Calculus of Variations, regularity of degenerate elliptic PDEs, optimal transport, geometric measure theory.

Mathematical physics by analytical methods, specifically spectral theory of ergodic Schrödinger operators and random matrices; homogenization theory; quantum spin systems; matrix inequalities and quantum information theory

Mathematical physics, probability, statistical mechanics, field theories, conformal symmetry, complex analysis, lattice models, exactly solvable models, neural networks.

Chair of Dynamics of Learning Algorithms (DOLA)
Lénaïc Chizat
Analysis of gradient-based learning. Optimization in the space of measures. Algorithmic regularization. Over-parameterization. Computational and statistical optimal transport.

Partial Differential Equations,mathematical physics, harmonic analysis, differential geometry.
Ergodic Theory, Topological and Symbolic Dynamics, (Ergodic) Ramsey Theory, Additive Combinatorics, Combinatorial Number Theory, Multiplicative Number Theory

Spectral Analysis of partial differential operators, partial differential equations, Quantum Mathematical Physics.

Analytic Number Theory, Analytic properties of Automorphic forms and their representations, Ergodic theory on arithmetic homogeneous spaces.