Archiv

## 2017

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Prof. Dr. Markus Reineke, RUB

Montag, den 13.11.2017, 14:15 in NA 2/24

Titel: Trägergarben für lineare Entartungen von Fahnenmanigfaltigkeiten

Abstract: In gemeinsamer Arbeit mit G. Cerulli Irelli, X. Fang, E. Feigin und G. Fourier wurde eine flache Familie so genannter linearer Entartungen von Fahnenmannigfaltigkeiten konstruiert. Im Vortrag wird das Verhalten der Kohomologie dieser Räume mittels des Konzepts der Trägergarben untersucht.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Jun.-Prof. Dr. Deniz Kus, RUB

Donnerstag, den 06.11.2017, 14:15 in NA 2/24

Titel: "Lattice path enumeration in representation theory"

Abstract: "Counting lattice paths is a classical topic in combinatorics which has applications in many fields of mathematics, as they encode various combinatorial objects and their properties. In this talk we will explain the connection to the representation theory of affine Lie algebras, ecpecially the relationship to maximal indecomposable highest weight modules. We introduce the notion of Demazure flags (a more general version of Jordan-Hölder series) and determine the graded multiplicities in these flags. It turns out that a suitable combinatorial model is given by certain lattice paths. "

### Vortrag im Oberseminar Arrangements

Vortragender: Prof. Dr. Michael Cuntz (Hannover)

Donnerstag, den 12.10.2017, 14:15 in NA 2/64

Titel: "Frieze patterns over subsets of the complex numbers"

Zusammenfassung: "Frieze patterns were introduced by Conway and Coxeter as certain arrays of positive integers with a condition on subdeterminants. They are closely related to cluster algebras, since every such pattern may be viewed as a specialization of cluster variables in type A, and they are in bijection with triangulations of a convex polygon by non-intersecting diagonals. Generalizing classical friezes leads to many interesting observations. In this talk, we consider frieze patterns with entries in an arbitrary ring. In this general setting, the combinatorics seem to get very complicated. However, for instance certain rings of integers produce new rules and transformations, as well as recursive constructions. This is a joint work with Thorsten Holm. "

### Vortrag im Oberseminar Lie-Theorie

Montag, den 25.09.2017, 14:15 in NA 2/64

Titel: "Complete Reducibility: The Good, the Bad and the Ugly"

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Melvin Dauter, RUB

Montag, den 24.07.2017, 14:15 in NA 2/64

Titel: " Beispiele und Anwendungen reduktive Paare bei linearen algebraischen Gruppen "

Zusammenfassung: "Reduktive Paare (G,H) linearer algebraischer Gruppen können verwendet werden, um gewisse Eigenschaften einer algebraischen Gruppe G auf die Untergruppe H zu übertragen. Wir werden sehen, wie Richardson den Begriff benutzt, um zu zeigen, dass eine halbeinfache Gruppe G in guter Charakteristik nur endlich viele unipotente Konjugationsklassen besitzt. Als weitere Anwendung werden wir G-vollständige Zerlegbarkeit untersuchen. Dabei werden wir auch kurz auf Fragen hinsichtlich der Existenz reduktiverPaare eingehen."

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Professor Dr. Gerhard Röhrle, RUB

Montag, den 17.07.2017, 14:15 in NA 2/64

Title: " Freeness of multi-reflection arrangements for complex reflection groups "

Abstract: "In 2002, Terao showed that every reflection multi-arrangement of a real reflection group with constant multiplicity is free. In this overview on joint work with T. Hoge, T. Mano, and C. Stump, we first generalize Terao's result to multi-arrangements stemming from well-generated unitary reflection groups, where the multiplicity of a hyperplane depends on the order of its stabilizer. Here the exponents depend on the exponents of the dual reflection representation. In a second step we extend our results further to all imprimitive irreducible unitary reflection groups (the bulk of which are not well-generated!). In this case the exponents turn out to depend on the exponents of a certain Galois twist of the dual reflection representation that comes from a Beynon-Lusztig type semi-palindromicity of the fake degrees. I shall try to explain our result in detail and outline how we generalized Yoshinaga's approach to Terao's result for Coxeter groups mentioned above making use of recent developments of flat systems of invariants due to Kato, Mano and Sekiguchi."

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Professor Graham Denham (University of Western Ontario, Kanada)

Montag, den 26.06.2017, 14:15 in NA 2/64

Title: "Critical points, matroids, and log-concave sequences"

Abstract: "It is well-known that complex hyperplane arrangements can be conveniently resolved to normal crossing divisors with the help of the permutohedral toric variety. The cohomology algebras of the resulting wonderful compactifications are not only matroid invariants, but Adiprasito, Huh and Katz (2015) found that Hodge-theoretic constraints imposed on them by complex geometry persist for arbitrary matroids. The maximal likelihood variety of a complex arrangement captures the set of critical points of all rational functions with poles and zeros on the arrangement. Its bidegree (as a biprojective variety) encodes a combinatorially significant sequence of integers, the h-vector of the broken circuit complex. I will describe work in progress with Federico Ardila and June Huh in which we construct a combinatorial analogue of the maximal likelihood variety for arbitrary (nonrealizable) matroids. In particular, this leads to a proof that the h-vector of the broken circuit complex is a log-concave sequence. "

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Dr. Tomohiro Uchiyama (National Taiwan University, National Center for Theoretical Sciences)

Montag, den 19.06.2017, 16:45 in NA 2/64

Title: "Complete reducibility, geometric invariant theory, and spherical buildings"

Abstract: "In this talk, I will talk about Serre's notion of complete reducibility for subgroups of reductive algebraic groups (matrix groups). Serre's notion of complete reducibility nicely generalizes completely reducible representations and it is useful to study the subgroup structure of reductive groups in positive characteristic. I will explain how to use geometric invariant theory (a branch of algebraic geometry) and Tits' spherical buildings (highly symmetrical combinatorial objects) to study complete reducibility. The recently proved 50-years-old center conjecture of Tits in spherical buildings comes into play. No background in algebraic groups or algebraic geometryis necessary."

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Prof. Gleb Koshevoy, Russian Academy of Sciences, Moskau

Montag, den 22.05.2017, 14 ct in NA 2/64

Title: "Combinatorics of crystals and Toda systems"

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Dr. Wassilij Gnedin, RUB

Montag, den 15.05.2017, 14:00 in NA 2/64

Title: "Tame categories of Harish-Chandra modules"

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Professor Masahiko Yoshinaga, Hokkaido University, Sapporo

Montag, den 08.05.2017, 14:00 in NA 2/64

Title: "The characteristic polynomial of Linial arrangement"

Abstract:
The (m-th extended) Linial arrangement is a certain finite truncation of affine Weyl arrangement associated to a root system. Postnikov and Stanley (2000) conjectured that the roots of the characteristic polynomial of Linial arrangement have the same real part. We will report that the application of Ehrhart theory and Eulerian polynomials enables us to make progress on the conjecture. This talk is based on the following two preprints.

https://arxiv.org/abs/1501.04955

https://arxiv.org/abs/1610.07841

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Dr. Ulrich Thiel, Universität Stuttgart

Mittwoch, den 08.03.2017, 16:00 in NA 2/64

Title: "Hyperplane arrangements associated to symplectic quotient singularities"

Abstract: To any symplectic reflection group there is an associated symplectic singularity. Namikawa constructed a hyperplane arrangement encoding certain geometric information of this singularity. In the special case of the symplectic reflection group defined by an ordinary complex reflection group we show that this hyperplane arrangement has a much more accessible representation-theoretic description via blocks of restricted rational Cherednik algebras, namely it equals the so-called Calogero-Moser locus which is quite interesting by itself. This result allows us on the one hand to explicitly compute Namikawa's geometrically defined hyperplane arrangement in many cases (in particular for many exceptional groups) and on the other hand it implies several, so far unknown, general properties of the Calogero-Moser locus. It is an interesting question whether properties of these hyperplane arrangements encode any further information and if they yield some new examples of hyperplane arrangements. This is joint work with G. Bellamy and T. Schedler.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Falk Bannuscher, RUB

Montag, den 23.01.2017, 16:00 in NA 2/64

Title: "Konjugationsklassen halbeinfacher algebraischer Gruppen und Lie Algebren"

Abstract:In der Gruppe der invertierbaren Matrizen, über einem algebraisch abgeschlossenen Körper, gibt es nur endlich viele Konjugationsklassen unipotenter Matrizen. Im Vortrag befassen wir uns damit, inwieweit sich dieses Resultat auf Untergruppen verallgemeinern lässt. Mit Hilfe von reduktiven Paaren werden wir diese Frage partiell für halbeinfache algebraische Gruppen beantworten.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Lukas Kühne, Universität Bonn

Montag, den 16.01.2017, 14:00 in NA 2/24

Title: Heavy hyperplanes in multiarrangements and their freeness

Abstract: One of the central topics among the theory of hyperplane arrangements is their freeness. Terao's conjecture tries to link the freeness with the combinatorics of an arrangement. One of the few categories of arrangements which satisfy this conjecture consists of 3-dimensional arrangements with an unbalanced Ziegler restriction. This means that the arrangement contains a lot of hyperplanes intersecting in one single line In this talk, we generalize this result to arbitrary dimensional arrangements in terms of flags by introducing unbalanced multiarrangements. For that purpose, we generalize several freeness criteria for simple arrangements, including Yoshinaga's freeness criterion, to unbalanced multiarrangements. This is joint work with Takuro Abe.

## 2016

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Dr. Xin Fang, Universität Köln

Montag, den 19.12.2016, 14:00 in NA 2/24

Title: "Toric degenerations of flag varieties and applications"

Abstract: In this talk I will explain a general framework to construct toric degenerations of flag varieties via birational sequences and Newton-Okounkov bodies. If time permits, I plan to apply these constructions to determine the Gromov widths of coadjoint orbits.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Dr. Christian Stump, Freie Universität Berlin

Montag, den 12.12.2016, 14:00 in NA 2/24

Title: "What are Coxeter elements in reflection groups?"

Abstract: In this talk, I aim to provide a conceptual reason why any two reflections in the symmetry group of a regular pentagon form a Coxeter system. I will do so by providing a conceptual definition of Coxeter elements in finite (well-generated) reflection groups. The main ingredient is to study properties of the Galois group of the field of definition. This is joint work with Vic Reiner and Vivien Ripoll.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Prof. Dr. Eamonn O'Brien, University of Auckland

Montag, den 05.12.2016, 14:00 in NA 2/24

Title: "Effective algorithms for matrix groups"

Abstract: How can we compute effectively with a matrix group whose entries lie in a finite field? We identify some inherent challenges, and outline a practical model which exploits randomness, geometry and detailed knowledge of the group structure.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Dr. Alistair Litterick, Universität Bielefeld

Montag, den 28.11.2016, 14:00 in NA 2/24

Title: "Subgroup Structure of Reductive Groups"

Abstract: A long-standing program seeks to understand the subgroup structure of reductive groups over algebraically closed fields. This program began in earnest with Dynkin in the 1950s, and continues to this day through work of Liebeck, Seitz, Saxl, Stewart, Testerman, Thomas, myself, and numerous others besides. We will discuss this ongoing effort, with a focus on reductive subgroups of exceptional simple algebraic groups and the notion of G-complete reducibility due to Serre, which provides a link with representation theory and streamlines the study of subgroup structure.

### 2 Vorträge im Oberseminar Lie-Theorie

Montag, den 21.11.2016, 14:00 in NA 2/24

Vortrag 1, 14 ct
Vortragende: Dr. Angela Carnevale, Universität Bielefeld

Title: "Orbit Dirichlet series and multiset permutations"

Abstract: We study Dirichlet series enumerating orbits of products of maps whose orbit distributions are modelled on the distributions of finite index subgroups of free abelian groups. We interpret Euler factors of such Dirichlet series in terms of generating polynomials for statistics on multiset permutations. As applications, we establish local functional equations, determine the (global)abscissae of convergence and exhibit natural boundaries. This is joint work with Christopher Voll.

Vortrag 2, 15 ct
Vortragender: Prof. Dr. Christopher Voll, Universität Bielefeld

Title: "Submodule zeta functions -- polynomiality and nonnegativity"

Abstract: Given a free module M of finite rank over the ring of integers of a number field K, together with a set A of linear operators on M, the associated submodule zeta function enumerates A-invariant submodules of M of finite additive index. Given, in addition, a grading on M, the associated graded submodule zeta function enumerates submodules which are homogeneous with respect to the grading. Submodule zeta functions -- graded or otherwise -- satisfy natural Euler product decompositions: the respective factors are rational functions, indexed by the finite places of K. We discuss a number of results illustrating what seem to be quite general polynomiality and nonnegativity properties satisfied by the coefficients of these rational functions. Some of them are due to Rossmann, whilst others are the outcome of joint work with Lee.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Arik Wilbert, Universität Bonn

Montag, den 14.11.2016, 14:00 in NA 2/24

Title: "Two-row Springer fibers in types C & D: Topology, Representation Theory & Combinatorics "

Abstract: tba

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Dr. Hans Franzen, RUB

Montag, den 07.11.2016, 14:00 in NA 2/24

Title: "The value of the Kac polynomial at I"

Abstract: We establish a formula for the value of the Kac polynomial at one in terms of Kac polynomials, evaluated at one, of the universal (abelian) covering quiver by applying torus localization methods to quiver varieties introduced by Hausel--Letellier--Rodriguez-Villegas.

### Eighteenth NWDR Workshop Ruhr-Universität Bochum

On Friday, 22 July 2016, 11:00 - 18:00

Speakers:

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.

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### Vortrag im Oberseminar Lie-Theorie

Montag, den 04.07.2016, 14:00 in NA 2/64

Title: "The Varchenko Determinant of a Coxeter Arrangement"

Abstract: The Varchenko determinant is a matrix determinant defined on hyperplane arrangements. The formula of this determinant is very beautiful, only it is impossible to compute it from a certain level of complexity. Precisely at this point, we provide an explicit formula of this determinant for the Coxeter arrangements. From this explicit one, the Varchenko determinant associated to any finite Coxeter group becomes computable. This a joint work with Goetz Pfeiffer.

### "Research Explorer Ruhr"

We are delighted to announce that the application of Dr. Hery Randriamaro (Antananarivo) within the Research Explorer Ruhr programme of the RUB Research School have been successful. The researcher will be visiting the Lehrstuhl in the period July 3 - 16. 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.

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### Vortrag im Oberseminar Lie-Theorie

Vortragender: Prof. Dr. Gerhard Roehrle, RUB

Montag, den 27.06.2016, 14:00 in NA 2/64

Title: "Serre's notion of complete reducibility and GIT"

Abstract: In the talk we outline Serre's notion of G-complete reducibility for subgroups of the reductive group G and show how methods from geometric invartiant theory can be employed to study this notion and to shed some light on the geometric nature of this concept.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Mikaël Cavallin, Technische Universität Kaiserslautern

Montag, den 20.06.2016, 14:00 in NA 2/64

Title: "On the natural embedding of SO(V) in SL(V)"

Abstract: Let V be a finite-dimensional vector space over an algebraically closed field K having characteristic p greater than or equal to 0. In this talk, we show how the natural embedding of X=SO(V) in Y=SL(V) can be used in order to determine the structure of certain Weyl modules for X. In addition, we see how this question relates to the problem of determining irreducible KY-modules on which X acts with exactly two composition factors.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Dr. Giovanni Cerulli-Irelli, Universität Rom I

Montag, den 13.06.2016, 14:00 in NA 2/64

Title: "Quiver Grassmannians of Dynkin type"

Abstract: Quiver Grassmannians are projective varieties parametrizing subrepresentations of quiver representations. In case the quiver is an orientation of a simply laced Dynkin diagram, we call them of Dynkin type. In this introductory talk I will present some results concerning the geometry of those projective varieties, which are based on techniques developed in collaboration with M. Reineke and E. Feigin. In particular I will show that the generic quiver Grassmannians have positive Euler characteristic, confiriming a conjecture by S. Fomin and A. Zelevinsky.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Dr. Oliver Goodbourn, RUB

Montag, den 06.06.2016, 14:00 in NA 2/64

Title: "Reductive pairs from representations of algebraic groups"

Abstract: Reductive pairs are a class of nice embeddings of reductive algebraic groups. They have been used to salvage some good behaviour observed in characteristic 0 in the positive characteristic case, for instance in work of Bate, Herpel, Martin and Röhrle on G-complete reducibility, and in providing uniform proofs of otherwise technical results. I will discuss work into determining when we get reductive pairs arising from representations of an algebraic group, including complete pictures for simple and Weyl modules for SL_2 in arbitrary characteristic.

### Vortrag im Oberseminar Lie-Theorie

Vortragende: Dr. Magdalena Boos, RUB

Montag, den 30.05.2016, 14:00 in NA 2/64

Title: "Finiteness criteria for parabolic conjugation"

Abstract: Motivated by the study of commuting varieties we consider a parabolic upper-block subgroup P of $\mathrm{GL}_n(\mathhb{C})$ and study its conjugation-action on the variety of nilpotent matrices in Lie(P). The main question posed in this talk is "For which P does the mentioned action only admit a finite number of orbits?" In order to approach such finiteness criterion, we make use of methods from Representation Theory of finite-dimensional algebras, for example covering techniques and Delta-filtrations. The talk will give an overview of the current status of results and conjectures. (This is work in progress, joint with M. Bulois)

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Prof. Dr. Gerhard Röhrle, RUB

Montag, den 23.05.2016, 14:00 in NA 2/64

Title: "Cocharacter-closure and the rational Hilbert-Mumford Theorem"

Abstract: I shall introduce the notion of cocharacter-closure and will explain how this leads to a rational version of the celebrated Hilbert-Mumford Theorem from geometric invariant theory. We will illustrate with some examples how this concept differs from the usual Zariski-closure and discuss some applications. This reports on joint work with M. Bate, S. Herpel and B. Martin.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Prof. Dr. Markus Reineke, RUB

Montag, den 09.05.2016, 14:00 in NA 2/64

Title: "Linear degenerations of flag varieties"

Abstract: Linear degenerations of SL(n)-flag varieties are constructed by relaxing the containment condition for the subspaces in a flag. We will discuss characterizations of flatness, irreducibility, normality, and other geometric properties of the resulting degenerations, in terms of linear algebra data. The underlying methods, quiver Grassmannians and PBW degenerations of representations, will be introduced. This is a report on recent joint work with G. Cerulli Irelli, X. Fang, E. Feigin and G. Fourier.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Marcel Maslovaric, Georg-August-Universität Göttigen

Montag, den 25.04.2016, 14:00 in NA 2/64

Title: "Variation of Geometric Invariant Theory and Birational Geometry"

Abstract: Forming a quotient with respect to a group action on a variety via Geometric Invariant Theory depends on the choice of a stability parameter. The variation of this parameter, the birational geometry of the quotients and the line bundles on the quotients are closely related. In this talk we discover a class of quotients (producing so called Mori dream spaces) where this relation is fundamental. We will see that moduli of representations of a quiver belong to this class.

### Vortrag im Oberseminar Lie-Theorie

Vortragender: Prof. Dr. Meinolf Geck, Universität Stuttgart

Montag, den 18.04.2016, 14:00 in NA 2/64

Title: "A new construction of semisimple Lie algebras"

Abstract: We work out a remark of Lusztig which leads to a simplified construction of a semisimple Lie algebra from a root system.

### Wegweiser der modernen Mathematik

Einer der weltweit bedeutendsten Mathematiker des 20. Jahrhunderts nimmt in dieser Woche an einer internationalen Tagung an der RUB teil. Die wissenschaftlichen Arbeiten von Jean-Pierre Serre waren wegweisend für die moderne Mathematik.

weiterlesen

### 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.

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## 2015

### 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.

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## 2014

### 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.

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