Prof. Dr. Gerhard Röhrle
Address:
Ruhr-Universität Bochum
Fakultät für Mathematik
Universitätsstraße 150
44801 Bochum
Room:
IB 2/133
Phone:
(+49)(0)234 / 32-28304
Bildarchiv des Mathematischen Forschungsinstituts Oberwolfach
Research Areas
- Algebraic Lie theory
- Algebraic groups
- Representation theory
- Finite groups of Lie type
- Hyperplane arrangements
- Reflection groups
Research projects
- DFG project: On Ziegler Extensions of Multiarrangements (within the DFG Priority Programme Combinatorial Synergies).
- DFG project: On connected subgraph arrangements (within the DFG Priority Programme Combinatorial Synergies).
- DFG project: Serre's notion of Complete Reducibility and Geometric Invariant Theory (within the DFG Priority Programme in Representation Theory).
- DFG project: Computational aspects of the Cohomology of Coxeter arrangements: On Conjectures of Lehrer-Solomon and Felder-Veselov (within the DFG Priority Programme "Algorithmic and experimental methods in Algebra, Geometry and Number Theory").
- DFG project: Arrangements of complex reflection groups: Geometry and combinatorics (joint with M. Cuntz (Kaiserslautern) within the DFG Priority Programme "Algorithmic and experimental methods in Algebra, Geometry and Number Theory").
- DFG project: Inductive freeness and rank-generating functions for arrangements of ideal type: Two conjectures of Sommers and Tymoczko revisited (within the DFG GEPRIS).
- DFG project: On the Cohomology of complements of complex reflection arrangements (within the DFG GEPRIS).
- DFG project: Inductive freeness of Ziegler's canonical multiplicity (within the DFG GEPRIS).
- DFG project: Overgroups of distinguished unipotent elements in reductive groups (within the DFG GEPRIS).
- DFG project: On hyperfactored and recursively factored arrangements (within the DFG GEPRIS).
Publications
Publications on zbMATH.
Publications on MathSciNet.
Recent preprints on the ArXiv.
Latest preprints:
On connected subgraph arrangements
with L. Giordani, T. Möller, and P. Mücksch
Abstract:
Recently, Cuntz and Kühne introduced a particular class of hyperplane arrangements stemming from a given graph G, so called connected subgraph arrangements A_G. In this note we strengthen some of the result from their work and prove new ones for members of this class. For instance, we show that aspherical members withing this class stem from a rather restricted set of graphs. Specifically, if A_G is an aspherical connected subgraph arrangement, then A_G is free with the unique possible exception when the underlying graph G is the complete graph on 4 nodes.
math.CO/2502.18144
Free multiderivations of connected subgraph arrangements
with Paul Mücksch and Sven Wiesner
Abstract:
Cuntz and Kühne introduced the class of connected subgraph arrangements A_G, depending on a graph G, and classified all graphs G such that the corresponding arrangement A_G is free. We extend their result to the multiarrangement case and classify all graphs G for which the corresponding arrangement A_G supports some multiplicity m such that the multiarrangement (A_G,m) is free.
math.CO/2406.19866
The subgroup structure of pseudo-reductive groups
with Michael Bate, Ben Martin, and Damian Sercombe
Abstract:
Let $k$ be a field. We investigate the relationship between subgroups of a pseudo-reductive $k$-group $G$ and its maximal reductive quotient $G'$, with applications to the subgroup structure of $G$. Let $k'/k$ be the minimal field of definition for the geometric unipotent radical of $G$, and let $\pi':G_{k'} \to G'$ be the quotient map. We first characterise those smooth subgroups $H$ of $G$ for which $\pi'(H_{k'})=G'$. We next consider the following questions: given a subgroup $H'$ of $G'$, does there exist a subgroup $H$ of $G$ such that $\pi'(H_{k'})=H'$, and if $H'$ is smooth can we find such a $H$ that is smooth? We find sufficient conditions for a positive answer to these questions. In general there are various obstructions to the existence of such a subgroup $H$, which we illustrate with several examples. Finally, we apply these results to relate the maximal smooth subgroups of $G$ with those of $G'$.
math.GR/2406.11286
