Lehrstuhl B für Mathematik
The research of the Lehrstuhl is located at the intersection of algebraic geometry, combinatorics, and representation theory. I would consider the representation theory of semi-simple or affine, complex Lie algebras as the core of my interests.
On the one hand, one studies modules for generalized loop algebras, such as Weyl modules and fusion products. On the other hand, standard monomial theory, degenerations of Lie algebras and algebraic groups, degenerations of spherical varieties are parts of the research. All this leads naturally to tropical geometry, Newton-Okounkov bodies, and cluster theory.
The methods in use originate from combinatorics and discrete mathematics, heavy use of mathematical software as well as geometric arguments.
Most research is done and will be done together with collaborators from institutes all over the world.
Supervised theses in the working group Fourier:
Phd theses (current)
- Kunda Kambaso: Linear degenerate Schubert varieties
- Kai Wehrmaker: The symplectic PBW degenerate flag variety
- Daniel Kalmbach: Essential bases and finitely generated semi groups
- George Balla: Combinatorics of PBW tableaux
- Verity Mackscheidt: PBW deformations arising from algebraic groups
Master theses (current):
- Dario Mathiä: Bumping for PBW tableaux