### Wissenschaftliche Arbeitsgebiete

- Algebraische Lie Theorie
- Algebraische Gruppen
- Endliche Gruppen vom Lie Typ
- Darstellungstheorie
- Hyperebenen- arrangements

### Vortrag im Oberseminar Lie-Theorie

Montag, den 08.07.19 um 16 ct in IA 1/181

Vortragender: Professor Dr. Götz Pfeiffer, National University of Ireland, Galway, EI

Titel: "Bisets and the Double Burnside Algebra of a Finite Group "

Abstract:

The double Burnside group $B(G, H)$ of two finite groups $G, H$ is the Grothendieck group of the category of finite $(G, H)$-bisets. Certain bisets encode relationships between the representation theories of $G$ and $H$. Bouc's biset category provides a framework for studying such relationships, it has finite groups as objects, and $B(G, H)$ as morphisms between $G$ and $H$, with composition induced by the tensor product of bisets. The endomorphism ring $B(G, G)$ is called the double Burnside ring of $G$. In contrast to the (ordinary) Burnside ring $B(G)$, the double Burnside ring $B(G, G)$ of a nontrivial group $G$ is not commutative. In general, little more is known about the structure of $B(G, G)$.
In the talk I'll describe a relatively small faithful matrix representation of the rational double Burnside algebra $\mathbb{Q}B(G,G)$ for certain finite groups $G, based on a recent decomposition of
the table of marks of the direct product $G \times G$, exhibiting the
cellular structure of the algebra $\mathbb{Q}B(G, G)$. This is joint
work with Sejong Park.

### Vortrag im Oberseminar Lie-Theorie

Montag, den 08.07.19 um 14 ct in IA 1/53

Vortragender: Professor Dr. Mohamed Barakat (Universität Siegen)

Titel: "Chevalley’s Theorem on constructible images made constructive "

Abstract:

Chevalley proved that the image of an algebraic morphism between algebraic varieties is a constructible set. Examples are orbits of algebraic group actions. A constructible set in a topological space is a finite union of locally closed sets and a locally closed set is the difference of two closed subsets. Simple examples show that even if the source and target of the morphism are affine varieties the image may neither be affine nor quasi-affine. In this talk I will present an Gröbner-basis-based algorithm which computes the constructible image of a morphism of affine spaces, along with applications to Terao’s freeness conjecture.

### Promotionen in 2019

Unsere wissenschaftlichen Mitarbeiter Maike Gruchot und Tilman Möller haben beide ihre Dissertationen erfolgreich verteidigt und ihre Promotion zum "Dr. rer. nat." mit Bravour abgeschlossen.

Frau Gruchot untersuchte in ihrer Dissertation zum Thema: "A Relative Variant of Complete Reducibility" eine Verallgemeinerung des Begriffes von Serre von G-vollständiger Zerlegbarkeit.

Herr Möller widmete sich in seiner Arbeit "Combinatorial properties of hyperplane arrangements and reflection arrangements" mehreren aktuellen Themen aus der Theorie der Hyperebenenarrangements.

Der Lehrstuhl für Algebra und Zahlentheorie gratuliert den beiden zu ihren herausragenden Leistungen recht herzlich und wünscht ihnen für ihre weitere Karriere alles Gute.

### Summer School - Perspectives in Linear Algebraic Groups

From Monday 19th August until Friday 23rd August, 2019 we will host a Summer School on
"Perspectives in Linear Algebraic Groups", on Ruhr-University Bochum Campus.

This summer school aims at introducing junior researchers to a variety of
topics in linear algebraic groups over arbitrary fields, with a focus on
pseudo-reductive groups and unusual behavior over fields which are not
algebraically closed.

The school will consist of four lecture series given over four days,
followed by a day of conference-style talks.

Lecture series will be given by Ben Martin (University of Aberdeen),
Bernhard Mühlherr (University of Giessen), Gopal Prasad (University of Michigan)
and Bertrand Rémy (Université Paris-Saclay). Additional talks will be given by
Philippe Gilles (Université Lyon 1, France), David Stewart (Newcastle University, UK),
Adam Thomas (Birmingham, UK) and Tomohiro Uchiyama (Soka University, Japan).

### Workshop on Hyperplane Arrangements and Reflection Groups

Leibniz Universität Hannover, Germany · September 23 - 27, 2019

Organizers:

Michael Cuntz (Hannover), Gerhard Röhrle (Bochum) and Christian Stump (Bochum)

Confirmed speakers:

Takuro Abe (Kyushu University)

Alexandru Dimca (Nice University)

Matthew Douglass (NSF)

Eva-Maria Feichtner (Bremen University)

Misha Feigin (University of Glasgow)

Lukas Kühne (Hebrew University of Jerusalem)

Jean Michel (Université Denis Diderot)

Tilman Möller (Bochum University)

Paul Mücksch (Bochum University)

Bernhard Mühlherr (Giessen University)

Luis Paris (Université de Bourgogne)

Götz Pfeiffer (National University of Ireland)

Anne Shepler (University of North Texas)

Jiro Sekiguchi (Tokyo University of Agriculture and Technology)

Hiroaki Terao (Hokkaido University)

Michele Torielli (Hokkaido University)

Masahiko Yoshinaga (Hokkaido University)

### Alexander von Humboldt Fellowship awarded to Dr Uchiyama

We are very pleased to announce that Dr Tomohiro Uchiyama has been awarded a competitive six-month Alexander von Humboldt Fellowship for Postdoctoral Researchers, hosted by Professor Gerhard Röhrle, with a research topic 'Complete reducibility, geometric invariant theory, and spherical buildings'.

Dr. Uchiyama's research focuses on subgroup structures of reductive algebraic groups (matrix groups). In particular, he studies Serre's notion of complete reducibility of subgroups of reductive groups via geometric invariant theory (a branch of algebraic geometry) and the theory of spherical buildings (highly symmetric combinatorial objects).
In this research project the recently proved 50-years-old center conjecture of Tits comes into play. He also investigates various relations between complete reducibility and pseudo-reductivity due to Conrad-Gabber-Prasad.

### Summer School – New Perspectives in Hyperplane Arrangements

In September 2018 we will host a summer school directed towards Ph. D. students and Postdocs interested in the theory of hyperplane arrangements. There will be minicourses on several topics from Monday to Thursday followed by a day of conference-style talks on Friday.

### Spring School on Complete Reducibility

In April 2018 we will host a spring school, aimed at introducing graduate students and junior researchers to the notion of G-complete reducibility, featuring a lecture series by Professor Ben Martin (Aberdeen), and a number of additional lectures.

### Sloan Visiting Professor Cohen

Professor Daniel Cohen from Louisiana State University in Baton Rouge, LA, USA is currently visiting the Department of Mathematics. Professor Cohen's visit to Bochum is supported by the Sloan Visiting Professor scheme (SVP) of the Mathematisches Forschungsinstitut Oberwolfach (MFO).

Professor Cohen's research focus is in topology, with connections to other areas such as combinatorics and geometric group theory. He is interested in hyperplane arrangements, configuration spaces, braid groups, and related objects. In addition to, and sometimes in relation with, these subjects, portions of his recent work have been on topological problems motivated by the motion planning problem from robotics.

Professor Cohen will present his work in two lectures during the week long visit. They are titled "Pure braid groups and direct products of free groups" and "Topological complexity of surfaces and their configuration spaces" which are held Monday 22.1.18, at 14:15 and Wednesday 24.1.18, at 14:15, respectively. Both venues take place in Wasserstrasse 221, Room 4/20. All are welcome to attend.

During his visit Professor Cohen is hosted by Professor Gerhard Röhrle.

### Alexander von Humboldt Fellowship awarded to Dr Litterick

We are very pleased to announce that Dr Alastair Litterick has been awarded a competitive two-year Alexander von Humboldt Fellowship for Postdoctoral Researchers, hosted by Professors Christopher Voll (Bielefeld University) and Gerhard Röhrle (Ruhr-University Bochum), with a research topic of 'Subgroup structure and generation properties in reductive groups'. Reductive groups are an important class of mathematical objects which lie at the intersection between algebra and geometry. Because of their multi-faceted nature, they are important throughout mathematics and beyond, arising naturally, for instance, in branches of theoretical physics such as string theory.

Dr Litterick's research focuses on algebraic properties of these groups. Although the groups themselves are easy to describe, several aspects of their subgroup structure remain mysterious. In particular, he is concerned with understanding subgroups which are themselves reductive group, and with subgroups containing elements of specified forms. Current approaches to these problems involve many diverse areas of pure mathematics, including algebraic geometry, computational algebra, geometric group theory, geometric invariant theory, Lie theory, cohomology theory, representation theory, and still more. Working in the diverse groups of Professors Voll and Röhrle, Dr Litterick intends to pursue all of these avenues towards the solutions of these problems.

### Visiting International Professor Fellowship

Professor Benjamin Martin
from the University of Aberdeen has been awarded a VIP Professorship by the
RUB-Research School.

Professor Martin is one of the worlds experts in algebraic groups,
representation varieties and representation growth,and related fields such as
representation theory and the theory of buildings. More specifically, he is a world leader in
the theory of complete reducibility for algebraic groups and geometric invariant theory associated with the action of reductive groups on affine varieties.

Over the course of the next two years
he will be visting the department of mathematics and
will contribute to the postgraduate
education within the chair of
Professor G. Röhrle

For the RUB-Research school and the VIP-Programme, see also here

## Archiv der laufenden Ankündigungen

#### Postadresse

Ruhr-Universität Bochum

Prof. Dr. Gerhard Röhrle

Fakultät für Mathematik

IB 2/133, Fach 69

D-44780 Bochum

#### Fon/Fax/Mail

Tel.: +49(0)234-32-28304

Fax: +49(0)234-32-14025

E-Mail: gerhard.roehrle@ruhr-uni-bochum.de