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.
There are currently three PhD-theses under the supervision of prof. Ghislain Fourier:
- Monomial bases for PBW degenerate Demazure modules
- The symplectic PBW degenerate flag variety
- Essential bases and finitely generated semi groups