We study the topology of algebraic varieties through arithmetic methods such as counting points and p-adic/motivic integration. Of particular interest are connections to other fields such as complex geometry, representation theory and theoretical physics.
The main focus of the Chair of Algebraic Geometry is the classification theory of higher-dimensional algebraic varieties, including exploring its connections to adjacent fields such as commutative algebra, arithmetic geometry and complex geometry.
Pure Mathematics. Emphasis on Geometry, Group Theory, Analysis, Dynamical systems.
Ergodic Theory, Topological and Symbolic Dynamics, (Ergodic) Ramsey Theory, Additive Combinatorics, Combinatorial Number Theory, Multiplicative Number Theory
Subgroup structure of semisimple linear algebraic groups and the related finite simple groups of Lie type. Representation theory of semisimple linear algebraic groups and finite reductive groups. Properties of unipotent elements in semisimple algebraic groups.
Analytic Number Theory, Analytic properties of Automorphic forms and their representations, Ergodic theory on arithmetic homogeneous spaces.
Theory of automorphic forms, applications of automorphic forms to harmonic analysis and differential equations, packing problems, optimal configuration of points in geometric spaces.