### Wissenschaftliche Arbeitsgebiete

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

### Mathematisches Forschungsinstitut Oberwolfach

Logarithmic Vector Fields and Freeness of Divisors and Arrangements: New perspectives and applications (online meeting)

24 January - 30 January 2021

Organizers:

Takuro Abe, Fukuoka

Alexandru Dimca, Nice

Eva-Maria Feichtner, Bremen

Gerhard Röhrle, Bochum

### Vortrag im Oberseminar Arrangements and Symmetries

Vortrag am Montag, 08.02.2021, 14:15 Uhr, via zoom

Vortragender: Prof. Dr Volkmar Welker (Marburg)

Titel: "Relative Arrangements"

Abstract:

Infoblatt

**Zugangsdaten**

https://ruhr-uni-bochum.zoom.us/j/92406796238?pwd=UTFvYUR4M2h5TDlhenM3aUx4K1hHZz09

Meeting-ID: 924 0679 6238

Passwort: ArrSym20

### Vortrag im Oberseminar Lie Theorie

Vortrag am Montag, 01.02.2021, 14:15 Uhr, via zoom

Vortragender: Professor Aner Shalev (Hebrew University of Jerusalem)

Titel: "Random Generation: from Groups to Algebras"

Abstract:

There has been considerable interest in recent decades in questions of random generation of finite and profinite groups,
with emphasis on finite simple groups. In this talk, based on a recent joint work with Damian Sercombe, we study similar notions for finite and profinite associative algebras.
Let $A$ be a finite associative, unital algebra over a (finite) field $k$. Let $P(A)$ be the probability that two random elements of $A$ will generate $A$ as a unital $k$-algebra. It is known that, if $A$ is simple, then $P(A) \to 1$ as $|A| \to \infty$. We extend this result for larger classes of finite associative algebras. For $A$ simple, we estimate the growth rate of $P(A)$ and find the best possible lower bound for it. We also study the random generation of $A$ by two special elements.
Finally, we let $A$ be a profinite algebra over $k$. We show that $A$ is positively finitely generated if and only if $A$ has polynomial maximal subalgebra growth. Related quantitative results are also obtained.

**Zugangsdaten**

https://ruhr-uni-bochum.zoom.us/j/99572000333?pwd=QlhGZDZtQmR5dGRqeVJCOFpuSGVnZz09

Meeting ID: 995 7200 0333

Password: math

### Vortrag im Oberseminar Arrangements and Symmetries

Vortrag am Montag, 18.01.2021, 12:15 Uhr, via zoom

Vortragender: Prof. Masahiko Yoshinaga (Hokkaido University)

Titel: "A geometric realization of combinatorial reciprocity of order polynomials"

Abstract:

The Euler characteristic of topological space can be considered as a generalization of the cardinality of a finite set. In previous work with Hasebe and Miyatani (2017), we
generalized Stanley's combinatorial reciprocity for order polynomials to an equality
of Euler characteristics of certain spaces of homomorphisms of posets.
In this talk, we discuss recent development of geometric realization of the combinatorial
reciprocity. The main result asserts that certain spaces of poset homomorphisms are
actually homeomorphic which clearly implies the Euler characteristics. The proof
is based on the detailed analysis of upper semicontinuous functions on metrizable
topological spaces. This is joint work with Taiga Yoshida.

**Zugangsdaten**

https://ruhr-uni-bochum.zoom.us/j/92406796238?pwd=UTFvYUR4M2h5TDlhenM3aUx4K1hHZz09

Meeting-ID: 924 0679 6238

Passwort: ArrSym20

### Vortrag im Oberseminar Lie Theorie

Vortrag am Montag, 18.01.2021, 14:15 Uhr, via zoom

Vortragender: Dr. Alexander Sistko (Manhattan College, New York)

Titel: "On quiver representations over the field with one element"

Abstract:

To any quiver, we can associate its category of finite-dimensional (nilpotent) representations over the field with one element. This category shares many basic properties with its analog over a field: in particular, a version of the Krull-Schmidt Theorem is satisfied. Inspired by the classical Tame-Wild Dichotomy for finite-dimensional algebras, we discuss a stratification of quivers based on the growth of their indecomposable F1-representations. In particular, we classify all quivers of bounded representation type over F1 and provide a functorial interpretation for unbounded quivers. As a consequence, we develop a general framework for interpreting F1-representations as certain quiver maps, which allows for a more combinatorial description of the Ringel-Hall algebras associated to these categories.

**Zugangsdaten**

https://ruhr-uni-bochum.zoom.us/j/99572000333?pwd=QlhGZDZtQmR5dGRqeVJCOFpuSGVnZz09

Meeting ID: 995 7200 0333

Password: math

### Vortrag im Oberseminar Arrangements and Symmetries

Vortrag am Montag, 18.01.2021, 16:15 Uhr, via zoom

Vortragender: Dr. Paul Mücksch (RUB)

Titel: "On Yuzvinsky's lattice sheaf cohomology for hyperplane arrangements
"

Abstract:

In my talk, I will establish the exact relationship between
the cohomology of a certain sheaf on the intersection lattice of a hyperplane
arrangement introduced by Yuzvinsky and the cohomology of the coherent sheaf
on punctured affine space respectively projective space
associated to the derivation module of the arrangement.
I will derive a Künneth formula connecting the cohomology theories,
answering a question posed by Yoshinaga.
This, in turn, gives a new proof of Yuzvinsky’s freeness criterion
and yields a stronger form of the latter.

**Zugangsdaten**

https://ruhr-uni-bochum.zoom.us/j/92406796238?pwd=UTFvYUR4M2h5TDlhenM3aUx4K1hHZz09

Meeting-ID: 924 0679 6238

Passwort: ArrSym20

### Vortrag im Oberseminar Lie Theorie

Vortrag am Montag, 11.01.2021, 14:15 Uhr, via zoom

Vortragender: Dr. Alex Malcolm (University of Bristol, UK)

Titel: "Finite simple groups, prime order elements and width"

Abstract:

The generation of finite simple groups has been a thriving area of research for many years. Since it was established that each is generated by a pair of elements, many interesting refinements have followed: for instance, determining the existence of generating pairs of prescribed orders.

More recently the notion of width has provided an additional perspective on generation, measuring how efficiently a chosen subset generates a group. For example we may ask, can every element be written as a product of at most 2, or perhaps 3, elements from a fixed conjugacy class? Answering such questions relies on a range of tools involving subgroup structure and character theory.

In this talk we will examine the width of finite simple groups with respect to elements of a fixed prime order. We will report on sharp bounds for particular families, and answer questions concerning Lie-type groups of unbounded rank.

**Zugangsdaten**

https://ruhr-uni-bochum.zoom.us/j/99572000333?pwd=QlhGZDZtQmR5dGRqeVJCOFpuSGVnZz09

Meeting ID: 995 7200 0333

Passwort: math

### Vortrag im Oberseminar Arrangements and Symmetries

Vortrag am Montag, 11.01.2021, 16:15 Uhr, via zoom

Vortragender: Dr. Georges Neaime (RUB)

Titel: "Lectures on Garside Theory"

Abstract:

Infoblatt

**Zugangsdaten**

https://ruhr-uni-bochum.zoom.us/j/92406796238?pwd=UTFvYUR4M2h5TDlhenM3aUx4K1hHZz09

Meeting-ID: 924 0679 6238

Passwort: ArrSym20

### 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)

Mario Salvetti (Università di Pisa)

Anne Shepler (University of North Texas)

Jiro Sekiguchi (Tokyo University of Agriculture and Technology)

Michele Torielli (Hokkaido University)

Masahiko Yoshinaga (Hokkaido University)

### 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).

### 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.

### 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 Tilmann Möller, Paul Mücksch, Gerhard Röhrle, and Anne Schauenburg held a summer school directed focusing on new developments in the theory of hyperplane arrangements and related topics.

The school was aimed towards Ph.D. students and young Postdocs in the field. The international set of speakers and the participants came from all over the globe.

The school consisted of six series of minicourses on several topics followed by a day of conference-style talks from international experts. The summer school was funded by RUB Research School.

### 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.

## Archiv der laufenden Ankündigungen

Briefanschrift | Paketanschrift | Fon/Fax/Mail |
---|---|---|

Ruhr-Universität Bochum Fakultät für Mathematik Prof. Dr. Gerhard Röhrle IB 2/133, Fach 69 D-44780 Bochum |
Ruhr-Universität Bochum Fakultät für Mathematik Prof. Dr. Gerhard Röhrle IB 2/133, Fach 69 Universitätsstraße 150 D-44801 Bochum |
Tel.: +49(0)234-32-28304 Fax: +49(0)234-32-14025 E-Mail: gerhard.roehrle@ruhr-uni-bochum.de |