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
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


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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



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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
Password: math


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
Password: math



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:
The double Burnside group $B(G, H)$ of two finite groups $G, H$ is the Grothendieck group of the category of finite $(G, H)$-bisets. Certain bisets encode relationships between the representation theories of $G$ and $H$. Bouc's biset category provides a framework for studying such relationships, it has finite groups as objects, and $B(G, H)$ as morphisms between $G$ and $H$, with composition induced by the tensor product of bisets. The endomorphism ring $B(G, G)$ is called the double Burnside ring of $G$. In contrast to the (ordinary) Burnside ring $B(G)$, the double Burnside ring $B(G, G)$ of a nontrivial group $G$ is not commutative. In general, little more is known about the structure of $B(G, G)$. In the talk I'll describe a relatively small faithful matrix representation of the rational double Burnside algebra $\mathbb{Q}B(G,G)$ for certain finite groups $G, based on a recent decomposition of the table of marks of the direct product $G \times G$, exhibiting the cellular structure of the algebra $\mathbb{Q}B(G, G)$. This is joint work with Sejong Park.



Vortrag im Oberseminar Lie-Theorie

Montag, den 08.07.19 um 14 ct in IA 1/53

Vortragender: Professor Dr. Mohamed Barakat (Universität Siegen)

Titel: "Chevalley’s Theorem on constructible images made constructive "

Abstract:
Chevalley proved that the image of an algebraic morphism between algebraic varieties is a constructible set. Examples are orbits of algebraic group actions. A constructible set in a topological space is a finite union of locally closed sets and a locally closed set is the difference of two closed subsets. Simple examples show that even if the source and target of the morphism are affine varieties the image may neither be affine nor quasi-affine. In this talk I will present an Gröbner-basis-based algorithm which computes the constructible image of a morphism of affine spaces, along with applications to Terao’s freeness conjecture.



Vortrag im Oberseminar Arrangements

Vortragender: Dr. Paul Mücksch (RUB)

Montag, den 29.04.2019, 14:15 in IA 1/53

Titel: "MAT-freie Spiegelungsarrangements"

Zusammenfassung:
Die algebraische Eigenschaft der Freiheit eines Hyperebenenarrangements mit seiner Kombinatorik zu verbinden ist ein wichtiges Problem in der Theorie der Hyperebenenarrangements. Hinreichende kombinatorische Bedingungen liefert Terao's Addition-Deletion Theorem. Dies motiviert die Klasse der induktiv freien Arrangements.

Motiviert durch das Multiple Addition Theorem (kurz MAT) von Abe, Barakat, Cuntz, Hoge und Terao werde ich die neue Klasse der MAT-freien Arrangements einführen. Erst kürzlich konnten Abe und Terao eine Verallgemeinerung des MAT, das Multiple Addition Theorem 2 (MAT2) zeigen. Mit Hilfe des MAT2 lässt sich wiederum die Klasse der MAT2-freien Arrangements definieren.

In meinem Vortrag werde ich eine Klassifikation aller Spiegelungsarrangements, die diesen neuen Freiheitsbegriffen genügen, vorstellen.

Außerdem möchte ich Beziehungen zu bekannten Freiheitsklassen kommentieren und damit verbundene Probleme vorstellen. Dies ist eine gemeinsame Arbeit mit Michael Cuntz (Hannover).



2018

Vortrag im Oberseminar Lie-Theorie

Dienstag, den 18.12.18 um 14 ct in IA 1/135

Vortragende: Prof. Dr. Cheryl Praeger (Perth, Australia)

Titel: "Finding involution centralisers efficiently in classical groups of odd characteristic"

Abstract:
Bray's involution centraliser algorithm plays a key role in recognition algorithms for classical groups over finite fields of odd order. It has always performed faster than the time guaranteed/justified by complexity analyses. Work of Dixon, Seress and I published this year gives a satisfactory analysis for SL(n,q). And we are slowly making progress with the other classical groups. The "we" are Colva Roney-Dougal, Stephen Glasby and me - and we have conquered the unitary groups so far.



Vortrag im Oberseminar Arrangements

Dienstag, den 11.12.18 um 14 ct in IB 1/103

Vortragender: Prof. Dr. Michael Cuntz (Hannover)

Titel: "Klassifikation der Weyl-Gruppoide"

Abstract:
Die Klassifikation der endlichen Weyl-Gruppoide (das sind gewisse simpliziale Arrangements in einem Gitter) beruht auf Rechnungen mit dem Computer. In diesem Vortrag möchte ich über Fortschritte berichten, die zu einem kürzeren Beweis führen. Die neuen Techniken können ferner zur Klassifikation größerer Klassen von Arrangements verwendet werden.



Vortrag im Oberseminar Lie-Theorie

Dienstag, den 13.11.18, von 14 - 16 Uhr, IA 01/131

Vortragender: Professor Dmitriy Rumynin, University of Warwick, UK

Titel: "Kac-Moody Groups: representations, localisation, duality"

Abstract:
We will look at representation theory of a complete Kac-Moody group G over a finite field. G is a locally compact totally disconnected group, similar, yet slightly different to the group of points of a reductive group scheme over a local field. After defining the group we discuss localisation of its category of smooth representations. We also discuss homological duality for this category.



Vortrag im Oberseminar Lie-Theorie

Dienstag, den 09.10.18, von 14 - 16 Uhr in der Wasserstraße 221, Raum 4/20

Vortragender: Prof. Dr. J. M. Douglass (NSF, Washington, DC, USA)

Titel: " A factorization of the T-equivariant K-theory of flag varieties"

Abstract:
Let G be a reductive, complex, algebraic group, B a Borel subgroup, T is a maximal torus in B, and P is a parabolic subgroup containing B. Then G/B is the "flag variety" of G and the projection from G/B to G/P is a G-equivariant fibre bundle with fibre P/B. As smooth varieties, G/B is locally isomorphic to the product G/P x P/B. The quotient P/B may be canonically identified with the flag variety of the Levi subgroup of P containing T and the "factorization" G/B = G/P x P/B may be viewed as a geometric incarnation of the factorization W = W^P x W_P, where W is the Weyl group of (G,T), W_P is the Weyl group of (P,T), and W^P is a set of left coset representatives of W_P in W. In this talk I will describe a factorization of the T-equivariant K-theory of G/B as a tensor product of the T-equivariant K-theory of G/P and the T-equivariant K-theory of P/B. The factorization theorem can be described in terms that make sense for any generalized cohomology/homology theory and the factorization in equivariant K-theory leads immediately to a uniform, geometric construction of corresponding factorizations in K-theory, equivariant cohomology, and ordinary cohomology.



Vortrag im Oberseminar Arrangements

Donnerstag, den 26.7.18 von 14 - 16 Uhr in der Wasserstraße 221 Raum 4/20

Vortragender: Dr. Paul Mücksch (RUB)

Titel: "New characterizations of freeness of hyperplane arrangements"

Abstract:
New characterizations of freeness of hyperplane arrangements This talk is a report on recent work by Anna Maria Bigatti, Elisa Palezzato, and Michele Torielli. In their article (arXiv:1801.09868) the authors investigate two commutative al- gebraic invariants of a hyperplane arrangement. They are the generic initial ideal and the sectional matrix of the Jacobian ideal of the arrangement. Starting from a classic characterization of freeness by Terao they derive charac- terizations in terms of the generic initial ideal and the sectional matrix. Further- more, under the assumption that the arrangement in question is free, the generic initial ideal is completely determined by the exponents of the arrangement and vice versa. Nonetheless, thinking of Teraos conjecture, there are non-free lattice equivalent arrangements having different generic initial ideals.



Vortrag im Oberseminar Arrangements

Montag, den 18.06.2018, 16:15 in NA 2/64

Vortragender: Prof Alexander Varchenko (University of North Carolina at Chapel Hill, zzt. MPI Bonn)

Title: Critical points of master functions and integrable hierarchies

Abstract: Critical points of master functions are non-isolated and come in "populations". I will discuss how the populations are related to integrable hierarchies and to representations of the affine Lie algebras.



Vortrag im Oberseminar Lie-Theorie

Montag, den 18.06.2018, 14:15 in NA 2/64

Vortragender: Christof Geiss (zzt. Universität Bonn)

Title: "Crystal graphs and semicanonical functions for symmetrizable Cartan matrices"

Abstract: In joint work with B. Leclerc and J. Schröer we propose a 1-Gorenstein algebra H, defined over an arbitrary field K, associated to the datum of a symmetrizable Cartan Matrix C, a symmetrizer D of C and an orientation $\Omega$. The H-modules of finite projective dimension behave in many aspects like the modules over a hereditary algebra, and we can associate to H a generalized preprojective algebra $\Pi$. If we look, for K algebraically closed, at the varieties of representations of $\Pi$ which admit a filtration by generalized simples, we find that the components of maximal dimension provide a realization of the crystal $B_C(-\infty)$. For K being the complex numbers we can construct, following ideas of Lusztig, an algebra of constructible functions which contains a family of "semicanonical functions", which are naturally parametrized by the above mentioned components of maximal dimensions. Modulo a conjecture about the support of the functions in the "Serre ideal" those functions would yield a semicanonical basis of the enveloping algebra U(n) of the positive part of the Kac-Moody Lie algebra g(C).



Vortrag im Oberseminar Lie-Theorie

Montag, den 23.04.2018, 14:15 in NA 2/64

Vortragender: Daniel Kalmbach, Universität zu Köln

Title: A Linear formula for the Schützenberger involution

Abstract: "The Schützenberger involution is a piecewise-linear function which was originally defined on Young tableaux. Its generalization to semi-standard Young-tableaux can be equivalently described by the action of the Bender-Knuth involutive operators translated into the language of Gelfand-Tsetlin patterns. A different approach is to define an automorphism on the generators of the quantum enveloping algebra U(g), which under a suitable parametrization of Lusztig’s basis in U(g) by Gelfand-Tsetlin patterns, acts as the Schützenberger involution. This was done by A. Berenstein and A. Zelevinsky. We show that by a good choice of parametrization of the canonical basis, we can give an explicit linear formula for the Schützenberger involution."



2 Vorträge im Oberseminar Arrangements

Montag, den 22.1.18, 14:15 Uhr, Wasserstrasse 221, Raum 4/20

Vortragender: Prof. Daniel C. Cohen (Louisiana State University, Baton Rouge, LA, USA)

Title: Pure braid groups and direct products of free groups

Abstract:
I'll discuss some properties and invariants of fundamental groups of complements of arrangements, largely in the context of the above classes. By the end of the talk, I should be able to pose a question we might discuss during the week.

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Mittwoch, den 24.1.18, 14:15 Uhr, Wasserstrasse 221, Raum 4/20

Vortragender: Prof. Daniel C. Cohen (Louisiana State University, Baton Rouge, LA, USA)

Title: Topological complexity of surfaces and their configuration spaces

Abstract:
Topological complexity is a numerical homotopy-type invariant introduced by M. Farber about 15 years ago, motivated by the motion planning problem from robotics. For a given space, this invariant provides a measure of the complexity of navigation in the space. Computing this invariant is sometimes easy, sometimes hard. I'll attempt to illustrate this, with surfaces and their configuration spaces.



Vortrag im Oberseminar Lie-Theorie

Montag, den 08.01.2018, 14:15 in NA 2/24

Vortragender: Balazs Elek, Cornell University

Title: Kirillov-Reshetikhin crystals and the Cactus group

Abstract: tba



2017

2 Vorträge im Oberseminar Lie-Theorie

Dienstag, den 05.12.2017, 14:15 in NA 1/58

Vortragender: Prof Benjamin Martin (University of Aberdeen)

Title: Generic stabilisers of actions of reductive groups

Abstract:
Actions of a topological or algebraic group G on a manifold or variety V play an important part in geometry. A fundamental problem is to understand the behaviour of the stabilisers G_v for v in V. Typically one finds that for generic v in V, the stabilisers are closely related - for instance, they are all conjugate or are all isomorphic to each other. If G is a linear algebraic group over a field k of characteristic p>0, however, then we can have more complicated behaviour. To understand what is going on, the notion of G-complete reducibility turns out to be very helpful. I will discuss work of Richardson in characteristic zero and some more recent work in positive characteristic.

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um 15:45 in NA 1/58

Vortragender: Dr Michael Bate (University of York)

Title: Orbit closures and Invariants

Abstract:
Following Ben's talk, I'll also talk about some work which aims to find the correct formulation in positive characteristic of classical results about algebraic groups and invariants in characteristic zero. I'll concentrate on a result of Luna from the 1970s which rests in part on his celebrated "Etale Slice Theorem". The Slice Theorem fails in positive characteristic, but we can still do something using the notion of G-complete reducibility. I'll focus on illustrative examples to motivate the results and to give an idea of the techniques used in the proof. This is joint work with Harry Geranios and Ben Martin.



Vortrag im Oberseminar Lie-Theorie

Vortragender: Dr. Gwyn Bellamy, University Glasgow

Freitag, den 01.12.2017, 14:15 in NA 3/24

Titel: Symplectic resolutions of quotient singularities

Abstract:
In this talk I will describe progress on a program, joint with Schedler, to classify those symplectic quotient singularities that admit symplectic resolutions I will explain how one can use the representation theory of symplectic reflection algebras in order to do this. I will also explain how one can use these algebras, combined with general theory developed by Namikawa, to compute the nef and movable cones of the minimal models of these quotient singularities. As a consequence, one can explicitly count the number of minimal models. Finally, I will describe a number of interesting problems in the field that are still open.



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

Vortragender: Dr. Adam Thomas (Bristol)

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."



Visiting International Professor Fellowship

Topicbild

Professor Benjamin Martin from the University of Aberdeen has been awarded a VIP Professorship by the RUB-Research School.

Professor Martin is one of the worlds experts in algebraic groups, representation varieties and representation growth,and related fields such as representation theory and the theory of buildings. More specifically, he is a world leader in the theory of complete reducibility for algebraic groups and geometric invariant theory associated with the action of reductive groups on affine varieties.

Over the course of the next two years he will be visting the department of mathematics and will contribute to the postgraduate education within the chair of Professor G. Röhrle

For the RUB-Research school and the VIP-Programme, see also here

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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."



"Research Explorer Ruhr"

Topicbild

We are delighted to announce that the application of Dr. Tomohiro Uchiyama (National Taiwan University, National Center for Theoretical Sciences) within the Research Explorer Ruhr programme of the RUB Research School have been successful. The researcher will be visiting the Lehrstuhl in the period June 19 - 30. 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. 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

Topicbild

Tilman Möller, Gerhard Röhrle

Bei der Akademischen Jahresfeier 2016 wurde Herr Tilman Möller mit dem RUB-Preis für seine Masterarbeit "Induktiv faktorisierte Arrangements und deren Abgeschlossenheit unter Lokalisierung" ausgezeichnet.


weiterlesen


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:

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

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Vortrag im Oberseminar Lie-Theorie

Vortragender: Dr. Hery Randriamaro, Universität Antananarivo, Madagaskar

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"

Topicbild

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.



DFG-Grant awarded to Professor Röhrle

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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.

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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

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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.


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Complete reducibility, geometric invariant theory, and buildings

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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

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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

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.





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New perspectives in hyperplane and reflection arrangements

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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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