AMCV
The AMCV group is the Chair of Mathematical Analysis, Calculus of Variations and PDEs (AMCV).
Our group conducts research on the Analysis of Partial Differential Equations, Calculus of Variations, Geometric Measure Theory, and their applications to mathematical models of concrete problems, such as equations in fluid dynamics, kinetic equations and meteorology.
In the pictures: flow visualization of a turbulent jet, minimal surface, branched transport from a point to the circle (numerical simulation by Oudet and Santambrogio), vector field in a tube, and branched transport competitor.
Interests: Analysis, PDEs, Applied Mathematics
PDE
The PDE group is the Chair of Partial Differential Equations (PDE).
Our group conducts research on nonlinear partial differential equations which arise in mathematical physics, particularly geometric wave equations. We aim at rigorously proving theorems about existence of solutions, ideally without any restrictions on data, as well as analyzing theoretically the asymptotic features of such solutions. Some of the motivation comes from numerical experiments conducted by physicists, which we try to put on solid theoretical foundation. Particular areas of interest are stability/instability of soliton type solutions, as well as precise blow up dynamics of solutions.
STOAN
The STOAN group is the Chair of Stochastic Analysis.
Our group investigates stochastic processes, stochastic equations. their dynamics and analytical properties. We have a broad range of research interests in analysis and randomness.
Our current topics are: stochastic differential equations, solution theory and large time dynamics, multi-scale stochastic dynamics, stochastic equations driven by rough paths, stochastic partial differential equations, Malliavin calculus, geometry of stochastic processes, stochastic processes on manifolds, limit and functional limit theorems, analysis on path and loop spaces.
CMGR
The CMGR group is the Chair of Mathematical General Relativity.
Our group explores questions about the geometric and analytic properties of spacetime solutions to the Einstein field equations in general relativity, as well as similar questions for other non-linear hyperbolic equations arising in mathematical physics. Examples of problems investigated by our group include the stability properties of special solutions of the Einstein equations, high-frequency limits of solutions, criteria for the formation of black holes, the well-posedness threshold for the associated initial value problem and the structure of singularities emerging dynamically from smooth initial data.