets , Mathematical Structurs in Computer Science 30 (2020) 314–341.
• Jade Master, Petri nets based on Lawvere theories , Mathematical Structures in Computer Science 30 (2020), 833–864.
• Tai-Danae Bradley, Martha Lewis, Jade Master and Brad Theilman, Translating and evolving: towards a model of language change in DisCoCat , Electronic Notes Theor. Comput. Sci. 283 (2018), 50–61.
• John Baez, Fabrizio Genovese, Jade Master and Michael Shulman, Categories of nets , in 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) , IEEE, Rome, Italy, 2021, pp. 1–13.
• Jade Master, Why is homology so powerful?
• Jade Master, The open algebraic path problem , in 9th Conference on Algebra and Coalgebra in Computer Science (CALCO 2021) , eds. Fabio Gadducchi and Alexandra Silva, Schloss Dagstuhl – Leibniz-Zentrum, Dagstuhl, Germany, 2021, pp. 20:1–20:20.
• Owen Lynch, Relational Composition of Physical Systems: A Categorical Approach , M.Sc. Thesis, Universiteit Utrecht, 2022, corrected and improved version at the arXiv.
• John Baez, Joe Moeller and Owen Lynch, Compositional thermostatics , Journal of Mathematical Physics 64 (2023), 023304.
• Christian Williams, The Metalanguage of Category Theory , Ph.D. Thesis, U. C. Riverside, 2023.
• John Baez and Christian Williams, Enriched Lawvere theories for operational semantics , Proceedings ACT 2019 , Electronic Proceedings Theoretical Computer Science 323 (2020), 106-135.

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Calculating space-charge-limited current density in nonplanar and multi-dimensional diodes

Calculating space-charge limited current (SCLC) is a critical problem in plasma physics and intense particle beams. Accurate calculations are important for validation and verification of particle-in-cell (PIC) simulations. The theoretical assessment of SCLC is complicated by the nonlinearity of the Poisson equation when combined with the energy balance and continuity equations. This dissertation provides several theoretical tools to convert the nonlinear Poisson equation into a corresponding linear differential equation, which is then solved for numerous geometries of practical interest.

The first and second chapters briefly summarize the application of variational calculus (VC) to solve for one-dimensional (1D) SCLC in cylindrical and spherical diode geometries by extremizing the current in the gap. Next, conformal mapping (CM) is presented to convert the concentric cylindrical diode geometry into a planar geometry to obtain the same SCLC solution as VC. In the next chapter, SCLC is determined for several geometries with curvilinear electron flow that cannot be solved using VC because the Poisson equation cannot be written easily. We then map a hyperboloid tip onto a plane to form a non-Euclidean disk (Poincaré disk). These mappings on to Poincaré disk are utilized to solve for SCLC in tip-to-tip and tip-to-plane geometries. Lie symmetries are then introduced to solve for SCLC with nonzero monoenergetic injection velocity, recovering the solutions for concentric cylinders, concentric spheres, tip-to-plane, and tip-to-tip for zero injection velocity. We then extend the SCLC calculations to account for any geometry in multiple dimensions by using VC and vacuum capacitance. First, we derive a relationship between the space-charge limited (SCL) potential and vacuum potential that holds for any geometry. This relationship is utilized to obtain exact closed-form solutions for SCLC in two-dimensional (2D) and three-dimensional (3D) planar geometries considering emission from the full surface of the cathode. PIC simulations using VSim were performed that agreed with the SCLC in 2D diode with a maximum error of 13%. In the final chapters, we extend these multidimensional SCLC calculations to nonzero monoenergetic emission. The SCLC in any orthogonal diode in any number of dimensions is obtained by relating it to the vacuum capacitance. The current in the bifurcation regime is also derived from first-principles from vacuum capacitance. The simulations performed in VSim agreed with the theory with a maximum error of 7%.

These mathematical techniques form a set of powerful tools that extend prior studies by yielding exact and approximate SCLC in numerous nonplanar and multidimensional diode geometries, thereby not requiring expensive and time-consuming PIC simulations. While more experiments are required to benchmark the validity of these calculations, these results may ultimately prove useful by providing a rapid first-principles approach to determine SCLC for many geometries that can be used to assess the validity of PIC simulations and facilitate multiphysics simulations.

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Home > Arts and Sciences > Physics > PHYSICSETD

Physics Theses, Dissertations, and Masters Projects

Theses/dissertations from 2023 2023.

Ab Initio Computations Of Structural Properties In Solids By Auxiliary Field Quantum Monte Carlo , Siyuan Chen

Constraining Of The Minerνa Medium Energy Neutrino Flux Using Neutrino-Electron Scattering , Luis Zazueta

Experimental Studies Of Neutral Particles And The Isotope Effect In The Edge Of Tokamak Plasmas , Ryan Chaban

From The Hubbard Model To Coulomb Interactions: Quantum Monte Carlo Computations In Strongly Correlated Systems , Zhi-Yu Xiao

Theses/Dissertations from 2022 2022

Broadband Infrared Microspectroscopy and Nanospectroscopy of Local Material Properties: Experiment and Modeling , Patrick McArdle

Edge Fueling And Neutral Density Studies Of The Alcator C-Mod Tokamak Using The Solps-Iter Code , Richard M. Reksoatmodjo

Electronic Transport In Topological Superconducting Heterostructures , Joseph Jude Cuozzo

Inclusive and Inelastic Scattering in Neutrino-Nucleus Interactions , Amy Filkins

Investigation Of Stripes, Spin Density Waves And Superconductivity In The Ground State Of The Two-Dimensional Hubbard Model , Hao Xu

Partial Wave Analysis Of Strange Mesons Decaying To K + Π − Π + In The Reaction Γp → K + Π + Π − Λ(1520) And The Commissioning Of The Gluex Dirc Detector , Andrew Hurley

Partial Wave Analysis of the ωπ− Final State Photoproduced at GlueX , Amy Schertz

Quantum Sensing For Low-Light Imaging , Savannah Cuozzo

Radiative Width of K*(892) from Lattice Quantum Chromodynamics , Archana Radhakrishnan

Theses/Dissertations from 2021 2021

AC & DC Zeeman Interferometric Sensing With Ultracold Trapped Atoms On A Chip , Shuangli Du

Calculation Of Gluon Pdf In The Nucleon Using Pseudo-Pdf Formalism With Wilson Flow Technique In LQCD , Md Tanjib Atique Khan

Dihadron Beam Spin Asymmetries On An Unpolarized Hydrogen Target With Clas12 , Timothy Barton Hayward

Excited J-- Resonances In Meson-Meson Scattering From Lattice Qcd , Christopher Johnson

Forward & Off-Forward Parton Distributions From Lattice Qcd , Colin Paul Egerer

Light-Matter Interactions In Quasi-Two-Dimensional Geometries , David James Lahneman

Proton Spin Structure from Simultaneous Monte Carlo Global QCD Analysis , Yiyu Zhou

Radiofrequency Ac Zeeman Trapping For Neutral Atoms , Andrew Peter Rotunno

Theses/Dissertations from 2020 2020

A First-Principles Study of the Nature of the Insulating Gap in VO2 , Christopher Hendriks

Competing And Cooperating Orders In The Three-Band Hubbard Model: A Comprehensive Quantum Monte Carlo And Generalized Hartree-Fock Study , Adam Chiciak

Development Of Quantum Information Tools Based On Multi-Photon Raman Processes In Rb Vapor , Nikunjkumar Prajapati

Experiments And Theory On Dynamical Hamiltononian Monodromy , Matthew Perry Nerem

Growth Engineering And Characterization Of Vanadium Dioxide Films For Ultraviolet Detection , Jason Andrew Creeden

Insulator To Metal Transition Dynamics Of Vanadium Dioxide Thin Films , Scott Madaras

Quantitative Analysis Of EKG And Blood Pressure Waveforms , Denise Erin McKaig

Study Of Scalar Extensions For Physics Beyond The Standard Model , Marco Antonio Merchand Medina

Theses/Dissertations from 2019 2019

Beyond the Standard Model: Flavor Symmetry, Nonperturbative Unification, Quantum Gravity, and Dark Matter , Shikha Chaurasia

Electronic Properties of Two-Dimensional Van Der Waals Systems , Yohanes Satrio Gani

Extraction and Parametrization of Isobaric Trinucleon Elastic Cross Sections and Form Factors , Scott Kevin Barcus

Interfacial Forces of 2D Materials at the Oil–Water Interface , William Winsor Dickinson

Scattering a Bose-Einstein Condensate Off a Modulated Barrier , Andrew James Pyle

Topics in Proton Structure: BSM Answers to its Radius Puzzle and Lattice Subtleties within its Momentum Distribution , Michael Chaim Freid

Theses/Dissertations from 2018 2018

A Measurement of Nuclear Effects in Deep Inelastic Scattering in Neutrino-Nucleus Interactions , Anne Norrick

Applications of Lattice Qcd to Hadronic Cp Violation , David Brantley

Charge Dynamics in the Metallic and Superconducting States of the Electron-Doped 122-Type Iron Arsenides , Zhen Xing

Dynamics of Systems With Hamiltonian Monodromy , Daniel Salmon

Exotic Phases in Attractive Fermions: Charge Order, Pairing, and Topological Signatures , Peter Rosenberg

Extensions of the Standard Model Higgs Sector , Richard Keith Thrasher

First Measurements of the Parity-Violating and Beam-Normal Single-Spin Asymmetries in Elastic Electron-Aluminum Scattering , Kurtis David Bartlett

Lattice Qcd for Neutrinoless Double Beta Decay: Short Range Operator Contributions , Henry Jose Monge Camacho

Probe of Electroweak Interference Effects in Non-Resonant Inelastic Electron-Proton Scattering , James Franklyn Dowd

Proton Spin Structure from Monte Carlo Global Qcd Analyses , Jacob Ethier

Searching for A Dark Photon in the Hps Experiment , Sebouh Jacob Paul

Theses/Dissertations from 2017 2017

A global normal form for two-dimensional mode conversion , David Gregory Johnston

Computational Methods of Lattice Boltzmann Mhd , Christopher Robert Flint

Computational Studies of Strongly Correlated Quantum Matter , Hao Shi

Determination of the Kinematics of the Qweak Experiment and Investigation of an Atomic Hydrogen Møller Polarimeter , Valerie Marie Gray

Disconnected Diagrams in Lattice Qcd , Arjun Singh Gambhir

Formulating Schwinger-Dyson Equations for Qed Propagators in Minkowski Space , Shaoyang Jia

Highly-Correlated Electron Behavior in Niobium and Niobium Compound Thin Films , Melissa R. Beebe

Infrared Spectroscopy and Nano-Imaging of La0.67Sr0.33Mno3 Films , Peng Xu

Investigation of Local Structures in Cation-Ordered Microwave Dielectric a Solid-State Nmr and First Principle Calculation Study , Rony Gustam Kalfarisi

Measurement of the Elastic Ep Cross Section at Q2 = 0.66, 1.10, 1.51 and 1.65 Gev2 , YANG WANG

Modeling The Gross-Pitaevskii Equation using The Quantum Lattice Gas Method , Armen M. Oganesov

Optical Control of Multi-Photon Coherent Interactions in Rubidium Atoms , Gleb Vladimirovich Romanov

Plasmonic Approaches and Photoemission: Ag-Based Photocathodes , Zhaozhu Li

Quantum and Classical Manifestation of Hamiltonian Monodromy , Chen Chen

Shining Light on The Phase Transitions of Vanadium Dioxide , Tyler J. Huffman

Superconducting Thin Films for The Enhancement of Superconducting Radio Frequency Accelerator Cavities , Matthew Burton

Theses/Dissertations from 2016 2016

Ac Zeeman Force with Ultracold Atoms , Charles Fancher

A Measurement of the Parity-Violating Asymmetry in Aluminum and its Contribution to A Measurement of the Proton's Weak Charge , Joshua Allen Magee

An improved measurement of the Muon Neutrino charged current Quasi-Elastic cross-section on Hydrocarbon at Minerva , Dun Zhang

Applications of High Energy Theory to Superconductivity and Cosmic Inflation , Zhen Wang

A Precision Measurement of the Weak Charge of Proton at Low Q^2: Kinematics and Tracking , Siyuan Yang

Compton Scattering Polarimetry for The Determination of the Proton’S Weak Charge Through Measurements of the Parity-Violating Asymmetry of 1H(E,e')P , Juan Carlos Cornejo

Disorder Effects in Dirac Heterostructures , Martin Alexander Rodriguez-Vega

Electron Neutrino Appearance in the Nova Experiment , Ji Liu

Experimental Apparatus for Quantum Pumping with a Bose-Einstein Condensate. , Megan K. Ivory

Investigating Proton Spin Structure: A Measurement of G_2^p at Low Q^2 , Melissa Ann Cummings

Neutrino Flux Prediction for The Numi Beamline , Leonidas Aliaga Soplin

Quantitative Analysis of Periodic Breathing and Very Long Apnea in Preterm Infants. , Mary A. Mohr

Resolution Limits of Time-of-Flight Mass Spectrometry with Pulsed Source , Guangzhi Qu

Solving Problems of the Standard Model through Scale Invariance, Dark Matter, Inflation and Flavor Symmetry , Raymundo Alberto Ramos

Study of Spatial Structure of Squeezed Vacuum Field , Mi Zhang

Study of Variations of the Dynamics of the Metal-Insulator Transition of Thin Films of Vanadium Dioxide with An Ultra-Fast Laser , Elizabeth Lee Radue

Thin Film Approaches to The Srf Cavity Problem: Fabrication and Characterization of Superconducting Thin Films , Douglas Beringer

Turbulent Particle Transport in H-Mode Plasmas on Diii-D , Xin Wang

Theses/Dissertations from 2015 2015

Ballistic atom pumps , Tommy Byrd

Determination of the Proton's Weak Charge via Parity Violating e-p Scattering. , Joshua Russell Hoskins

Electronic properties of chiral two-dimensional materials , Christopher Lawrence Charles Triola

Heavy flavor interactions and spectroscopy from lattice quantum chromodynamics , Zachary S. Brown

Some properties of meson excited states from lattice QCD , Ekaterina V. Mastropas

Sterile Neutrino Search with MINOS. , Alena V. Devan

Ultracold rubidium and potassium system for atom chip-based microwave and RF potentials , Austin R. Ziltz

Theses/Dissertations from 2014 2014

Enhancement of MS Signal Processing for Improved Cancer Biomarker Discovery , Qian Si

Whispering-gallery mode resonators for nonlinear and quantum optical applications , Matthew Thomas Simons

Theses/Dissertations from 2013 2013

Applications of Holographic Dualities , Dylan Judd Albrecht

A search for a new gauge boson , Eric Lyle Jensen

Experimental Generation and Manipulation of Quantum Squeezed Vacuum via Polarization Self-Rotation in Rb Vapor , Travis Scott Horrom

Low Energy Tests of the Standard Model , Benjamin Carl Rislow

Magnetic Order and Dimensional Crossover in Optical Lattices with Repulsive Interaction , Jie Xu

Multi-meson systems from Lattice Quantum Chromodynamics , Zhifeng Shi

Theses/Dissertations from 2012 2012

Dark matter in the heavens and at colliders: Models and constraints , Reinard Primulando

Measurement of Single and Double Spin Asymmetries in p(e, e' pi(+/-,0))X Semi-Inclusive Deep-Inelastic Scattering , Sucheta Shrikant Jawalkar

NMR study of paramagnetic nano-checkerboard superlattices , Christopher andrew Maher

Parity-violating asymmetry in the nucleon to delta transition: A Study of Inelastic Electron Scattering in the G0 Experiment , Carissa Lee Capuano

Studies of polarized and unpolarized helium -3 in the presence of alkali vapor , Kelly Anita Kluttz

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Arguments Showing that Descartes’ Physics is Mathematical

• First Online: 27 April 2024

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I would like to present four arguments in support of the thesis that Cartesian physics was a mathematical physics. The first two are historical, the other two of a systematic nature. I believe that together they form a compelling case for rehabilitating Cartesian physics as a mathematical physics.

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This is not to say that Galileo did not argue in his texts. I only claim that his arguments had the form of a sequence of deductive steps, as in a mathematical proof, and not of a chain of relations between cause and effect. In other words, the deductive synthesis of Galileo’s physics was mathematical and not physical.

I do not claim that Descartes’ description of interaction works. Newton showed conclusively that it generally does not. I would only like to claim that it is a non-functioning system of mathematical physics.

Newton gives this law of Descartes as Corollary 3 to the third law of motion.

Descartes was convinced of the correctness of the Copernican system that forms the background of Le Monde . When he learned of Galileo’s condemnation in 1633, he decided not to publish Le Monde . In a letter of 26 April 1643, he wrote to Mersenne about a new understanding of motion, according to which motion is a change in which a body leaves the proximity of other bodies. According to Machamer and McGuire, this is the first mention of Descartes’ new definition of motion as relative displacement (Machamer and McGuire 2009, p. 135). The latter makes it possible to speak of motion of the earth relative to the sun and at the same time to assert its immobility. This enabled Descartes to insert a large part of the material from Le Monde (after due revisions) into the Principia . Newton used the argument with the bucket to refute the idea of the relativity of rotational motion. However, it is questionable to what extent the relativity of motion was really believed by Descartes, and to what extent it was a disguising manoeuvre, successful in a similar manner to the thesis of the innateness of the idea of God.

It circumvented them in the sense that during interaction the acting body does not have to touch the body it is acting on, but the action is transmitted through space without any material mediation. If action need not be by contact, there is no need for the vortex of fine matter. Gravity is provided by a force acting at a distance, and we are liberated from the hydrodynamic complications of mechanics. It is a trick, an ingenious one, but still a trick that allowed Newton to establish a mechanics that is mathematical both at the ontological level (like Descartes’) and at the phenomenal level (like Galileo’s). The fact that Descartes did not find this trick does not give us the right to deny the mathematical character of his physics.

It was this fact that completely changed my view of Descartes’ physics when I came across it several years ago.

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Kvasz, L. (2024). Arguments Showing that Descartes’ Physics is Mathematical. In: Descartes on Mathematics, Method and Motion. SpringerBriefs in Philosophy. Springer, Cham. https://doi.org/10.1007/978-3-031-57061-2_6

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• perseverance and creativity in solving problems

Subject-specific admission requirements

The Bavarian Higher Education Act (BayHSchG) requires a "special qualification" for enrolling in a Master's degree program.

For the Master's Program Mathematical Physics at the University of Würzburg, the substantive requirements are essentially:

• Degree in a Bachelor's program (with 180 ECTS credits) in Mathematical Physics or a comparable degree program,
• Competencies amounting to at least 30 ECTS credits in the following sub-areas of mathematics: calculus (differential and integral calculus in one and more variables) and linear algebra.
• Competences amounting to at least 10 ECTS credits from other branches of mathematics, e.g. ordinary differential equations, partial differential equations, geometric analysis, differential geometry, functional theory, functional analysis, numerical mathematics, stochastics, optimization, et.
• Competences amounting to at least 21 ECTS points in the following areas of theoretical physics: classical mechanics, quantum mechanics, statistical physics and electrodynamics.
• Competences amounting to at least 19 ECTS credits from other branches of Experimental or Theoretical Physics.
• Competences amounting to a further 30 ECTS credits from any field of Mathematics, Experimental or Theoretical Physics.
• A thesis with a minimum of 10 ECTS credits in Mathematical Physics, Mathematics, Phyics or a comparable degree program.

To enable an uninterrupted transition from undergraduate to postgraduate study, a "conditional" admission can be applied, provided that one of the degrees mentioned in point 1 above can be used to prove the acquisition of 150 ECTS credits as well as the awarding of a corresponding thesis in 7. The requirements mentioned from 2 to 6 must be achieved in any case. For a final admission to the Master's degree program in Mathematics, the requirements listed from 1 to 7 must be submitted before the end of the registration deadline for the third semester.

The following deadlines must be met:

• Until  July 15 (if applying for the winter semester) or until January 15 (if applying for the summer semester), an online application must be submitted under WueStudy . JMU students can use their JMU account, external applicants must first register for an applicant account. (Since December 9, 2021, the online application will no longer be made on the JMU Master's portal.)
• Until September 15 (if applying for the winter semester) or until March 15 (if applying for the summer semester), proof of first degree or proof of performance can be submitted later.

Attention : application for a semester after the deadlines July 15 and Januar 15, respectively, is not possible. On the other hand, documents can be submitted by the second specified deadlines. After receiving your online application on the Master-Portal, we will contact you by e-mail and let you know the status of your application.

Information and contact

If you have any questions about the aptitude test, please contact the study advisors for Mathematical Physics .

Career prospects

Mathematics and Physics are two of the major sciences of our society, that are developed both for the sake of knowledge as well as for addressing direct applications in real life. Therefore, a general study of Mathematical Physics can provides an essential introductory knowledge that promotes

• ability related to abstract thinking,
• profound competencies in the fields of mathematics and physics,

as well as the ability

• to get quickly used to complex contexts,
• to localize the essential elements of a problem,
• to find creative solutions.

This "complete package" provides you with excellent job prospects and the ticket to numerous fields of application in industry, science and research.

Course content and curriculum

The Master's program in Mathematical Physics is divided into three sections: compulsory Mathematical Physics (20 ECTS), compulsory and elective subjects of Mathematical Physics (50 ECTS) (that are subdivised into Mathematics, Physics and applications) and a final exam (50 ECTS) which is related to a master's thesis (30 ECTS)

Specifying a course of study course makes little sense here, since there are only two compulsory modules (see module overview). We recommend to do these modules during the first two semesters (regardless of the beginning of study in summer or winter), as there is no dependence between them.

Control test

A control examination does not exist in this master program.

If you have earned 120 ECTS credits under the Examination Regulations, you will receive the academic degree of Master of Science.

Study and examination regulations

• General Study and Examination Regulations for Bachelor and Master Courses (ASPO)
• Subject-specific provisions for the Master's program Computational Mathematics (PO 2016)

The examination board is u.a. responsible

• Recognition questions at the beginning of studies for achievements acquired in previous study programs or at another study location,
• Recognition questions in the current study
• Gender Equality

To the current cast

Overview of the module areas

There are three subsections in the Master program of Mathematical Physics, which are subdivided as follows:

• Analysis and geometry of classical systems (10 ECTS)
• Algebra and dynamics of quantum systems (10 ECTS)
• Subcategory Mathematics (at least 8 ECTS)
• Subcategory Physics (at least 8 ECTS)
• working groups (minimum 10 ECTS)
• Subject Specialization in Mathematical Physics (10 EcTS)
• Methodological Knowledge and project planning in Mathematical Physics (10 ECTS)
• Master thesis (30 ECTS)

A list of all possible modules for the subcategory of mathematics, physics and working groups can be found in the subject-specific regulations and in the module handbook.

The modules related to the specialization in mathematical physics as well as method knowledge and project planning allow to prepare the master thesis and are selected in agreement with the supervisor. In addition, we would like to draw your attention to the Learning by Teaching module from the Mathematics sub-section (see below). You can find out more about the current event offer in the course catalog.

Learning by Teaching

Learning by Teaching means supervising an exercise or tutorial group in the bachelor's program under the guidance of the respective lecturer. This can be done twice for every 5 ECTS.

These modules require appropriate skills. Application is made directly to the teaching coordinator.

Master Thesis

The master's thesis is the last major exam in your master's program. This written work is designed to show that you are able to work on a problem of mathematical physics within a defined period of time (six months).

The modules of specialization as well as the methodological knowledge and the project planning are required for the preparation of the master thesis. Furthermore, their successful completion requires the registration of the Master Thesis. You are advised to start your Master thesis at the latest before the beginning of your 6th semester, so that you can use the full remaining time to complete the work before the beginning of your 7th semester. After the beginning of the 7th semester, your master's degree program is considered failed for the first time!

The topic of a master's thesis usually is selected from a seminar or a working group. You should personally contact a lecturer in mathematics or physics in accordance with your interests and decide directly on a subject (your own suggestions are possible!). Potential supervisors are all lecturers in mathematics and physics.

If you have found a supervisor and a topic for your thesis, print out this form , fill it out together with your supervisor and hand it in to the Service center of Mathematics (eg Ms. Schmid, Mathematik Ost, Zi. 00.016) or in the Service Center of Physics  (Physik, Zi. B-024). This will make the topic of your thesis and the date of submission (date of issue of the topic + 6 months) official and binding.

Only in very restricted cases, the processing time can be extended upon request to the Examination Board and in consultation with the supervisor.

The thesis has to be printed three times and stored on an electronic medium "in a common format and in readable form" (pdf file on a data CD is a viable option). It then must be taken to the examination office and to Mrs. Feineis . There, compliance with the processing time is documented and your work is passed on to the designated reviewers.

There is no colloquium for the Master Thesis.

For students who started their studies in winter 2015 or earlier

Start of studies winter semester 2015/2016 or earlier.

Subject specific provisions for the Master program in Mathematical Physics (PO 2013) or  Modulhandbuch database.

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Graduate studies, commencement 2019.

The Harvard Department of Physics offers students innovative educational and research opportunities with renowned faculty in state-of-the-art facilities, exploring fundamental problems involving physics at all scales. Our primary areas of experimental and theoretical research are atomic and molecular physics, astrophysics and cosmology, biophysics, chemical physics, computational physics, condensed-matter physics, materials science, mathematical physics, particle physics, quantum optics, quantum field theory, quantum information, string theory, and relativity.

Our talented and hardworking students participate in exciting discoveries and cutting-edge inventions such as the ATLAS experiment, which discovered the Higgs boson; building the first 51-cubit quantum computer; measuring entanglement entropy; discovering new phases of matter; and peering into the ‘soft hair’ of black holes.

Our students come from all over the world and from varied educational backgrounds. We are committed to fostering an inclusive environment and attracting the widest possible range of talents.

We have a flexible and highly responsive advising structure for our PhD students that shepherds them through every stage of their education, providing assistance and counseling along the way, helping resolve problems and academic impasses, and making sure that everyone has the most enriching experience possible.The graduate advising team also sponsors alumni talks, panels, and advice sessions to help students along their academic and career paths in physics and beyond, such as “Getting Started in Research,” “Applying to Fellowships,” “Preparing for Qualifying Exams,” “Securing a Post-Doc Position,” and other career events (both academic and industry-related).

We offer many resources, services, and on-site facilities to the physics community, including our electronic instrument design lab and our fabrication machine shop. Our historic Jefferson Laboratory, the first physics laboratory of its kind in the nation and the heart of the physics department, has been redesigned and renovated to facilitate study and collaboration among our students.

Members of the Harvard Physics community participate in initiatives that bring together scientists from institutions across the world and from different fields of inquiry. For example, the Harvard-MIT Center for Ultracold Atoms unites a community of scientists from both institutions to pursue research in the new fields opened up by the creation of ultracold atoms and quantum gases. The Center for Integrated Quantum Materials , a collaboration between Harvard University, Howard University, MIT, and the Museum of Science, Boston, is dedicated to the study of extraordinary new quantum materials that hold promise for transforming signal processing and computation. The Harvard Materials Science and Engineering Center is home to an interdisciplinary group of physicists, chemists, and researchers from the School of Engineering and Applied Sciences working on fundamental questions in materials science and applications such as soft robotics and 3D printing.  The Black Hole Initiative , the first center worldwide to focus on the study of black holes, is an interdisciplinary collaboration between principal investigators from the fields of astronomy, physics, mathematics, and philosophy. The quantitative biology initiative https://quantbio.harvard.edu/  aims to bring together physicists, biologists, engineers, and applied mathematicians to understand life itself. And, most recently, the new program in  Quantum Science and Engineering (QSE) , which lies at the interface of physics, chemistry, and engineering, will admit its first cohort of PhD students in Fall 2022.

We support and encourage interdisciplinary research and simultaneous applications to two departments is permissible. Prospective students may thus wish to apply to the following departments and programs in addition to Physics:

• Department of Astronomy
• Department of Chemistry
• Department of Mathematics
• John A. Paulson School of Engineering and Applied Sciences (SEAS)
• Biophysics Program
• Molecules, Cells and Organisms Program (MCO)

If you are a prospective graduate student and have questions for us, or if you’re interested in visiting our department, please contact  [email protected] .

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Recent Master's Theses - Applied Mathematics

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Master's Theses 2024

Master's theses 2023, master's theses 2022, master's theses 2019, master's theses 2018, master's theses 2017, master's theses 2016, master's theses 2015, master's theses 2014, master's theses 2013, master's theses 2012, master's theses 2011, master's theses 2010, master's theses 2009, master's theses 2008, master's theses 2007.

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Mathematics PhD theses

A selection of Mathematics PhD thesis titles is listed below, some of which are available online:

2022   2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Melanie Kobras –  Low order models of storm track variability

Ed Clark –  Vectorial Variational Problems in L∞ and Applications to Data Assimilation

Katerina Christou – Modelling PDEs in Population Dynamics using Fixed and Moving Meshes  

Chiara Cecilia Maiocchi –  Unstable Periodic Orbits: a language to interpret the complexity of chaotic systems

Samuel R Harrison – Stalactite Inspired Thin Film Flow

Elena Saggioro – Causal network approaches for the study of sub-seasonal to seasonal variability and predictability

Cathie A Wells – Reformulating aircraft routing algorithms to reduce fuel burn and thus CO 2 emissions  

Jennifer E. Israelsson –  The spatial statistical distribution for multiple rainfall intensities over Ghana

Giulia Carigi –  Ergodic properties and response theory for a stochastic two-layer model of geophysical fluid dynamics

André Macedo –  Local-global principles for norms

Tsz Yan Leung  –  Weather Predictability: Some Theoretical Considerations

Jehan Alswaihli –  Iteration of Inverse Problems and Data Assimilation Techniques for Neural Field Equations

Jemima M Tabeart –  On the treatment of correlated observation errors in data assimilation

Chris Davies –  Computer Simulation Studies of Dynamics and Self-Assembly Behaviour of Charged Polymer Systems

Birzhan Ayanbayev –  Some Problems in Vectorial Calculus of Variations in L∞

Penpark Sirimark –  Mathematical Modelling of Liquid Transport in Porous Materials at Low Levels of Saturation

Adam Barker –  Path Properties of Levy Processes

Hasen Mekki Öztürk –  Spectra of Indefinite Linear Operator Pencils

Carlo Cafaro –  Information gain that convective-scale models bring to probabilistic weather forecasts

Nicola Thorn –  The boundedness and spectral properties of multiplicative Toeplitz operators

James Jackaman  – Finite element methods as geometric structure preserving algorithms

Changqiong Wang - Applications of Monte Carlo Methods in Studying Polymer Dynamics

Jack Kirk - The molecular dynamics and rheology of polymer melts near the flat surface

Hussien Ali Hussien Abugirda - Linear and Nonlinear Non-Divergence Elliptic Systems of Partial Differential Equations

Andrew Gibbs - Numerical methods for high frequency scattering by multiple obstacles (PDF-2.63MB)

Mohammad Al Azah - Fast Evaluation of Special Functions by the Modified Trapezium Rule (PDF-913KB)

Katarzyna (Kasia) Kozlowska - Riemann-Hilbert Problems and their applications in mathematical physics (PDF-1.16MB)

Anna Watkins - A Moving Mesh Finite Element Method and its Application to Population Dynamics (PDF-2.46MB)

Niall Arthurs - An Investigation of Conservative Moving-Mesh Methods for Conservation Laws (PDF-1.1MB)

Samuel Groth - Numerical and asymptotic methods for scattering by penetrable obstacles (PDF-6.29MB)

Katherine E. Howes - Accounting for Model Error in Four-Dimensional Variational Data Assimilation (PDF-2.69MB)

Jian Zhu - Multiscale Computer Simulation Studies of Entangled Branched Polymers (PDF-1.69MB)

Tommy Liu - Stochastic Resonance for a Model with Two Pathways (PDF-11.4MB)

Matthew Paul Edgington - Mathematical modelling of bacterial chemotaxis signalling pathways (PDF-9.04MB)

Anne Reinarz - Sparse space-time boundary element methods for the heat equation (PDF-1.39MB)

Adam El-Said - Conditioning of the Weak-Constraint Variational Data Assimilation Problem for Numerical Weather Prediction (PDF-2.64MB)

Nicholas Bird - A Moving-Mesh Method for High Order Nonlinear Diffusion (PDF-1.30MB)

Charlotta Jasmine Howarth - New generation finite element methods for forward seismic modelling (PDF-5,52MB)

Aldo Rota - From the classical moment problem to the realizability problem on basic semi-algebraic sets of generalized functions (PDF-1.0MB)

Sarah Lianne Cole - Truncation Error Estimates for Mesh Refinement in Lagrangian Hydrocodes (PDF-2.84MB)

Alexander J. F. Moodey - Instability and Regularization for Data Assimilation (PDF-1.32MB)

Dale Partridge - Numerical Modelling of Glaciers: Moving Meshes and Data Assimilation (PDF-3.19MB)

Joanne A. Waller - Using Observations at Different Spatial Scales in Data Assimilation for Environmental Prediction (PDF-6.75MB)

Faez Ali AL-Maamori - Theory and Examples of Generalised Prime Systems (PDF-503KB)

Mark Parsons - Mathematical Modelling of Evolving Networks

Natalie L.H. Lowery - Classification methods for an ill-posed reconstruction with an application to fuel cell monitoring

David Gilbert - Analysis of large-scale atmospheric flows

Peter Spence - Free and Moving Boundary Problems in Ion Beam Dynamics (PDF-5MB)

Timothy S. Palmer - Modelling a single polymer entanglement (PDF-5.02MB)

Mohamad Shukor Talib - Dynamics of Entangled Polymer Chain in a Grid of Obstacles (PDF-2.49MB)

Cassandra A.J. Moran - Wave scattering by harbours and offshore structures

Ashley Twigger - Boundary element methods for high frequency scattering

David A. Smith - Spectral theory of ordinary and partial linear differential operators on finite intervals (PDF-1.05MB)

Stephen A. Haben - Conditioning and Preconditioning of the Minimisation Problem in Variational Data Assimilation (PDF-3.51MB)

Jing Cao - Molecular dynamics study of polymer melts (PDF-3.98MB)

Bonhi Bhattacharya - Mathematical Modelling of Low Density Lipoprotein Metabolism. Intracellular Cholesterol Regulation (PDF-4.06MB)

Tamsin E. Lee - Modelling time-dependent partial differential equations using a moving mesh approach based on conservation (PDF-2.17MB)

Polly J. Smith - Joint state and parameter estimation using data assimilation with application to morphodynamic modelling (PDF-3Mb)

Corinna Burkard - Three-dimensional Scattering Problems with applications to Optical Security Devices (PDF-1.85Mb)

Laura M. Stewart - Correlated observation errors in data assimilation (PDF-4.07MB)

R.D. Giddings - Mesh Movement via Optimal Transportation (PDF-29.1MbB)

G.M. Baxter - 4D-Var for high resolution, nested models with a range of scales (PDF-1.06MB)

C. Spencer - A generalization of Talbot's theorem about King Arthur and his Knights of the Round Table.

P. Jelfs - A C-property satisfying RKDG Scheme with Application to the Morphodynamic Equations (PDF-11.7MB)

L. Bennetts - Wave scattering by ice sheets of varying thickness

M. Preston - Boundary Integral Equations method for 3-D water waves

J. Percival - Displacement Assimilation for Ocean Models (PDF - 7.70MB)

D. Katz - The Application of PV-based Control Variable Transformations in Variational Data Assimilation (PDF- 1.75MB)

S. Pimentel - Estimation of the Diurnal Variability of sea surface temperatures using numerical modelling and the assimilation of satellite observations (PDF-5.9MB)

J.M. Morrell - A cell by cell anisotropic adaptive mesh Arbitrary Lagrangian Eulerian method for the numerical solution of the Euler equations (PDF-7.7MB)

L. Watkinson - Four dimensional variational data assimilation for Hamiltonian problems

M. Hunt - Unique extension of atomic functionals of JB*-Triples

D. Chilton - An alternative approach to the analysis of two-point boundary value problems for linear evolutionary PDEs and applications

T.H.A. Frame - Methods of targeting observations for the improvement of weather forecast skill

C. Hughes - On the topographical scattering and near-trapping of water waves

B.V. Wells - A moving mesh finite element method for the numerical solution of partial differential equations and systems

D.A. Bailey - A ghost fluid, finite volume continuous rezone/remap Eulerian method for time-dependent compressible Euler flows

M. Henderson - Extending the edge-colouring of graphs

K. Allen - The propagation of large scale sediment structures in closed channels

D. Cariolaro - The 1-Factorization problem and same related conjectures

A.C.P. Steptoe - Extreme functionals and Stone-Weierstrass theory of inner ideals in JB*-Triples

D.E. Brown - Preconditioners for inhomogeneous anisotropic problems with spherical geometry in ocean modelling

S.J. Fletcher - High Order Balance Conditions using Hamiltonian Dynamics for Numerical Weather Prediction

C. Johnson - Information Content of Observations in Variational Data Assimilation

M.A. Wakefield - Bounds on Quantities of Physical Interest

M. Johnson - Some problems on graphs and designs

A.C. Lemos - Numerical Methods for Singular Differential Equations Arising from Steady Flows in Channels and Ducts

R.K. Lashley - Automatic Generation of Accurate Advection Schemes on Structured Grids and their Application to Meteorological Problems

J.V. Morgan - Numerical Methods for Macroscopic Traffic Models

M.A. Wlasak - The Examination of Balanced and Unbalanced Flow using Potential Vorticity in Atmospheric Modelling

M. Martin - Data Assimilation in Ocean circulation models with systematic errors

K.W. Blake - Moving Mesh Methods for Non-Linear Parabolic Partial Differential Equations

J. Hudson - Numerical Techniques for Morphodynamic Modelling

A.S. Lawless - Development of linear models for data assimilation in numerical weather prediction .

C.J.Smith - The semi lagrangian method in atmospheric modelling

T.C. Johnson - Implicit Numerical Schemes for Transcritical Shallow Water Flow

M.J. Hoyle - Some Approximations to Water Wave Motion over Topography.

P. Samuels - An Account of Research into an Area of Analytical Fluid Mechnaics. Volume II. Some mathematical Proofs of Property u of the Weak End of Shocks.

M.J. Martin - Data Assimulation in Ocean Circulation with Systematic Errors

P. Sims - Interface Tracking using Lagrangian Eulerian Methods.

P. Macabe - The Mathematical Analysis of a Class of Singular Reaction-Diffusion Systems.

B. Sheppard - On Generalisations of the Stone-Weisstrass Theorem to Jordan Structures.

S. Leary - Least Squares Methods with Adjustable Nodes for Steady Hyperbolic PDEs.

I. Sciriha - On Some Aspects of Graph Spectra.

P.A. Burton - Convergence of flux limiter schemes for hyperbolic conservation laws with source terms.

J.F. Goodwin - Developing a practical approach to water wave scattering problems.

N.R.T. Biggs - Integral equation embedding methods in wave-diffraction methods.

L.P. Gibson - Bifurcation analysis of eigenstructure assignment control in a simple nonlinear aircraft model.

A.K. Griffith - Data assimilation for numerical weather prediction using control theory. .

J. Bryans - Denotational semantic models for real-time LOTOS.

I. MacDonald - Analysis and computation of steady open channel flow .

A. Morton - Higher order Godunov IMPES compositional modelling of oil reservoirs.

S.M. Allen - Extended edge-colourings of graphs.

M.E. Hubbard - Multidimensional upwinding and grid adaptation for conservation laws.

C.J. Chikunji - On the classification of finite rings.

S.J.G. Bell - Numerical techniques for smooth transformation and regularisation of time-varying linear descriptor systems.

D.J. Staziker - Water wave scattering by undulating bed topography .

K.J. Neylon - Non-symmetric methods in the modelling of contaminant transport in porous media. .

D.M. Littleboy - Numerical techniques for eigenstructure assignment by output feedback in aircraft applications .

M.P. Dainton - Numerical methods for the solution of systems of uncertain differential equations with application in numerical modelling of oil recovery from underground reservoirs .

M.H. Mawson - The shallow-water semi-geostrophic equations on the sphere. .

S.M. Stringer - The use of robust observers in the simulation of gas supply networks .

S.L. Wakelin - Variational principles and the finite element method for channel flows. .

E.M. Dicks - Higher order Godunov black-oil simulations for compressible flow in porous media .

C.P. Reeves - Moving finite elements and overturning solutions .

A.J. Malcolm - Data dependent triangular grid generation. .

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Dean of Studies Prof. Dr. Christoph Zielhofer

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Vice-Dean Prof. Dr. Johannes Quaas

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Deanery Dr. Annett Kaldich

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Master Mathematical Physics

In the English-language master’s course of study Mathematical Physics you will learn general principles of mathematical physics and acquire in-depth knowledge of selected topics. You apply the knowledge to describe, analyse and solve complex problems. You transfer concepts to related questions in other or interdisciplinary areas. You will train to read and understand current specialist literature. Under supervision, you will learn to perform independent research and complete your studies with an independent research work, the 23-week master's thesis.

In our commitment to diversity, we welcome people of all backgrounds and cultures. We are particularly proud of the fact that more than 1500 students from 38 countries are currently studying in our German and international courses. For an international faculty like ours, diversity and inclusion are important resources for incorporating multifaceted approaches and ways of thinking into innovative teaching and research. We are therefore committed to cosmopolitan coexistence, where everyone is welcome regardless of origin, gender and religion.

Information on the Course of Study

Find out more about the requirements, contents and application for the course of study here:

Additional Information on the Application

First university degree obtained in germany.

You obtained your first university degree in Germany and would like to apply for the master’s course of study in Mathematical Physics? Then please apply via AlmaWeb and submit the following documents in addition by e-mail or by mail to the dean of our faculty :

Application for evaluation of admission requirements (informal letter or email)

Transcript of records/certificate of a first degree qualifying for a profession which includes:

• 30 credit points of algebra and analysis; up to ten credit points can be accepted from other areas of mathematics,
• 20 credit points of theoretical physics or in areas that are related to theoretical physics in terms of content (e.g. quantum mechanics, experimental physics, complex and meteorological systems, dynamic systems, differential equations).

Short curriculum vitae in tabular form

Proof of knowledge of the English language at the level B2 of the Common European Framework of Reference (or equivalent)

Please submit these documents by 1 September for a start in the winter semester of the same year.

The master's admissions committee uses these documents to check whether you meet the requirements for the admission to the master's course of study. You will receive a written notification about this, which you should submit to the Studierendensekretariat with the other documents for your enrolment.

Please apply via AlmaWeb by 15 September for a start in the winter semester of the same year.

First University Degree Obtained Abroad

You obtained your first university degree abroad ? In this case, please apply directly via  uni-assist e.V. by 31 May for a start in the winter semester of the same year.

Structure of the Course of Study

You will learn the general principles of mathematics and theoretical physics in two fundamental courses on mathematical physics. Basing on your knowledge in analysis, algebra and theoretical physics obtained during your bachelor's courses, you will deepen your expertise on topics like symmetries, geometry, field theory and quantum mechanics. You will gain in-depth knowledge on selected fields by taking elective courses. The course structure allows for multiple individual choices – you can shape the programme along your own preferences.

The master’s course of study Mathematical Physics consists of two one-year phases: a first phase in which the physics knowledge is deepened and widened, followed by a research phase.

The information on the module numbers and credit points can be found in the detailed overview .

The foundations in the first phase are the two modules on mathematical physics. These build on your basic knowledge of mathematics and theoretical physics. They form the basis for the special modules that you will take later.

In the research phase, you will be guided in a selected specialised field to work on issues relating to current national and international research. In the fourth semester, the focus is on the master's thesis . You can also do this in cooperation with domestic or foreign companies, universities or research institutions.

The master's course of study Mathematical Physics is offered jointly by the Faculty of Mathematics and Computer Science and the Faculty of Physics and Earth Sciences. Modules starting with numbers 10-MAT- are administered by the study office of the Faculty of Mathematics and Computer Science , modules with numbers 12-PHY- by our study office . Semester schedules can be found in the course catalogue from mathematics (click path: Nach Studiengängen – Math.MP ) and the course catalogue from physics .

Elective Areas

Elective area 1 (physics).

For the elective area 1 (physics) , you choose a module from the following compulsory elective modules:

Elective Area 2 (Mathematics)

For the elective area 2 (mathematics) , you choose a module from the following compulsory elective modules:

Elective Area 3 (Advanced Seminar)

In the elective area 3 (advanced seminar) , the focus is not only on imparting specialist knowledge, but also on developing and improving methodological skills. These are literature research, presentation skills and academic writing. In each semester, aspects of current topics from the research areas of both institutes are studied in the advanced seminars. Possible topics in the field of theoretical and mathematical physics are, for example: quantum field theory, gravity, condensed matter theory, quantum theory of condensed matter, quantum statistical physics, complex systems and complex quantum systems. You choose a module from the following compulsory elective modules:

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The free elective area comprises elective modules totalling 30 CP , at least 20 CP from free elective area 1 and up to ten CP from free elective area 2. Alternatively, you can choose additional modules from the elective areas 1 (physics) and 2 (mathematics) as well as another advanced seminar from elective area 3.

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Computer Science > Computation and Language

Title: exploring the limits of fine-grained llm-based physics inference via premise removal interventions.

Abstract: Language models can hallucinate when performing complex and detailed mathematical reasoning. Physics provides a rich domain for assessing mathematical reasoning capabilities where physical context imbues the use of symbols which needs to satisfy complex semantics (\textit{e.g.,} units, tensorial order), leading to instances where inference may be algebraically coherent, yet unphysical. In this work, we assess the ability of Language Models (LMs) to perform fine-grained mathematical and physical reasoning using a curated dataset encompassing multiple notations and Physics subdomains. We improve zero-shot scores using synthetic in-context examples, and demonstrate non-linear degradation of derivation quality with perturbation strength via the progressive omission of supporting premises. We find that the models' mathematical reasoning is not physics-informed in this setting, where physical context is predominantly ignored in favour of reverse-engineering solutions.

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A mathematical bridge between the huge and the tiny

by University of Science and Technology of China

A mathematical link between two key equations—one that deals with the very big and the other, the very small—has been developed by a young mathematician in China.

The mathematical discipline known as differential geometry is concerned with the geometry of smooth shapes and spaces. With roots going back to antiquity, the field flourished in the early 20th century, enabling Einstein to develop his general theory of relativity and other physicists to develop quantum field theory and the Standard Model of particle physics.

Gao Chen, a 29-year-old mathematician at the University of Science and Technology of China in Hefei, specializes in a branch known as complex differential geometry. Its complexity is not in dealing with complicated structures, but rather because it is based on complex numbers—a system of numbers that extends everyday numbers by including the square root of -1.

This area appeals to Chen because of its connections with other fields. "Complex differential geometry lies at the intersection of analysis, algebra, and mathematical physics ," he says. "Many tools can be used to study this area."

Chen has now found a new link between two important equations in the field: the Kähler–Einstein equation, which describes how mass causes curvature in space–time in general relativity, and the Hermitian–Yang–Mills equation, which underpins the Standard Model of particle physics.

Chen was inspired by his Ph.D. supervisor Xiuxiong Chen of New York's Stony Brook University, to take on the problem. "Finding solutions to the Hermitian–Yang–Mills and the Kähler–Einstein equations are considered the most important advances in complex differential geometry in previous decades," says Gao Chen. "My results provide a connection between these two key results."

"The Kähler –Einstein equation describes very large things, as large as the universe, whereas the Hermitian–Yang–Mills equation describes tiny things, as small as quantum phenomena," explains Gao Chen. "I've built a bridge between these two equations." Gao Chen notes that other bridges existed previously, but that he has found a new one.

"This bridge provides a new key, a new tool for theoretical research in this field," Gao Chen adds. His paper describing this bridge was published in the journal Inventiones mathematicae in 2021.

In particular, the finding could find use in string theory —the leading contender of theories that researchers are developing in their quest to unite quantum physics and relativity. "The deformed Hermitian–Yang–Mills equation that I studied plays an important role in the study of string theory," notes Gao Chen.

Gao Chen now has his eyes set on other important problems, including one of the seven Millennium Prize Problems. These are considered the most challenging in the field by mathematicians and carry a $1 million prize for a correct solution. "In the future, I hope to tackle a generalization of the Kähler–Einstein equation ," he says. "I also hope to work on other Millennium Prize problems, including the Hodge conjecture."

Provided by University of Science and Technology of China

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• Schools & departments

Mathematical Physics PhD

Awards: PhD

Study modes: Full-time, Part-time

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Programme website: Mathematical Physics

Upcoming Introduction to Postgraduate Study and Research events

Join us online on the 19th June or 26th June to learn more about studying and researching at Edinburgh.

Choose your event and register

Research profile

We are a multidisciplinary research group with close connections with the School’s Algebra and Geometry & Topology groups.

You’ll benefit from being not only in one of the largest mathematics research groups in the UK but also part of the Edinburgh Mathematical Physics Group – a joint research collective formed in 1999 with Heriot- Watt University and now part of the Maxwell Institute.

The School of Mathematics is a vibrant community of more than 60 academic and related staff supervising 60 students.

Our group pursues wide-ranging interests spanning a number of disciplines. A central goal is to understand the principles behind quantum gravity, through the study of black holes, cosmologies and spacetime singularities, and via the use of holography and the interplay with quantum gauge field theory through the gauge/gravity correspondence.

Particularly fruitful areas of research are the geometry of higher-dimensional black holes and their near-horizon geometries in the context of higher-dimensional generalisations of general relativity.

We’re fascinated by the various manifestations of supersymmetry: in string theory, supergravity and gauge theory. This has led us to several classification results on supersymmetric supergravity backgrounds, including a recent proof of the homogeneity conjecture. In addition we study gauge theoretic moduli spaces using supersymmetry and via integrable systems techniques, displaying an interplay between the algebraic geometry of curves and their associated function theory. This research has led to computer implementations of various algebro-geometric constructions.

Recently we have made progress in some purely mathematical problems suggested by the gauge/gravity correspondence: namely, the classification of certain exotic algebraic structures related to superconformal field theories, as well as that of certain types of homogeneous supergravity backgrounds.

Training and support

Mathematics is a discipline of high intellect with connections stretching across all the scientific disciplines and beyond, and in Edinburgh you can be certain of thriving in a rich academic setting. Our School is one of the country’s largest mathematics research communities in its own right, but you will also benefit from Edinburgh’s high-level collaborations, both regional and international.

Research students will have a primary and secondary supervisor and the opportunity to network with a large and varied peer group. You will be carrying out your research in the company of eminent figures and be exposed to a steady stream of distinguished researchers from all over the world.

Our status as one of the most prestigious schools in the UK for mathematics attracts highly respected staff. Many of our 60 current academics are leaders in their fields and have been recognised with international awards.

Researchers are encouraged to travel and participate in conferences and seminars. You’ll also be in the right place in Edinburgh to meet distinguished researchers from all over the world who are attracted to conferences held at the School and the various collaborative centres based here. You’ll find opportunities for networking that could have far-reaching effects on your career in mathematics.

As well as experiencing a vibrant research environment that brings you into contact with a broad group of your peers, your membership of the Edinburgh Mathematical Physics Group will give you access to a dynamic programme of seminars, lecture courses and conferences. There is a dedicated website and blog, and a comprehensive range of graduate activities:

• Edinburgh Mathematical Physics Group

You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to generous library provision for research at the leading level, including the new Noreen and Kenneth Murray Library at King’s Buildings.

Students have access to more than 1,400 computers in suites distributed across the University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have your own desk with desktop computer.

We provide all our mathematics postgraduates with access to software packages such as Maple, Matlab and Mathematica. Research students are allocated parallel computing time on ‘Eddie’ – the Edinburgh Compute and Data Facility. It is also possible to arrange use of the BlueGene/Q supercomputer facility if your research requires it.

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These entry requirements are for the 2024/25 academic year and requirements for future academic years may differ. Entry requirements for the 2025/26 academic year will be published on 1 Oct 2024.

A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

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We accept the following English language qualifications at the grades specified:

• IELTS Academic: total 6.5 with at least 6.0 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
• TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
• C1 Advanced ( CAE ) / C2 Proficiency ( CPE ): total 176 with at least 169 in each component.
• Trinity ISE : ISE II with distinctions in all four components.
• PTE Academic: total 62 with at least 59 in each component.

Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS , TOEFL, Trinity ISE or PTE , in which case it must be no more than two years old.

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

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We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries (non-MESC).

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If you are not a national of a majority English speaking country, then your degree must be no more than five years old* at the beginning of your programme of study. (*Revised 05 March 2024 to extend degree validity to five years.)

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If you are not an EU , EEA or Swiss national, you may need an Academic Technology Approval Scheme clearance certificate in order to study this programme.

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Programmes studied on a part-time intermittent basis are not eligible.

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Select your programme and preferred start date to begin your application.

PhD Mathematical Physics - 3 Years (Full-time)

Phd mathematical physics - 6 years (part-time), application deadlines.

We strongly recommend you submit your completed application as early as possible, particularly if you are also applying for funding or will require a visa. We may consider late applications if we have places available. All applications received by 22 January 2024 will receive full consideration for funding. Later applications will be considered until all positions are filled.

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Stunning image shows atoms transforming into quantum waves — just as Schrödinger predicted

A new imaging technique, which captured frozen lithium atoms transforming into quantum waves, could be used to probe some of the most poorly understood aspects of the quantum world.

For the first time ever, physicists have captured a clear image of individual atoms behaving like a wave.

The image shows sharp red dots of fluorescing atoms transforming into fuzzy blobs of wave packets and is a stunning demonstration of the idea that atoms exist as both particles and waves — one of the cornerstones of quantum mechanics . 

The scientists who invented the imaging technique published their findings on the preprint server arXiv , so their research has not yet been peer reviewed. 

"The wave nature of matter remains one of the most striking aspects of quantum mechanics," the researchers wrote in the paper. They add that their new technique could be used to image more complex systems, giving insights into some fundamental questions in physics.  

First proposed by the French physicist Louis de Broglie in 1924 and expanded upon by Erwin Schrödinger two years later , wave particle duality states that all quantum-sized objects, and therefore all matter, exists as both particles and waves at the same time. 

Related: Tweak to Schrödinger's cat equation could unite Einstein's relativity and quantum mechanics, study hints

Schrödinger's famous equation is typically interpreted by physicists as stating that atoms exist as packets of wave-like probability in space, which are then collapsed into discrete particles upon observation. While bafflingly counterintuitive, this bizarre property of the quantum world has been witnessed in numerous experiments . 

Sign up for the Live Science daily newsletter now

Get the world’s most fascinating discoveries delivered straight to your inbox.

To image this fuzzy duality, the physicists first cooled lithium atoms to near-absolute zero temperatures by bombarding them with photons, or light particles, from a laser to rob them of their momentum. Once the atoms were cooled, more lasers trapped them within an optical lattice as discrete packets.

With the atoms cooled and confined, the researchers periodically switched the optical lattice off and on — expanding the atoms from a confined near-particle state to one resembling a wave, and then back. 

A microscope camera recorded light emitted as the atoms grew and shrank between each state, building up a picture of sharp particle dots within wave-like smudges that  perfectly demonstrated Schrödinger's equation. 

— Otherworldly 'time crystal' made inside Google quantum computer could change physics forever

— China claims fastest quantum computer in the world

— Bizarre particle that can remember its own past created inside quantum computer

"This imaging method consists in turning back on the lattice to project each wave packet into a single well to turn them into a particle again — it is not a wave anymore," study co-author Tarik Yefsah , a physicist at the French National Centre for Scientific Research and the École normale supérieure in Paris, told Live Science. "You can see our imaging method as a way to sample the wavefunction density, not unlike the pixels of a CCD camera." A CCD camera is a common type of digital camera that uses a charge-coupled device to capture its images.

The scientists say this image is just a simple demonstration. Their next step will be using it to study systems of strongly interacting atoms that are less well understood.

"Studying such systems could improve our understanding of strange states of matter, such as those found in the core of extremely dense neutron stars , or the quark-gluon plasma that is believed to have existed shortly after the Big Bang ," Yefsah said.  

Ben Turner is a U.K. based staff writer at Live Science. He covers physics and astronomy, among other topics like tech and climate change. He graduated from University College London with a degree in particle physics before training as a journalist. When he's not writing, Ben enjoys reading literature, playing the guitar and embarrassing himself with chess.

Tweak to Schrödinger's cat equation could unite Einstein's relativity and quantum mechanics, study hints

Scientists made the coldest large molecule on record — and it has a super strange chemical bond

DARPA's autonomous 'Manta Ray' drone can glide through ocean depths undetected

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May 10 – Doctor of Philosophy Thesis Defence – Christopher Wicks

Tuesday, April 30, 2024 | By jsteepe

Doctor of Philosophy Thesis Defence in Chemistry

Christopher Wicks, Doctor of Philosophy candidate in the Department of Chemistry, will defend his thesis titled “Towards the total synthesis of semi-synthetic opiate species

and presilphiperfolan-1-ol” on Friday, May 10 at 11 AM., virtually.

The examination committee includes Elizabeth Vlossak, Chair; Costa Metallinos, Supervisor; Michael A. Kerr, External Examiner (Western University); Ian Patterson, Internal External Examiner; Dustin Duncan and Louis Barriault (University of Ottawa), Committee Members.

Tags: Chemistry , FMS , Thesis defence Categories: News

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