Events
Lecture Series "Matroidal polynomials and their singularities''
A lecture series by
Uli Walther (Purdue University, USA)
to be held at Ruhr-University Bochum within the DFG Priority Programme 2458 "Synergies in Combinatorics"
Schedule:
There will be a series of four talks. The talks will take place on
Monday 10.06.24 and Tuesday 11.06.24
where the two talks of the day will be given between
14:00 - 15:00 and 16:00 - 17:00.
in ID 03/653
Topics to be covered:
- Matroids, matroidal polynomials, examples of these, including Kirchhoff polynomials, configuration polynomials, multivariable Tutte polynomials, matroid support polynomials.
- Feynman diagrams and Feynman integrands (which are also matroidal). A discussion on torus actions on these hypersurfaces. The singular locus of certain matroidal polynomials: for configuration polynomials when the matroid is sufficiently connected, discuss irreducibility, size of singular locus, comparison between Jacobian ideal and a certain corank 2 determinantal ideal, Cohen-Macaulayness of these. The special case of the free resolution of the singular locus of the Kirchhoff polynomial of a complete graph.
- For matroidal polynomials in general, it will be explained that they have rational singularities, and in the homogeneous case that they are F-regular.
- Time permitting there will also be a discussion about the resolution of singularities.
Workshop Algebraic Groups and Representation Theory
Es finden am Montag, 04.12.2023, drei Vorträge statt
Vortrag 1
2:15 pm, IA 1/177
Vortragender: Alastair Litterick (University of Essex, UK)
Title: "Complete Reducibility: The Good, the Bad and the Conjugacy"
Abstract: The concept of a "completely reducible subgroup" generalises the representation-theoretic notion (the special case of the general linear group) to other reductive algebraic groups. This turns out to have deep interpretations in terms of algebraic geometry and geometric invariant theory. A long-running project seeks to harness complete reducibility to classify reductive subgroups of reductive groups, particularly the exceptional simple groups. As in representation theory, the study becomes more difficult the smaller the prime, with characteristic 2 presenting qualitative difficulties that do not arise elsewhere. We will discuss these, and give an overview of the current state of the classification.
Vortrag 2
3:30 pm, IA 1/177
Vortragende: Jacinta Torres (Jagiellonian University in Krakow, Poland)
Title: "Atoms and charge beyond type A"
Abstract: We present a new phenomenon which allows to compute certain atomic and preatomic decompositions of crystals. This phenomenon provides a conceptual explanation, as well as generalization to type C_n, of the preatomic decompositions and the cyclage map in type A_n. We also present the charge statistic for type C_2 crystals, giving positive combinatorial formulas for Kostka-Foulkes polynomials. This is joint work with Leonardo Patimo.
Vortrag 3
5:30 pm, IA 1/109
Vortragender: Benjamin Martin (University of Aberdeen, UK)
Title: "Smooth stabilisers for actions of algebraic groups"
Abstract: Let G be a linear algebraic group over an algebraically closed field k of characteristic p≥0, and let X be an affine variety on which G acts. Given a closed subvariety Y of X, we denote by C_G(Y) and N_G(Y) respectively the pointwise and setwise stabilisers of Y, regarded as closed subschemes of G. There are many situations where one wishes to know whether C_G(Y) and N_G(Y) are smooth. Some results are known in specific settings: for instance, if G is connected and reductive and G acts on X:=G by conjugation then C_G(Y) is smooth for any closed subgroup Y of G if p is very good for G, whereas C_G(Y) = Z(G) is not smooth if G= SL_n, Y= G and p divides n. Smoothness always holds when p=0 by a well-known result of Cartier. Examples like the one above suggest that smoothness should hold as long as p is sufficiently large, but it is not easy to make precise what ``sufficiently large’’ should mean. David Stewart, Lewis Topley and I recently formulated and proved some results along these lines. I will state some of our theorems and discuss the ideas behind the proofs, which combine the Lefschetz principle from model theory with Gröbner basis techniques.
Spring School on "Real, Complex, and Symplectic Reflection Groups"
From Monday 6 March until Friday 10 March, 2023 we will host a Spring School on "Real, Complex, and Symplectic Reflection Groups", on the Ruhr-University Bochum Campus.
This spring school aims at introducing junior researchers to a variety of topics in the theory of reflection groups, reflection arrangements, and related topics. The school will consist of three lecture series given over four days, followed by a day of conference-style talks.
Lecture series will be given by Götz Pfeiffer (Galway), Ulrich Thiel (Kaiserslautern), and Masahiko Yoshinaga (Osaka). Additional talks will be given by Eirini Chavli (Stuttgart), Michael Cuntz (Hannover), Paul Mücksch (Kyushu), and Tan Tran (Bochum).
Organisers: Georges Neaime, Gerhard Röhrle, Christian Stump
Oberwolfach Seminar June 2022
"G-Complete Reducibility, Geometric Invariant Theory and Spherical Buildings"
5 June - 11 June, 2022
Summary:
The "Oberwolfach Seminar 2223b" is in a core area of algebraic group theory and at the interdisciplinary cross roads of algebra and representation theory on the one hand, geometry and geometric invariant theory on the other. The notion of G-complete reducibility for subgroups of a reductive algebraic group G was introduced by J-P. Serre in the 1990s as a natural generalization of the notion of complete reducibility in representation theory (which corresponds to the case where G is the general linear group). Since its introduction, this notion has been widely studied, both as an important concept in its own right, with applications to the structure of linear algebraic groups, and also as a useful tool with applications in representation theory, geometric invariant theory, the theory of buildings, and number theory.
The aim of this Oberwolfach seminar is to introduce participants to G-complete reducibility and explain some of its many applications across pure mathematics — participants will learn some rich and deep modern algebra, and leave equipped with an understanding of how this mathematics continues to be applied to solve a diverse range of problems, particularly in the theory of algebraic groups.
Please see the detailed program and a recommended reading list on the website of the seminar.
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
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).
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.
Eighteenth NWDR Workshop Ruhr-Universität Bochum
On Friday, 22 July 2016, 11:00 - 18:00
Speakers:
- Arkady Berenstein (Eugene): Hecke-Hopf algebras
- Joseph Bernstein (Tel Aviv): Stacks in Representation Theory --- how should we think about continuous representations of algebraic groups
- Grzegorz Bobinski (Torun): Derived classification of the gentle two-cycle algebras
- Lennart Galinat (Cologne): Geometric Aspects of the Classical Yang-Baxter Equation
- Alexander Kleshchev (Eugene): RoCK blocks of symmetric groups and Hecke algebras
The workshop will take place in lecture hall NA 01/99.
There will be a joint dinner at Restaurant Amalfi at 19:00.
More info via the webpage of the workshop at
Complete reducibility, geometric invariant theory, and buildings
An international workshop in Bochum February 15 - 19, 2016
The workshop is intended to bring together experts in the field in connection with the notion of G-complete reducibility. We aim to concentrate on recent advances by means of geometric invariant theory, cohomology, and the theory of buildings.
Hyperplane Arrangements and Reflection Groups
An international workshop in Hannover August 10 - 12, 2015
The intention of this workshop is to provide a forum on new developments in the theory of hyperplane and in particular reflection arrangements. The contributions by international leading experts will concentrate on geometric, combinatorial and computational aspects.
New perspectives in hyperplane and reflection arrangements
on Monday, February 10, 2014
The intention of this workshop is to provide a forum on new developments in the theory of hyperplane and reflection arrangements. The contributions by international leading experts will concentrate on geometric, combinatorial and computational aspects.
