Chair of Algebra and Representation Theory
Contact
Research
The research of the Lehrstuhl is located at the intersection of algebraic geometry, combinatorics, and representation theory:
- Representation theory of semi-simple (complex) Lie algebras, GL_n and other algebraic groups
- Combinatorics of (monomial) bases and Standard Monomial theory
- Computeralgebra and Gröbner bases
- Degenerations of Lie algebras and homogeneous spaces, quiver grassmannians
- Tropical geometry x Representation theory = ?
- Polyhedral geometry x Representation theory = ?
- Weyl modules, Kirillov-Reshetikhin modules of loop algebras
The methods in use may 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
Master Theses (Completed)
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Ibrahim Ahmad: The Hibi-Li-Conjecture for Almost Complete Comparability Graphs, 2023
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Maria Magdalena Reitzenstein: The Blended Learning Concept "Flipped Classroom" in a Mathematics Teaching Context, 2023
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Alena Meyer: The Free Abelian Category on One Generator, 2022
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Astrid Hagemeyer: (Co)limits and Finitely Presented Functors, 2021
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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
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Darius Dramburg: Flat Degenerations of Quiver Grassmannians, 2020
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Tom Görtzen: Improvements on the Schur Positivity Conjecture, 2020
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Dario Mathiä: Bumping for PBW Tableaux, 2019
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Frederik Gutsche: Hochschild Cohomology, PBW Deformations and Hecke Algebras, 2019
Bachelor Theses (Completed)
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Leon Steinhoff: The vanishing ideal of the toric FFLV-variety
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León van Eß: Gröbner bases of simple, integrable sl_n-modules, 2022
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Dilay Boyacı: Reflexive Polytopes in Representation Theory via Ehrhart Theory, 2022
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Julian Hompesch: Galoisgruppen über Q und Berechnung in Spezialfällen, 2022
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Michael Schlößer: Totale Positivität von Grassmann-Varietäten und Clusteralgebren, 2021
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Lukas Schnelle: The Gelfand-Tsetlin Bases, Now and Then, 2021
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Jan Rodriguez: Linear Degeneration of Type E Quiver, 2021
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Ibrahim Ahmad: Marked Poset Polytopes of Almost Complete Comparability Graphs, 2021
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Wilkosz, Leon: On Representations of Posets, 2021
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Lena Porschen: Topologische Galoistheorie, 2021
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Maria Magdalena Reitzenstein: Die Erstellung und Erprobung stochastischer Lernmaterialien im DaZ-Kontext des Mathematik-Vorkurses für Geflüchtete und international Studierende der RWTH Aachen, 2020
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David Schlang: Isomorphismenklassen von Köcherdarstellungen: Typ A, 2020
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Marius Wesle: Darstellungen von halbeinfachen Lie-Algebren und algebraischen Gruppen: Eine Äquivalenz von Kategorien, 2019