Center for Mathematical Physics

The Center for Mathematical Physics is a hub for interdisciplinary activities in the area of Mathematics, Physics and related Sciences in Leipzig. It brings together research groups from the Institute for Theoretical Physics and the Institute of Mathematics at the University of Leipzig, as well as the Max Planck Institute for Mathematics in the Sciences.

Mission

Mathematical Physics is a research area at the interface of theoretical physics and mathematics, which profits from a high degree of cross-fertilisation between physical intuition and mathematical rigour, benefitting both physics and mathematics.

Leipzig has a long tradition in this area, associated with names such as Werner Heisenberg, Felix Klein, Felix Bloch, Sophus Lie, Peter Debye, and Bartel van der Waerden. With the Max Planck Institute for Mathematics in the Sciences and many research groups across the University, Leipzig offers a unique research environment in Mathematical Physics.

The Center for Mathematical Physics facilitates and coordinates interdisciplinary research and teaching activities in this area at all levels: research, promotion of young researchers, graduate and undergraduate teaching. In particular, it is involved in the International Graduate School Mathematics in the Sciences (IMPRS MiS) and the international master's programme Mathematical Physics M.Sc..

It is in particular involved in the International Graduate School Mathematics in the Sciences (IMPRS MiS) and the International Master Program in Mathematical Physics.

People

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Judith Brinkschulte

Professor at Institute of Mathematics

Complex Analysis and Geometry

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Alexey Bufetov

Professor at Institute of Mathematics

Probability Theory

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Jan Burczak

Researcher at Institute of Mathematics

Fluid dynamics

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Daniela Cadamuro

Emmy-Noether Group Leader at the Institute for Theoretical Physics

Relativistic Quantum Field Theory

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Marc Casals

Research Associate at the Institute for Theoretical Physics

Quantum Field Theory in Space-Time

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Stefan Czimek

Professor at Institute of Mathematics

General Relativity

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Dejan Gajic

Professor at Institute for Theoretical Physics

Mathematical Physics

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Stefan Hollands

Professor at Institute for Theoretical Physics

Elementary Particle Physics

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Klaus Kroy

Professor at Institute for Theoretical Physics

Soft Condensed Matter Theory

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Felix Otto

Director of the Max-Planck-Institute for Mathematics in the Sciences

Pattern Formation, Energy Landscapes and Scaling Laws

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Felix Pogorzelski

Professor at Institute of Mathematics

Dynamical Systems

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Hans-Bert Rademacher

Professor at Institute of Mathematics

Differential Geometry

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Daniel Roggenkamp

Professor at the Max-Planck-Institute for Mathematics in the Sciences and the Institute for Theoretical Physics

Mathematical Structures in Physics

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Artem Sapozhnikov

Professor at Institute of Mathematics

Probability Theory, Statistical Mechanics, Graph Theory and Combinatorics

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Matthias Schwarz

Professor at Institute of Mathematics

Symplectic Geometry

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Inti Sodemann

Professor at Institute for Theoretical Physics

Quantum Condensed Matter Theory

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Bernd Sturmfels

Director of the Max Planck Institute for Mathematics in the Sciences

Nonlinear Algebra

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László Székelyhidi

Director of the Max-Planck-Institute for Mathematics in the Sciences

Applied Analysis

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Simon Telen

Research Group Leader at Max-Planck-Institute for Mathematics in the Sciences

Non-linear Algebra

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Rainer Verch

Professor at Institute for Theoretical Physics

Quantum Field Theory and Gravity

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Jürgen Vollmer

Professor at Institute for Theoretical Physics

Statistical Physics

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Max von Renesse

Professor at Institute of Mathematics

Business Mathematics and Stochastics

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Anna Wienhard

Director of the Max Planck Institute for Mathematics in the Sciences

Geometry, Groups and Dynamics

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Jochen Zahn

Research Associate at the Institute for Theoretical Physics

Quantum Field Theory in non-trivial Backgrounds

Activities

If you want to keep informed about activities of the CMP please sign up in our mailing list
announcements-join@cmp-leipzig.de with the subject "subscribe".

Research Seminars

Center for Mathematical Physics Colloquium

Alessandra Buonanno (MPI for Gravitational Physics (AEI), Potsdam)
Title: Illuminating the Dark Universe with Gravitational Waves
Date: Friday, 21 February 2025 at 16:30
Location: Leibniz lecture hall, MPI for Mathematics in the Sciences

For centuries, we have explored the Universe and discovered novel astrophysical sources and phenomena through the observation of electromagnetic waves. In 2015, we observed the first gravitational wave passing through the Earth produced by the merger of two black holes. Since then, a few hundred gravitational waves have been detected, including the gravitational signal produced by the coalescence of two neutron stars, accompanied by a plethora of electromagnetic counterparts observed around the world. In this talk, I will highlight the theoretical work underpinning these observations and review the main results in astrophysics, cosmology and fundamental physics. I will then discuss the discovery potential of future observatories in space and on the ground.
Poster


Hofie Hannesdottir (IAS Princeton)
Title: Mathematical properties of scattering observables
Date: Tuesday, 10 April 2025 at 16:30
Location: Leibniz lecture hall, MPI for Mathematics in the Sciences
Unfortunately, this colloquium has to be canceled.

Center for Mathematical Physics Colloquium (former)

Peter Hinz (ETH Zürich)
Title: Perturbations and weak interactions of black holes
Date: Tuesday 11 June 2024 at 15:15
Location: Leibniz lecture hall, MPI for Mathematics in the Sciences

Following an introduction to general relativity, the Einstein field equations, and an overview of recent results on the stability of black holes, I will discuss work in progress towards the construction of singular perturbations of spacetimes via the insertion of small black holes. This aims to provide the first rigorous examples of spacetimes describing the merger of two black holes with extreme mass ratios.
Poster
Massimiliano Gubinelli (University of Oxford)
Title: New directions & open problems in stochastic analysis
Date: Friday 19 May 2023 at 16:00
Location: Leibniz lecture hall, MPI for Mathematics in the Sciences

Stochastic analysis makes precise the intuition that paths of Markov diffusions look like Brownian motion. The struggle for similar precision applied to a larger class of random fields led to the invention of controlled paths and regularity structures and opened the way to a new approach to Euclidean qua ntum field theory. However, despite a lot of progress, it feels that we are still at the infancy of this rich field where analysis, geometry and algebra meet with probability theory in new ways. I will try to name few problems which I think are important to our deeper understanding of these connections
Poster

Colloquium (former)

Daniel Baumann (University of Amsterdam)
Title: Positive geometry in cosmology
Date: Tuesday 13 Feb 2024 at 16:30
Location: University of Leipzig (Theory Lecture Hall, Linnestr. 5, 04103 Leipzig)

Cosmology is famously an observational rather than an experimental science. No experimentalists were present in the early universe, and the birth and subsequent evolution of the universe cannot be repeated. Instead, we can only measure the spatial correlations between cosmological structures at late times. A central challenge of modern cosmology is to construct a consistent "history" of the universe that explains these correlations. Recently, a new bootstrap approach was developed to understand this history using physical consistency conditions alone. In this colloquium, I will explain the basic idea behind this "cosmological bootstrap". I will also describe the search for new geometrical structures, called "positive geometries", which may underlie the theory of cosmological correlations. Finding such structures is one of the central aims of the ERC Synergy Grant project UNIVERSE+. I hope to make the talk accessible to a broad audience, and will not assume any background in cosmology or particle physics.

Workshops

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Workshops (former)

Lectures

Lectures (former)

IMPRS MiS

Leipzig hosts the International Max-Planck Research School Mathematics in the Sciences, a prestigious graduate school in mathematics focused on interdisciplinary research topics at the interface between mathematics and the sciences.

Mathematical Physics M.Sc.

The University of Leipzig offers the two-year English-language master’s programme "Mathematical Physics M.Sc.". This is an interdisciplinary programme bridging mathematics and theoretical physics. Interested students can find more information here.

Topics

Quantum Information
Stefan Hollands
Operator Algebras
Stefan Hollands, Rainer Verch
Quantum Defects
Daniel Roggenkamp
Classical and Quantum Integrable Models
Alexey Bufetov, Daniela Cadamuro
Scaling Laws, Phase Transitions, Criticality
Felix Otto, Artem Sapozhnikov, Daniel Roggenkamp
Fluid Dynamics
Jan Burczak, Felix Otto, László Székelyhidi
Quantum Field Theory
Daniela Cadamuro, Marc Casals, Stefan Hollands, Daniel Roggenkamp, Rainer Verch, Jochen Zahn
Pattern Formation
Felix Otto
Scattering Amplitudes
Bernd Sturmfels, Simon Telen
Condensed Matter
Klaus Kroy, Inti Sodemann
Partial Differential Equations
Judith Brinkschulte, Stefan Czimek, Dejan Gajic, László Székelyhidi
Topological Phases of Matter
Inti Sodemann
Non-equilibrium Physics
Klaus Kroy, Inti Sodemann, Max von Renesse
Stochastic PDEs
Max von Renesse
Complex Systems
Jürgen Vollmer
Positivity
Bernd Sturmfels, Simon Telen, Anna Wienhard
Higher Teichmüller Theory
Anna Wienhard
General Relativity
Marc Casals, Stefan Czimek, Dejan Gajic, Stefan Hollands, Rainer Verch
Percolation
Artem Sapozhnikov
Gravitational Waves
Marc Casals, Stefan Czimek, Dejan Gajic
Cluster Algebras
Anna Wienhard
Dynamical Systems
Felix Pogorzelski, Matthias Schwarz
Differential Geometry
Stefan Czimek, Bernd Rademacher, Matthias Schwarz, Anna Wienhard
Optimal Transport
Max von Renesse
Black Holes
Marc Casals, Stefan Czimek, Dejan Gajic
Dirac Operators
Bernd Rademacher
Symplectic Geometry
Matthias Schwarz

Contact

  • c/o Max-Planck-Institut für Mathematik in den Naturwissenschaften
    Katharina Matschke
    Inselstr. 22, 04103 Leipzig, Sachsen