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.
Homotopy theory and category theory are particular areas of expertise in pure mathematics of our research group.
Pure Mathematics. Emphasis on Geometry, Group Theory, Analysis, Dynamical systems.
Non-linear wave equations, kinetic theory and Lorentzian geometry.
Algebraic topology and its applications, primarily to the life sciences, in particular to neuroscience.