Wissenschaftliche Arbeitsgebiete

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


Vortrag im Oberseminar Arrangements and Symmetries

Online-Vortrag (Zoom) am Montag, 18.5.2020, 14: 15 Uhr

Vortragender: Dr. Georges Neaime (Universität Bielefeld)

Titel: "Garside theory and the $K(\pi,1)$ conjecture"

Abstract:
Garside theory was developed in order to better understand Artin groups and their generalizations. Based on the work of Bessis for complex braid groups and of Paris on Artin groups, as well as recent inventions by McCammond--Sulway and Paolini--Salvetti for affine Artin groups, we provide additional evidence of the link between Garside theory and the topology of complements of hyperplane arrangements. Actually, the theory provides a proof in full generality of the K(\pi,1) conjecture for complex braid groups, and for spherical and affine Artin groups.

Zugangsdaten
https://ruhr-uni-bochum.zoom.us/j/92406796238?pwd=UTFvYUR4M2h5TDlhenM3aUx4K1hHZz09
Meeting-ID: 924 0679 6238
Passwort: ArrSym20



Vortrag im Oberseminar Arrangements and Symmetries

Online-Vortrag (Zoom) am Montag, 11.5.2020, 14: 15 Uhr

Vortragender: Herr Florian Kranhold (Mathematisches Institut der Universität Bonn)

Titel: "Gekoppelte Konfigurationen"

Abstract:
Die Räume geordneter Konfigurationen in der komplexen Ebene haben sehr bekannte Eigenschaften und Anwendungen: Sie sind Komplemente eines komplexen Hyperebenen-Arrangements, klassifizieren die reinen Zopfgruppen, haben eine einfache Zellzerlegung und sind homotopieäquivalent zu den Komponenten der kleinen 2-Kuben-Operade, deren Homologie Poisson-Algebren klassifiziert. Diese Operade wirkt auf vielen interessanten Räumen, zum Beispiel auf den Modulräumen Riemannscher Flächen mit genau einer Randkurve. Möchte man Modulräume von Flächen mit mehreren Randkurven betrachten, ist eine Färbung der 2-Kuben-Operade naheliegend. Um diese Wirkung nun in verschiedenen simplizialen Modellen betrachten zu können, muss eine spezielle Unteroperade betrachtet werden. Deren Komponenten sind Konfigurationsräume mit einer speziellen Kopplungsbedingung: Einige Punkte haben stets den gleichen Realteil. Wir haben einige Eigenschaften dieser Räume verstanden: Auch sie lassen sich als Komplement eines Hyperebenen-Arrangements schreiben, haben eine vergleichsweise einfache Zellzerlegung und ihre Homologie kann mithilfe diskreter Morsetheorie berechnet werden. Ein großer Unterschied ist das Fehlen von Fadell-Neuwirth-Faserungen, weswegen die Asphärizität dieser Räume nach wie vor eine offene Frage ist.

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

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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)

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Summer School - Perspectives in Linear Algebraic Groups

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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).

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Promotionen in 2019

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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

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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

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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.

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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.

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Sloan Visiting Professor Cohen

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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

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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

Archiv





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