### Wissenschaftliche Arbeitsgebiete

- Algebraische Lie Theorie
- Algebraische Gruppen
- Endliche Gruppen vom Lie Typ
- Darstellungstheorie
- Hyperebenenarrangements

### Vortrag im Oberseminar Lie Theorie

Montag, den 09.10.18, von 14 - 16 Uhr in der Wasserstraße 221, Raum 4/20

Vortragender: Prof. Dr. J. M. Douglass (NSF, Washington, DC, USA)

Titel: " A factorization of the T-equivariant K-theory of flag varieties"

Abstract:

Let G be a reductive, complex, algebraic group, B a Borel subgroup, T is a maximal torus in B, and P is a parabolic subgroup containing B. Then G/B is the "flag variety" of G and the projection from G/B to G/P is a G-equivariant fibre bundle with fibre P/B. As smooth varieties, G/B is locally isomorphic to the product G/P x P/B. The quotient P/B may be canonically identified with the flag variety of the Levi subgroup of P containing T and the "factorization" G/B = G/P x P/B may be viewed as a geometric incarnation of the factorization W = W^P x W_P, where W is the Weyl group of (G,T), W_P is the Weyl group of (P,T), and W^P is a set of left coset representatives of W_P in W. In this talk I will describe a factorization of the T-equivariant K-theory of G/B as a tensor product of the T-equivariant K-theory of G/P and the T-equivariant K-theory of P/B. The factorization theorem can be described in terms that make sense for any generalized cohomology/homology theory and the factorization in equivariant K-theory leads immediately to a uniform, geometric construction of corresponding factorizations in K-theory, equivariant cohomology, and ordinary cohomology.

### 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

### "Research Explorer Ruhr"

We are delighted to announce that the application of Dr. Tomohiro Uchiyama (National Taiwan University, National Center for Theoretical Sciences) within the Research Explorer Ruhr programme of the RUB Research School have been successful. The researcher will be visiting the Lehrstuhl in the period June 19 - 30. During his visit he will be able to explore possible research interactions and collaboration possibilities within our research group. At the same time the Research school offers an accompanying programme which will provide information about various possibilities for funding a postdoc position, so that he potentially might return to the Ruhr-University as Postdoc.

For more information on the Research Explorer Ruhr programme of the RUB, see here.

Tilman Möller, Gerhard Röhrle

Bei der Akademischen Jahresfeier 2016 wurde Herr Tilman Möller mit dem RUB-Preis für seine Masterarbeit "Induktiv faktorisierte Arrangements und deren Abgeschlossenheit unter Lokalisierung" ausgezeichnet.

### DFG-Grant awarded to Professor Röhrle

**Inductive freeness and rank generating functions
of arrangements of ideal type: two conjectures of
Sommers and Tymoczko revisited **

The grant provides financial support for a research post for three years.
The topic of the research project focuses on the interplay on the one hand of Lie theoretic and combinatorial aspects of root systems and on the other on geometric and algebraic properties of a particular class of real hyperplane arrangements stemming from certain subsets of the set of positive roots of a reduced root system.

## IRB Research Grant

**Anne Schauenburg** obtained one of the competitive IRB research grants from the Ruhr University Research School PLUS, funded by Germany’s Excellence Initiative [DFG GSC 98/3]. The IRB targets doctoral researchers in the first year who want to enrich their doctorate by several international activities. It is planned that Ms Schauenburg will use her grant to intensify international collaboration and networking with researchers working in the area of her doctorate via research stays and conference participation.

research-school

## Archiv der laufenden Ankündigungen

#### Postadressse

Prof. Dr. Gerhard Röhrle

Ruhr-Universität Bochum

Fakultät für Mathematik

D-44780 Bochum

**Besucheranschrift**

Wasserstraße 221

4.Etage/Raum 4.10

Bochum Wiemelhausen

#### Fon/Fax/Mail

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

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

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