Mathematics in Physics and Philosophy Group

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Welcome

Welcome to the website of the Mathematics in Physics and Philosophy Group at the Department of Mathematics at LMU Munich. The group was founded in 2014 as a Junior Research Group "Interaction between Light and Matter" supported by a grant from the Elite Network of Bavaria until 2022.

Research

The research activities of the Mathematics in Physics and Philosophy Group bring together work in the fields of fundamental physics, artificial intelligence, and natural philosophy. The unifying theme is characterized by a high degree of mathematical precision and the use of mathematics as a tool for clarifying conceptual questions and guiding theory construction. These activities encompass the construction and analysis of mathematical models in classical and quantum physics, as well as foundational studies of learning and rational agency. The group also engages in philosophical analysis of physical theories, methodology, and ontology, informed by and grounded in formal results. Across all areas, the emphasis lies on foundational insight and structural understanding rather than on purely phenomenological or technological applications.

Current Research Focus

Interaction between Light and Matter Interaction between Light and Matter This area focuses on the non-perturbative construction of classical and quantum field-theoretic models describing the interaction between light and matter, developed under full mathematical control. Central topics include classical and quantum electrodynamics, in particular with regard to radiation reaction and particle–antiparticle pair creation. The emphasis lies on precise control of limiting procedures and consistency beyond perturbative approximations. The aim is to contribute by elucidating the structural and conceptual foundations of fundamental physical interactions, including principles of theory construction and methodological assumptions underlying field-theoretic models.
Foundations of Quantum Theory Foundations of Quantum Theory Research in this area addresses the foundational problems of quantum mechanics using methods from mathematical physics. It develops rigorous interpretational frameworks, such as Bohmian mechanics, and examines less explored quantum phenomena, including time-of-flight distributions. Particular attention is given to the precise formulation of measurement, dynamics, and temporal observables. The overarching aim is to contribute to a coherent and mathematically well-founded understanding of quantum theory, informed by explicit interpretational frameworks and precise accounts of ontology, dynamics, and measurement.
Gravity, Entropy, and Time Gravity, Entropy, and Time This area investigates foundational questions related to gravity, statistical mechanics, and the arrow of time. Topics include entropy, irreversibility, shape dynamics, and the emergence of temporal structure. Here, mathematical analysis is closely interwoven with conceptual inquiry into spacetime, dynamics, and cosmology. The focus lies on contributing to the understanding of how macroscopic temporal phenomena arise from underlying physical laws, linking formal analysis with conceptual investigations of spacetime, dynamics, and ontology.
Mathematical Learning Theory Mathematical Learning Theory This research area studies learning, control, and planning from a foundational and mathematically precise standpoint. It analyzes models that describe how agents adapt to unknown data or environments, with emphasis on representation, approximation, and complexity. The central goal is to contribute to this area through the derivation of rigorous statistical guarantees and performance bounds for learning systems.

Current Thesis Project Proposals

Depending on our capacities, we regularly offer supervision of BA/BSc/MSc Mathematics, Physics, and TMP thesis projects, all with a certain focus on conceptual and mathematical rigor. If you already have topical ideas within our research interests, you can contact us directly under the Members section. Here are some ideas for proposals from current research topics:

  • Radiation damping: Definition of radiation, radiation detector/antenna, regularity of the classical radiation field of a point charge, numerical integrator for the Lorentz-Abraham-Dirac equation, numerical fixed-point iteration for a single charge in its radiation field, existence of dynamics for a single charge in its radiation field, long time asymptotes for two charge scattering, black body radiation, quantisation of the photon field, quantum radiation damping, Lamb shift, Unruh effect, reformulation of electrodynamics in Koopman-von Neumann mechanics
  • Quantum vacuum: Analysis of the polarisation current, vacuum polarisation, pair creation, motion of tracer particles in the Dirac sea, Casimir effect
  • Quantum dynamics: Numerical integration of the Schrödinger equation for long times/distances, stability analysis of quantum backflow in realistic experimental setups, simple and rigorous models of a quantum measurement
  • Reinforcement learning algorithms: Numerical simulation, stochastic approximation, algorithmic convergence, complexity, state-action-space reduction, goal-oriented behavior and survival
  • Autoregressive models: Discrete Markov process with memory, neural ODEs with delay, representation, approximation, complexity, statistical guarantees, application in large language models, genome sequences, forecasting models
  • Mathematical tools of learning theory: Generalizations of the law of large numbers from Chebyshev's inequality to concentration inequalities, Generalizations of complexity measures such as Rademacher complexity and VC-dimension from binary to multi-label classification such as Natarajan-dimension

Current Activities

Laws of Nature Series

The Laws of Nature Series is an initiative that seeks to support and encourage the discussion between our communities in Physics, Mathematics, and Philosophy. It is currently organised by A. Bassi, Univ. Trieste, D.-A. Deckert, LMU, Dr. W. Struyve, KU Leuven, and P. Reichert, LMU. If you would like to receive announcements of our open online seminar series on Zoom, sign up by email here.

Group Seminar

The Mathematics in Physics and Philosophy group’s weekly working seminar takes place on Mondays from 16:15 to 17:45 in Room B006 at the Department of Mathematics at LMU Munich (Theresienstraße 39). The schedule for the Winter Semester 2026/27 can be found below:

Date Speaker Title
The schedule will be announced here.

For more information and regular updates, you can enroll yourself or contact Fabian Nolte to be added to our mailing list.

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