Our research focus is the analysis of continuum models that originate in materials science and fluid mechanics. Our technical expertise is in the calculus of variations and partial differential equations.

Our research focusses on fundamental problems in algebra, geometry and combinatorics that are relevant for nonlinear models.

The main focus of this group is on rigorous applied mathematics, mainly involving partial differential equations and the calculus of variations. We bridge several mathematical sub-disciplines by applying methods originally developed for differential geometry (Gromov) to fluid dynamics and nonlinear elasticity.

We conduct fundamental research in geometry, group theory, and dynamics, explore applications and interactions with other sciences and engage in communicating mathematics to the broader public.

The emeritus group of Jürgen Jost is an interdisciplinary research team that carries out research in pure mathematics and explores new approaches to complex systems in a wide range of domains, bringing in the spectrum of mathematical concepts and methods in novel ways.

We are interested in applications of Stochastic Analysis in Mathematical Physics, more specially in using probability to study Gibbs measures coming from Quantum Field Theory and Statistical Mechanics.

We explore discrete sets linked to geometric objects, focusing on Riemann surfaces, particularly those formed by gluing polygons. Our research spans number theory, dynamics, transcendental functions, and data science connections.

We are interested in various geometric structures on surfaces and 3-manifolds and the understanding of their geometry and deformations. Some deformations yield dynamical systems on moduli spaces; ergodic theory offers new perspectives on these objects.

Our focus is on the study of stochastic partial differential equations (SPDEs), nonlinear partial differential equations, stochastic dynamics, interacting particle systems, machine learning, and fluid dynamics.

We are dedicated to developing cutting-edge software that serves as a bridge between mathematical fields and interdisciplinary research areas. Our goal is to advance mathematical knowledge and make it more accessible to a wider audience.

We advance key problems in Deep Learning Theory using geometric analysis. Our mission is to consolidate the theoretical foundations for the success of Deep Learning and make them more broadly applicable. We draw on innovative mathematics to streamline progress into new frontiers.

We focus on the mathematical foundations of inference and learning. We develop methodological innovations for inference and learning and apply them to biology, biomedicine, and clinical challenges. Our goal is to advance these fields through rigorous mathematical analysis.

We want to build new bridges between Tropical Geometry and Algebraic Geometry using computational methods. This involves the study of fundamental problems in tropical geometry and the use and development of state-of-the-art software.

Our goal is to explore and broaden the scope of algebraic geometry and its connections with different branches of math & sciences. We are driven by the belief that this field transcends traditional boundaries, promoting collaboration & practical applications.

We use probabilistic and variational techniques to better understand nonlinear partial differential equations. We apply our findings to kinetic theory, statistical physics, materials science, and quantum mechanics. Our projects include optimal transportation, singular stochastic PDEs, effective equations, pattern formation problems, and density functional theory.

We conduct research at the interface of mathematics and theoretical physics, making use of a high degree of cross-fertilization between physical ideas and intuition on the one hand and rigorous mathematical theory on the other.

Algebraic analysis tackles linear differential equations and their solution functions by means of algebraic geometry. We are concerned with the concise study of these equations and explore further algebraic structures behind important functions in the sciences. We put a particular focus on Feynman integrals.

We study fundamental problems in differential geometry with a focus on symmetric spaces, harmonic maps, and geometric structures. We use classical methods as well as finding new approaches inspired by algebraic geometry, number theory, and dynamics.

We explore the topology of random combinatorial and geometric structures. Our research includes percolation models on lattices, configuration spaces, and random simplicial and cubical complexes. We also investigate extremal topological structures and their properties.

We are dedicated to developing advanced algorithms and theory to tackle the ancient problem of solving polynomial equations. In addition, we delve into related problems such as polynomial optimization, variable elimination, and tensor decomposition.