## 2021

### 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

### 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

### 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

weiterlesen

## 2020

### Vortrag im Oberseminar Arrangements and Symmetries

Vortrag am Montag, 21.12.2020, 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

weiterlesen

### Vortrag im Oberseminar Lie Theorie

Vortrag am Montag, 14.12.2020, 14:15 Uhr via zoom

Vortragender: Prof. Alexander Premet (University of Manchester)

Titel: "Modular representations of Lie algebras and Humphreys' conjecture"

Abstract:
Infoblatt

Zugangsdaten

https://ruhr-uni-bochum.zoom.us/j/99572000333?pwd=QlhGZDZtQmR5dGRqeVJCOFpuSGVnZz09
Meeting ID: 995 7200 0333

weiterlesen

### Vortrag im Oberseminar Arrangements and Symmetries

Vortrag am Montag, 14.12.2020, 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

weiterlesen

### Vortrag im Oberseminar Lie Theorie

Vortrag am Montag, 07.12.2020, 14:00 Uhr via zoom

Vortragender: Assistant Professor Jethro van Ekeren (Universidade Federal Fluminense (UFF))

Titel: "Singular support of the Ising model and a new modular Nahm sum"

Abstract: (joint work with G. E. Andrews and R. Heluani) As part of an ongoing project to understand chiral homology of elliptic curves with coefficients in a vertex algebra V, we are led to study the associated graded algebra of V with respect to its Li filtration. The spectrum of this algebra is known as the singular support of V. For boundary Virasoro minimal models, i.e., those of type (2, p), p odd, the singular support is known to be isomorphic to an arc space. For the Ising model this is already not the case, and we show that its singular support is instead a ''differential hypersurface'' in an arc space, that is, it is defined by the vanishing of a single differential polynomial and all its derivatives. We obtain this result as a corollary of a new q-series identity of Rogers-Ramanujan type, which at the same time yields a new example of a modular Nahm sum.

Zugangsdaten

https://ruhr-uni-bochum.zoom.us/j/99572000333?pwd=QlhGZDZtQmR5dGRqeVJCOFpuSGVnZz09
Meeting ID: 995 7200 0333

### Vortrag im Oberseminar Arrangements and Symmetries

Montag, 7. Dezember 2020, 16:15-17:45

René Marczinzik, Universität Stuttgart

Distributive lattices and Auslander regular algebras

Abstract: We show that the incidence algebra of a finite lattice L is Auslander regular if and only if L is distributive. As an application we show that the order dimension of L coincides with the global dimension of its incidence algebra when L has at least two elements and we give a categorification of the rowmotion bijection for distributive lattices. At the end we discuss the Auslander regular property for other objects coming from combinatorics. This is joint work with Osamu Iyama.

### Vortrag im Oberseminar Arrangements and Symmetries

Vortrag am Montag, 30. November 2020, 16:15-17:30, via Zoom

Vortragender: Lukas Kühne (Max-Planck-Institut Leipzig)

Titel: "The Resonance Arrangement"

Abstract: The resonance arrangement is the arrangement of hyperplanes which has all nonzero 0/1-vectors in R^n as normal vectors. It is also called the all-subsets arrangement. Its chambers appear in algebraic geometry, in mathematical physics and as maximal unbalanced families in economics.

In this talk, I will present a universality result of the resonance arrangement. Subsequently, I will report on partial progress on counting its chambers. Along the way, I will review some of the combinatorics of general hyperplane arrangements. If time permits I will also touch upon the related threshold arrangement which encodes Boolean functions that are linearly separable.

Zugangsdaten

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

### Vortrag im Oberseminar Arrangements and Symmetries

Montag, 23. November 2020, 16:00-17:30, per Zoom

Theo Douvropoulos, University of Massachusetts Amherst

Recursions and proofs in Coxeter-Catalan combinatorics

Abstract: The noncrossing partition lattice NC(W) associated to a finite Coxeter group W has become a central object in Coxeter-Catalan combinatorics during the last 25 years. We focus on two recursions on the simple generators of W; the first due to Deligne (and rediscovered by Reading) determines the chain number of NC(W) and the second, more general, due to Fomin-Reading recovers the whole zeta polynomial. The resulting formulas have nice product structures and are key players in the field, but are still not well understood; in particular, they are derived by the (case-free) recursions separately for each type.
A uniform derivation of the formulas from these recursions requires proving certain identities between the Coxeter numbers and invariant degrees of a group and those of its parabolic subgroups. In joint work with Guillaume Chapuy, we use the W-Laplacian (for W of rank n, this is an associated nxn matrix that we introduced in earlier work and which generalizes the usual graph Laplacian) to prove the required identities for the chain number of W. We give a second proof by using the theory of multi-reflection arrangements and the local-to-global identities for their characteristic polynomials. This latter approach is in fact applicable to the study of the whole zeta polynomial of NC(W) although it, currently, falls short of giving a uniform derivation of Chapoton's formula for it.

### Vortrag im Oberseminar Arrangements and Symmetries

Vortrag am Montag, 16.11.2020, 16:15 Uhr, in HIA
zusätzlich online 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

### Vortrag im Oberseminar Arrangements and Symmetries

Vortrag am Montag, 09.11.2020, 16:15 Uhr, in HIA
zusätzlich online 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

### Vortrag im Oberseminar Lie Theorie

Vortrag am Montag, 02.11.2020, 14:15 Uhr, in HZO 70
zusätzlich online via zoom

Vortragender: Dr. Damian Sercombe (RUB)

Titel: "Maximal connected subgroups of maximal rank in reductive k-groups"

Abstract: Let k be any field. Let G be a connected reductive algebraic k-group. Associated to G is an invariant that is called the index of G. Tits showed that, up to k-anisotropy, the k-isogeny class of G is uniquely determined by its index. Moreover, for the cases where G is absolutely simple, Tits classified all possibilities for the index of G. Let H be a connected reductive k-subgroup of maximal rank in G. We introduce an invariant of the pair H

Zugangsdaten

https://ruhr-uni-bochum.zoom.us/j/94548565437?pwd=amM2VVRlcVZUME9JWHlCZnRTMnh3Zz09
Meeting-ID: 945 4856 5437
Passwort: 415419

### Vortrag im Oberseminar Arrangements and Symmetries

Vortrag am Montag, 02.11.2020, 16:15 Uhr, in HIB
zusätzlich online 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

### Vortrag im Oberseminar Arrangements and Symmetries

Online-Vortrag (Zoom) am Montag, 13.7.2020, 14:15 Uhr

Vortragender: Prof. Dr. Michael Cuntz (Leibniz Universität Hannover)

Titel: "A greedy algorithm to compute arrangements of lines"

Abstract:
We present a greedy algorithm optimizing arrangements of lines with respect to a property and apply this algorithm to the case of simpliciality. An implementation produces a database with many surprising examples.

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, 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

### Vortrag im Kolloquium Algebra, Geometrie und Kombinatorik

Mittwoch, den 29.01.20 um 16 st in IA 01/473

Vortragender: Prof. Dr. Eric Opdam (Universiteit van Amsterdam, NL)

Titel: "Square integrable hypergeometric functions for root systems"

Abstract:
Classifying the square integrable solutions of the system of hypergeometric equations for root systems is relevant to understanding the discrete series for real symmetric spaces. We will discuss this connection and explain some aspects of this classification.

### Vortrag im Oberseminar Lie-Theorie

Montag, den 13.01.20 um 14 ct in IA 1/135

Vortragender: Prof. Dr. Sergey Mozgovoy (Trinity College Dublin)

Titel: "Commuting matrices and Higman's conjecture"

Abstract: Higman's conjecture states that the number of conjugacy classes in the group of upper triangular matrices over F_q is polynomial in q. It can be also formulated as a problem of counting commuting upper triangular matrices over a finite field. I will introduce a generalisation of this problem in terms of quiver representations and prove relations between various counting invariants that arise. In particular, I will show that the original conjecture is equivalent to polynomial-count of certain absolutely indecomposable quiver representations.

## 2019

### Vortrag im Oberseminar Lie-Theorie

Montag, den 02.12.19 um 14 ct in IA 1/135

Vortragender: Dr. Gleb A. Koshevoy (CEMI, Russian Academy of Sciences, Moskau)

Titel: "Cubillages of ciclic zonotopes and higher Auslander-Reiten theory"

Abstract: Cubillages of cyclic zonotopes studied by Kapranov and Voevodskii in relations to higher Bruhat orders, Zamolodchikov equations, and polycategories. Combinatorics of two-dimensional cubillages related to quasi-commuting collections of qunatum determinants due to Leclerc and Zelevinsky, cluster algebras, and Auslander-Reiten theory . For an odd integer $r> 0$ and an integer $n > r$, we introduce a notion of weakly $r$-separated subsets of $[n] = \{1, 2, \ldots n\}$. When $r =1$, this corresponds to the concept of weak separation introduced and studied by Leclerc and Zelevinsky. We extend results due to Leclerc-Zelevinsky, and develop a geometric approach to combinatorics maximal weakly $r$-separated collections. From this we get a combinatorical view point to the higher Auslander-Reiten theory due to Iyama and higher cluster categoris due to Oppermann and Thomas. This is a joit work with V.Danilov and A.Karzanov

### Vortrag im Oberseminar Lie-Theorie

Montag, den 25.11.19 um 14 ct in IA 1/135

Vortragender: Dr. Jens Eberhardt (MPI, Bonn)

Titel: "Motives in Geometric Representation Theory"

Abstract:
Categories of representations arising in Lie theory can often be modeled geometrically in terms of constructible sheaves on certain spaces, as for example on the flag variety, affine Grassmannian or the nilpotent cone.
Recent developments in the theory of motives allow to consider so called "motivic sheaves", an algebro-geometric analogue of constructible sheaves. In this talk we will explain how one can practically work with motivic sheaves (using Grothendieck's six functor formalism) and apply them in representation theory. We will show how motivic sheaves can be used to model Category O associated to a reductive complex Lie algebra, modular Category O associated to a split reductive group over a finite field and categories of representations of convolution algebras, such as the graded affine Hecke algebra and KLR-algebras. We also will explain how more "exotic" versions of motivic sheaves provide exciting new opportunities in geometric representation theory.

### Vortrag im Oberseminar Lie-Theorie und Arrangements and Symmetries

Montag, den 18.11.19 um 14 ct in IA 1/135

Vortragender: Dr. Jenny August (MPI, Bonn)

Titel: "Contraction Algebras, Hyperplane Arrangements and K(pi,1)"

Abstract:
Contraction algebras are a class of finite dimensional algebras used to study minimal models in geometry. While they are very useful in this area, this talk will instead focus on their connection to simplicial hyperplane arrangements. I will explain how each contraction algebra has an associated hyperplane arrangement, which in special cases is an ADE root system, and further, I will describe how this arrangement controls all the homological information of the algebra. In particular, we show the space of stability conditions of the algebra is the universal cover of the complexified complement and thus, as this space is known to be contractible, we obtain a new homological proof of the K(pi,1) theorem for finite type ADE braid groups.

### Vortrag im Oberseminar Lie-Theorie

Montag, den 04.11.19 um 14 ct in IA 1/135

Vortragender: Professor Wim H. Hesselink (Bernoulli Institute, University of Groningen, NL)

Titel: "Nilpotent conjugacy classes for G2 and classical groups"

Abstract:
The Mumford-Kempf instability theory is sketched. It is applied to the Lie algebra of the group G2. The nullcone of G2 is shown to have five strata. If char(K) differs from 3, each of the strata is a single orbit. If char(K) = 3, one stratum splits into two orbits. The nullcone has singularities in the points of the nonregular orbits. Cross sections are used to prove this and to analyse the singularities. Are the singularities different in different orbits? The answer is yes, except for characteristic 2. A measure of singularity is introduced to prove this.

If time permits: Classical nilpotency in characteristic 2, revisiting a paper of 40 years ago. The paper covers 8 cases: the orthogonal case and the symplectic case, the group and the Lie algebra, chararacteristic 2 and different from 2. Conjugacy is translated into isomorphy between modules with forms over the ring of formal power series. A new way is presented to determine and distinguish the indecomposable form modules. An unconvincing proof about compositions of indecomposables must be repaired.

### Vortrag im Oberseminar Lie-Theorie

Montag, den 07.10.19 um 14 ct in IA 1/135

Vortragender: Dr. Travis Schedler (Imperial College, London)

Titel: "Symplectic resolutions of Hamiltonian reductions "

Abstract:
Given a symplectic representation of a reductive group, one considers the Hamiltonian reduction, in physics called “Higgs branch” varieties. This includes quiver and toric hyperkähler varieties. I will discuss the question of existence of symplectic resolutions of these, and how one might go about constructing them via geometric invariant theory. This is joint work with Gwyn Bellamy, and heavily uses work of Herbig, Schwarz, and Seaton.

### Vortrag im Oberseminar Lie-Theorie

Montag, den 08.07.19 um 16 ct in IA 1/181

Vortragender: Professor Dr. Götz Pfeiffer, National University of Ireland, Galway, EI

Titel: "Bisets and the Double Burnside Algebra of a Finite Group "

Abstract:

### 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.

### 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.

More

### 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.

More

## 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.

More

## 2014

### 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.

weiterlesen

### 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.

More