Chair of Algebra and Representation Theory

Contact

Fourier © Copyright: Peter Winandy

Phone

work
+49 241 80 94528

Email

E-Mail
 

Research

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

https://prezi.com/view/7xbFm92RXjrRTm174yDn/

 

Supervised Theses

 
 

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
 

Master Theses (Current)

     

    Master Theses (Completed)

    • Michael do Nascimento Vaz: Development and evaluation of learning untis on the topics of bascis of maths and analytical geometry for a math course for refugees and international students, 2020
    • Darius Dramburg: Flat Degenerations of Quiver Grassmannians, 2020
    • Tom Görtzen: Improvements on the Schur Positivity Conjecture, 2020
    • Dario Mathiä: Bumping for PBW Tableaux, 2019
    • Frederik Gutsche: Hochschild Cohomology, PBW Deformations and Hecke Algebras, 2019
     

    Bachelor Theses (Current)

    • Lena Porschen: Toplogische Galoistheorie
    • Jan Rodriguez: Linear Degeneration of Type E Quiver
     

    Bachelor Theses (Completed)

    • 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, 2020
    • David Schlang: Isomorphismenklassen von Köcherdarstellungen: Typ A, 2020
    • Marius Wesle: Darstellungen von halbeinfachen Lie-Algebren und algebraischen Gruppen: Eine Äquivalenz von Kategorien, 2019