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.

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.

- HEP – QFT Seminar: Tuesdays at 15:15,
*ITP* - Physics Colloquium: Tuesdays at 16:30,
*main physics building* - Research Seminar ('Oberseminar') Analysis-Probability: Tuesdays 15:15 and 16.45 (irregularly),
*MPI for Mathematics in the Sciences* - Oberseminar Analysis: Thursdays at 15:15,
*Augusteum* - Emmy-Noether seminar: Thursdays at 15:00,
*ITP/online* - Webinar: Analysis, Quantum Fields, and Probability: Thursdays at 17:00 (irregularly),
*online* - Leipzig General Relativity seminar series: Fridays at 15:15,
*ITP* - Colloquium: Local Quantum Physics Crossroads: biannually,
*online*

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.

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

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.

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- Geometry Day 2023 in Leipzig: March 29-30, 2023,
*Mathematical Institute, University of Leipzig* - Women in Mathematical Relativity: April 14, 2023,
*online* - Summer School on PDEs and Randomness: May 10-24, 2023,
*MPI for Mathematics in the Sciences* - Positive Geometry in Particle Physics and Cosmology: February 12 - 16, 2024,
*MPI for Mathematics in the Sciences*

- IMPRS Ringvorlesung: date and time to be confirmed,
*MPI for Mathematics in the Sciences*

- Introduction to Tropical Geometry, Mondays and Tuesdays at 9 am,
*MPI for Mathematics in the Sciences*

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.

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.