Chair of Algebra and Representation Theory
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.
The research has been presented to the mathematics students on 25.06.2019. You can find the presentation online
Die Forschung der Arbeitsgruppe wurde am Tag der Mathematik, 25.06.2019, den Studierenden der Fachgruppe vorgestellt. Die Präsentation ist hier abrufbar
Ph.D. 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
Bachelor Theses (Current)
Maria Magdalena Reitzenstein: The production and try-out of learning materials covering stochastics focussing on the challenges in the mathematics preparing course for refugees and international students of RWTH Aachen
David Schlang: Isomorphismenklassen von Köcherdarstellungen: Typ A