Guest Seminar Groups and Representations (AG Malle)

Summer Semester 2024

Organisers Jun.-Prof. Dr. Caroline LassueurProf. Dr. Gunter Malle

Room: 48-436

 

  • Thursday, 23rd of May 2024:
    • 17:00-17:50: Emmanuel Letellier [Université Paris Cité]
    • Title: Ennola duality for decomposition of tensor products
      Abstract: In this talk I will explain how to use geometry to understand the decomposition of tensor products of unipotent characters of finite general linear groups and finite unitary groups. 
       
  • Thursday, 6th of June 2024:
    • 17:00-17:50: Hong Yi Huang [University of Bristol]
    • Titel: Permutations, bases and low rank groups
      Abstract: Let G = GL(V), where V is a finite-dimensional vector space, and recall that any element in G is uniquely determined by its action on a basis for V. In addition, any two pairs of linearly independent vectors can be mapped to each other by an element of G. These two basic linear algebra properties can be interpreted in the language of permutation groups, which leads us naturally to the definitions of base and rank of a permutation group. In this talk, I will present some of my recent results on bases for primitive permutation groups, and I will report on recent progress with C.H. Li and Y.Z. Zhu towards a classification of the rank three groups.
       
  • Thursday, 13th of June 2024:
    • 17:00-17:50: Sam Miller [UC, Santa Cruz]
    • Titel: The classification of endotrivial complexes
      Abstract: Let G be a finite group and k a field with prime characteristic p. Endotrivial chain complexes are the invertible elements of the bounded homotopy category of p-permutation modules, $K^b({}_{kG}\mathbf{triv})$, a tensor-triangulated category which admits a quotient equivalent to $D^b({}_{kG}\mathbf{mod})$ by recent work of Balmer and Gallauer. These chain complexes connect to many other well-studied topics in modular representation theory, including (relatively) endotrivial modules, endo-p-permutation modules, splendid Rickard equivalences, and the trivial source ring. Moreover, the group $\mathcal{E}_k(G)$, which parameterizes indecomposable endotrivial complexes of $kG$-modules, can be endowed with rational p-biset functor structure. In this talk, I will highlight some of these connections and describe how we have obtained a complete classification of the endotrivial complexes.  
     
  • Tuesday, 2nd of July: Felix Klein Colloquium Talk by P.-E. Caprace
     
  • Thursday, 4th of July 2024:
    • 17:00-17:50: Tommaso Scognamiglio [Université Paris Cité]
    • Titel: Multiplicities for tensor product of representations of Gln(Fq)
      Abstract: The complex irreducible characters of Gln(Fq) have been known since the 50s, thank to Green's works, who gave a combinatorial description of them. Later, Lusztig and Srinivasan gave a geometric description of this character table, in terms of the Deligne-Lusztig induction.  However, not much is known in general about the decomposition of tensor products. I will present a result about the computation of multiplicities of semisimple split characters in tensor product of semisimple split characters of Gln(Fq).  I prove that these multiplicities are polynomial in q with non-negative integer coefficients and  obtain a criterion for their non-vanishing. I give moreover an interpretation of these polynomials in terms of the counting of the representations of star-shaped quivers, generalizing a previous result of Hausel, Letellier and Rodriguez-Villegas concerning multiplicities for tensor product of generic k-tuples of irreducible characers.

 

Frühere Semester

Organisers Jun.-Prof. Dr. Caroline LassueurProf. Dr. Gunter Malle
 

The seminar of the Winter Semester 2023/24 was essentially replaced by the meeting Representation Theory at the Villa Denis 2023

  • Friday,  6th of October
    • 09:30 - 10:15 Noelia Rizo: Minimal heights and defect groups with two character degrees
    • 10:20 - 10:50 Jonas Hetz: The values of unipotent characters at unipotent elements for groups of type E8
    • 11:20 - 12:00 Marie Roth: Character sheaves of the principal series restricted to a conjugacy class
    • 14:00 - 14:30: Sergio David Cia Luvecce: On a formula for the Lusztig induction over the unipotent representations of O_2^{\pm}(F_q)
    • 14:35 - 15:05 Laura Voggesberger: Maximal Subgroups of Connected Reductive Groups
    • 15:30 - 16:15 Jay Taylor: Real Elements in Finite Reductive Groups
  • Saturday,  7th of October
    • 09:30 - 10:15 Marc Cabanes: On the McKay Conjecture
    • 10:45 - 11:15 Linda Hoyer: Oddness of orthogonal determinants of even-dimensional Specht modules
    • 11:15 - 12:00 Eirini Chavli: The center of walled Brauer algebras

Organisers Jun.-Prof. Dr. Caroline LassueurProf. Dr. Gunter Malle

The talks take place in Room 48-436.
 

  • Thursday, 20th of April 2023:  No Seminar
     
  • Thursday, 27th of April 2023 
    • 17:00-17:50 :  Nadia Romero  [Universidad de GuanajuatoA semisimplicity criterion for Green biset functors, with one application
       
    • Abstract :  We will prove a criterion giving conditions for the category of modules over a Green biset functor to be semisimple. The criterion is not hard to prove and it is useful for applications. As an example, we will see that for any fields \(k\) and \(F\) of characteristic \(0\) and any finite group \(T\), the category of modules over the shifted Green biset functor \((kR_F)_T\) of \(F\)-linear representations, is semisimple. This is joint work with Serge Bouc.

     
  • Thursday, 4th of May 2023:
    • 17:00-17:50 :  Nicola Grittini [RPTU Kaiserslautern-Landau] Character degrees and characters values
       
    • Abstract: Character theory of finite groups is traditionally focused on the study of character degrees, since they are relatively easy to control and they can provide much information on group structure. The rest of the character table, on the other hand, is often overlooked, with few exceptions, as when rational-valued and real-valued characters are considered. Even in this case, however, one may ask if the characters having values in the fields \(\mathbb{Q}\) and \(\mathbb{R}\) are actually special, or if the theorems involving these characters are just special cases of some more general properties.
      In recent years, a more systematic research on character fields of values has begun, possibly as a consequence of the study on the so-called Galois-McKay conjecture. We will see some of the problems and recent results concerning characters (fields of) values, and we will talk about why they can be interesting and how they interact with known results on rational and real-valued characters.
     
  • Thursday, 11th of May 2023:
    • 17:00-17:50 :Andrew P. Turner [University of Pennsylvania (UPENN)] F-Theory and Singular Elliptic Fibrations
       
    • Abstract : I will discuss a powerful geometric approach to string theory called F-theory, and its mathematical foundations. The primary objects of interest are singular elliptically fibered Calabi–Yau manifolds and their resolutions. I will introduce and discuss elliptic fibrations, as well as various associated quantities and techniques we are interested in, and will briefly allude to their physical significance. This talk is associated with an ongoing effort with Martin Bies and many others in the OSCAR community to create a system of tools within OSCAR for doing F-theory computations.
     
  • Thursday, 18th of May 2023: No Seminar (Christi Himmelfahrt)
     
  • Thursday, 25th of May 2023:
    • 17:00-17:50 : Jérémie Guilhot [Université de Tours] Recognising Kazhdan-Lusztig cells using representations
       
    • Abstract : The aim of this talk is to show on various examples that one can recognize Kazhdan-Lusztig cells using representations of Hecke algebras. This idea is especially interesting in the case of affine Weyl groups where one can use representations that have a very nice combinatorial descriptions in terms of alcove paths. (Joint work with James Parkinson)
       
  • Thursday, 1st of June 2023:
    • 17:00-17:50 : Loïc Poulain d'Andecy [Université de Reims Champagne Ardenne]  KLR-type presentation of affine Hecke algebras of classical types
       
    • Abstract: KLR algebras of type A have been a revolution in the representation theory of Hecke algebras of a type A flavour, thanks to the the Brundan-Kleshchev-Rouquier isomorphism relating them explicitly to the affine Hecke algebra of type A. KLR algebras of other types exist but are not related to affine Hecke algebras. In this talk I will present a generalisation of the KLR presentation for the affine Hecke algebra of type B/C (involving so-called orientifold KLR algebras) and I will discuss some applications. This talk is based on joint works with Salim Rostam and Ruari Walker.
     
  • Thursday, 8th of June 2023: No Seminar (Fronleichnam)
     
  • Thursday, 15th of June 2023:
    • 17:00-17:50 : Eda Kaja   [TU Darmstadt] Classification of non-solvable groups whose power graph is a cograph
       
    • Abstract : A recent, active branch of research in algebraic graph theory studies constructions of graphs whose vertex set is a group \(G\) and whose edges reflect the structure of \(G\) in some way. An important example of such a graph is the power graph of a group \(G\). Its vertices are the elements of \(G\) and there is an edge between distinct vertices \(x\) and \(y\) of \(G\) if and only if \(x\) is a power of \(y\) or \(y\) is a power of \(x\).

      We are interested in groups whose power graph is a cograph, i.e. it does not contain an induced subgraph isomorphic to a path of length four. We call such groups power-cograph groups. The problem of classifying power-cograph groups was posed by Cameron, Manna and Mehatari. They solved this problem for nilpotent groups and provided a classification in the case of finite simple groups relative to number theoretic problems. In this talk, I will present our classification of non-solvable power-cograph groups relative to the same number theoreticn problems. Additionally, our techniques allow us to precisely describe the structure of solvable power-cograph groups.
     
  • Thursday, 22nd of June 2023:
    • 17:00-17:50: Yasir Kızmaz   [Halle / Bilkent] A generalization of Alperin Fusion theorem and its applications
       
    • Abstract: Let $\F$ be a saturated fusion system on a finite \(p\)-group \(S\), and let \(P\) be a strongly $\F$-closed subgroup of \(S\). We define the concept ``$\F$-essential subgroups with respect to \(P\)" which are some proper subgroups of \(P\) satisfying some technical conditions, and show that an $\F$-isomorphism between subgroups of \(P\) can be factorised by some automorphisms of \(P\) and $\F$-essential subgroups with respect to \(P\). When \(P\) is taken to be equal to \(S\), the Alperin-Goldschmidt fusion theorem can be obtained as a special case. We also show that $P\unlhd \F$ if and only if there is no $\F$-essential subgroup with respect to \(P\). The following definition is made: A \(p\)-group \(P\) is \textit{strongly resistant} in saturated fusion systems if $P\unlhd \F$ whenever there is an over \(p\)-group \(S\) and a saturated fusion system $\F$ on \(S\) such that \(P\) is strongly $\F$-closed. We shall discuss and show the existence of several classes of \(p\)-groups which are strongly resistant.
     
  • Thursday, 29th of June 2023: No Seminar
     
  • Thursday, 6th of July 2023
    • 15:30-17:00: John Murray    [Maynooth University] Walking through the Alperin-McKay conjecture
    • Abstract: The Alperin-McKay conjecture (AMC) asserts that the number of height zero characters in a block of a finite group can be determined locally. AMC has been known to hold for symmetric groups for a long time. For 2-blocks, there is even an explicit bijection proving AMC. Seeking a certain local compatibility for all 2-blocks of fixed weight, I was led to formulate a very general conjecture about certain Littlewood-Richardson (L-R) coefficients. Each L-R coefficient gives the multiplicity of an irreducible character of a symmetric group in a character induced from a maximal Young subgroup. Each L-R coefficient equals the number of triangular configurations called honeycombs, which have given edges. In this talk I will describe a very simple model for honeycombs, which I call source-sink world. Then using ideas of Burgisser-Ikenmeyer, I will outline a possible proof for my conjecture which uses the notion of admissible walks on honeycombs.

     
  • Monday, 10th of July 2023
    • 15:30-17:00: Valentina Grazian  [Milano-Bicocca]   Fusion Systems: What is Known
    • Abstract:  Fusion systems made their first appearance in a 2006 paper by Puig and have since then been investigated by many researchers around the world. An important research direction involves the study of the behavior of exotic fusion systems (in particular at odd primes).
      In this talk we will present an overview of recent results concerning the classification of fusion systems on certain families of finite p-groups, highlighting the developments on the understanding of exotic fusion systems at odd primes.
     
  • Thursday, 13th of July 2023: No Seminar
     
  • Thursday, 20th of July 2023: No Seminar

Organisatoren: Jun.-Prof. Dr. Caroline Lassueur und Prof. Dr. Gunter Malle

Die Vorträge finden in Raum 48-436 statt.

 

  • Donnerstag, 27. Oktober 2022: Kein Seminar
    • Am Fr. 28.10. und Sa. 29.10. finden die Darstellungstheorietage 2022 in Kaiserslautern statt.
       
      • Fr. 14:00 - 14:50: Nicolas JaconCores and weights for Ariki-Koike algebras
      • Fr. 15:00 - 15:30: Lucas Ruhstorfer: The Alperin--McKay conjecture and groups of Lie type B and C
      • Fr. 16:10 - 17:00: Magdalena BoosFrom type A to all classical Lie types: Let's discuss Symmetric Representation Theory 
      • Fr. 17:10 - 17:40: Frank LübeckGreen functions and permutation characters 
      • Sa. 09:00 - 09:50: Benjamin SambaleSylow structure from the character table
      • Sa. 10:00 - 10:30: Damiano Rossi: Alternating sums for unipotent characters
      • Sa. 11:00 - 11:50: Thorsten HeidersdorfDeligne categories and complex representations of the finite linear group
      • Sa. 12:00 - 12:30: Alexander MillerFoulkes characters
         
  • Donnerstag, 3. November 2022:
    • 17:00-17:50 Uhr: Peter Symonds [University of Manchester]: The Module structure of a Group Action on a Ring 

      Consider a finite group \(G\) acting on a graded Noetherian \(k\)-algebra \(S\), for some field \(k\) of characteristic \(p\); for example \(S\) might be a polynomial ring. Regard \(S\) as a \(kG\)-module and consider the multiplicity of a particular indecomposable module as a summand in each degree. We show how this can be described in terms of homological algebra and how it is linked to the geometry of the group action on the spectrum of \(S\).

       
  • Donnerstag, 10. November 2023Kein Seminar
  • Donnerstag, 17. November 2022:
    • 17:00-17:50 Uhr: Patrick Serwene [TU Dresden]: Exotic and block-exotic fusion systems
       

      One of the main problems in the theory of fusion systems is the conjecture whether a fusion system arises in the form of a finite group if and only if it arises in the form of a \(p\)-block of a finite group. After discussing some applications, we present some advances tackling this conjecture. We introduce classes of fusion systems for which we know it holds true and also discuss the status for fusion systems of blocks of finite simple groups. We introduce a category, generalising block fusion systems, which plays an important role in our strategy to prove the conjecture.

       

  • Freitag, 18. November 2022:
    • Um 14:00 Uhr findet in Hörsaal 46-280 die Disputation von Birte Johansson statt. 
      Titel: The inductive McKay-Navarro condition for finite groups of Lie type
       
  • Donnerstag, 24. November 2022:
    • 17:00-17:50 Uhr: Margherita Piccolo [Heinrich Heine Universität Düsseldorf] : Representation growth of semisimple profinite groups

      A profinite group is called semisimple if it is the Cartesian product of finite simple groups. The representation growth of such groups can be studied looking at the distribution of irreducible representations by means of a zeta function, that is a Dirichlet generating function. Under certain restrictions, the representation growth is polynomial with a wide range of growth.
      Moreover, given a profinite group, it is generally a difficult question to determine if it is, in fact, isomorphic to a profinite completion of an abstract group. In this talk, I discuss a result of Kassabov and Nikolov which provides a criteria for a semisimple profinite group to be a profinite completion. Based on this, I report on my work which is aimed at constructing semisimple profinite groups with specified polynomial representation growth that
      arise as profinite completions of abstract groups (with the same representation growth).

       
  • Donnerstag, 1. Dezember 2022:
    • 17:00-17:50 Uhr: Kein Seminar
      Am Freitag, 2. Dezember 2022, um 14:00 Uhr findet in Hörsaal 48-208 die Disputation von Laura Voggesberger statt.
      Titel: Nilpotent Pieces in Lie Algebras of Exceptional Type in Bad Characteristic
       
  • Donnerstag, 8. Dezember 2022: Kein Seminar
    • Am Fr. 9.12. und Sa. 10.12.2022 findet die Nikolauskoferenz in Aachen statt.
       
  • Donnerstag, 15. Dezember 2022: Kein Seminar

     
  • Donnerstag, 5. Januar 2023:
    • 17:00-17:50 Uhr: Jason Semeraro[University of Leicester]: An Alperin-type conjecture for p-local compact groups

      If \(G\) is a finite group \(H\), the fusion system \(F\) of \(H\) is a category whose objects are subgroups of a (fixed) Sylow \(p\)-subgroup \(S\) and whose morphisms are \(H\) conjugation maps. An \(F\)-weight s a defect zero character of an \(F\)-automorphism group (taken up to conjugacy). Alperin's Weight Conjecture for the principal block \(B\) of \(H\) asserts that the number \(w(F)\) of \(F\)-weights is equal to the number of simple \(B\)-modules. If \(H=G(q)\) is a finite group of Lie type, then generically this number is \(|Irr(W)|\) where \(W\) is the Weyl group of G and is, in particular, independent of \(q\). This motivates the study of \(F\)-weights for the algebraic group \(G\) itself, where \(F\) is a \(p\)-local compact group, a fusion system on a discrete \(p\)-toral group \(S\). When \(F\) is connected - that is, when every \(p\)-element is conjugate to a toral element - we conjecture that \(w(F)=|Irr(W)\), and prove this holds (even for exotic examples) whenever \(v_p(|W|) < 2\) using the theory of blocks with cyclic defect group. Very recent additional work with Kessar and Malle establishes this conjecture in type \(A\), building on work of Oliver, Alperin, Fong and others. If time permits, I will also discuss a version of the Alperin-McKay conjecture in this context.

       
  • Donnerstag, 12. Januar 2023:
    • 17:00-17:50 Uhr: Abel Lacabanne [Université Clermont Auvergne]: Verma Howe duality and LKB representations of braid groups

      One of the most classical form of Howe duality relates the commuting action of two general linear Lie algebra on a polynomial ring. We will first discuss this duality in the specific case of \(\mathfrak{gl}_2\) and \(\mathfrak{gl}_n\). Specifically, we will explain how the polynomial ring decomposes as a direct sum of finite dimensional bimodules over \(\mathfrak{gl}_2 \times \mathfrak{gl}_n\). Then, we extend this duality in a context where Verma modules replace the finite dimensional representations of \(\mathfrak{gl}_2\). Surprisingly the dual picture leaves the realm of lowest and highest weight modules.
      As an application, we use a quantized version of this duality to study the irreducibility of the Lawrence--Krammer--Bigelow representations of braid groups.
      This is joint work with D. Tubbenhauer and P. Vaz.
       
  • Donnerstag, 19. Januar 2023:
    • 17:00-17:50 Uhr: Aluna Rizzoli [Ecole Polytechnique Fédérale de Lausanne] : Isometry groups of norms

      For a closed subgroup \(H\) of \(\mathrm{GL}_n(\mathbb{R})\), define \(\hat{H}\) to be the largest subgroup of \(\mathrm{GL}_n(\mathbb{R})\) that has the same orbits as \(H\) on \(\mathbb{R}^n\). We prove that \(H\) is the full isometry group of a norm on \(\mathbb{R}^n\) if and only if \(\pm I\in H\) and \(H=\hat{H}\). Using this, we show that every compact Lie group with a central involution can be realised as the isometry group of a norm. We then study the relationship between \(H\) and \(\hat{H}\) for compact \(H\leq \mathrm{GL}_n(\mathbb{R})\), showing that, with specified exceptions, \(H\) and \(\hat{H}\) have the same connected component of the identity. This is joint work with Emmanuel Breuillard, Martin Liebeck and Assaf Naor. 
       
  • Donnerstag, 26. Januar 2023:
    • 17:00-17:50 Uhr: J. Miquel Martínez [Universitat de València]: Character correspondences and counting conjectures

      We discuss situations in which it is possible to find character correspondences for the McKay and Alperin—McKay conjectures with good properties. In particular, we explore how these correspondences can interact with character degrees and decomposition numbers. This is joint work with Damiano Rossi.
       
  • Donnerstag, 2. Februar 2023:
    • 17:00-17:50 Uhr: TBA
       
  • Donnerstag, 9. Februar 2023Kein Seminar

 

Organisatoren Jun.-Prof. Dr. Caroline Lassueur und Dr. Lucas Ruhstorfer

Die Vorträge finden in Raum 48-436 statt.

 

  • Donnerstag, 28. April 2022:
    • 17:00-17:50 Uhr: Georges Neaime (Universität Bielefeld & Ruhr-Universität Bochum): Towards the Linearity of Complex Braid Groups Abstract
  • Donnerstag, 2. Juni 2022:
    • 17:00-17:50 Uhr: Deniz Yilmaz (LAMFA, Université de Picardie Jules Verne): Functorial equivalence of blocks of finite groups Abstract
  • Donnerstag, 9. Juni 2022:
    • 17:00-17:50 Uhr: Nicola Grittini (Università Cattolica del Sacro Cuore, Brescia): On characters with small cyclotomic fields of values Abstract
  • Donnerstag, 23. Juni 2022:
    • 17:00-17:50 Uhr: Norman MacGregor (University of Birmingham): Tame blocks of finite groups Abstract
  • Dienstag, 19. Juli 2022 (48-562):
    • 8:30-9:10 Uhr Michael Geline (Northern Illinois University): Schur indices are controlled by local subgroups Abstract
    • 9:20-10:00 Uhr Emily Norton (University of Kent): Chunks of the decomposition matrix of a finite classical group that we can understand Abstract​​​​​​​

Organisatoren Jun.-Prof. Dr. Caroline Lassueur und Dr. Lucas Ruhstorfer

Dieses Semester findet das Seminar als hybrides Seminar zusammen mit dem Lehrstuhl für Algebra und Zahlentheorie der RWTH Aachen statt.

Die Vorträge finden entweder in Raum 48-582 oder online statt. Die Präsenzvorträge werden dabei auch gestreamt.

 

Termin: kein regelmäßiger Termin. Zur Anmeldung als externer Gast verwenden Sie bitte diesen Link.

 

  • Donnerstag, 13. Januar 2022 (Online):
    • 16:15-17:00 Uhr: Nicolas Jacon (Université de Reims Champagne-Ardenne): On the computation of the Mullineux involution for symmetric groups and Hecke algebras Abstract
    • 17:15-18:00 Uhr: William Murphy (City, University of London): The first Hochschild cohomology of blocks of finite group algebras Abstract
  • Donnerstag, 20. Januar 2022 (vor Ort):
  • Donnerstag, 27. Januar 2022 (Online):
    • 16:15-17:00 Uhr:  Carolina Vallejo (Universidad Autónoma de Madrid): Groups with a 2-generated Sylow 2-subgroup Abstract
    • 17:15-18:00 Uhr: Claudio Marchi (University of Manchester): Picard groups for blocks with normal defect group Abstract
  • Donnerstag, 10. Februar 2022 (vor Ort):
    • 17:00-18:00 Uhr: Julian Brough (Bergische Universität Wuppertal): Characters of normalisers of d-split Levi subgroups in Sp2n(q) Abstract

     

    Organisatoren Jun.-Prof. Dr. Caroline Lassueur, Dr. Lucas Ruhstorfer und M.Sc. Damiano Rossi (Bergische Universität Wuppertal)

    Dieses Semester findet das Seminar als virtuelles Seminar zusammen mit der Arbeitsgruppe Algebra und Zahlentheorie der Bergischen Universität Wuppertal statt.

    Termin: kein regelmäßiger Termin. Zur Anmeldung als externer Gast verwenden Sie bitte diesen Link.

     

    • Dienstag, 27. April 2021:
      • 16:00-16:45 Uhr: Eugenio Giannelli (Università degli Studi di Firenze): On a conjecture of Malle and Navarro  Abstract
      • 17:00-17:45 Uhr: Noelia Rizo (Universidad del País Vasco): On the trivial intersection block conjecture Abstract
    • Dienstag, 11. Mai 2021:
      • 16:00-16:45 Uhr: Virgilius-Aurelian Minuta (Babes-Bolyai University, Cluj-Napoca): Relations between module triples Abstract
      • 17:00-17:45 Uhr: Sofia Brenner (Friedrich-Schiller Universität Jena): On Socles of Centers of Group Algebras Abstract
    • Dienstag, 25. Mai 2021:
      • 16:00-16:45 Uhr: Scott Harper (University of Bristol): The spread of a finite group Abstract
      • 17:00-17:45 Uhr: Justin Lynd (University of Louisiana at Lafayette): Punctured groups for exotic fusion systems Abstract
    • Dienstag, 8. Juni 2021:
      • 16:00-16:45 Uhr: Michael Geline (Northern Illinois University): An overview of Knörr lattices for finite groups Abstract
      • 17:00-17:45 Uhr: Andrei Marcus (Babes-Bolyai University, Cluj, Napoca): Extending basic Morita equivalences Abstract
    • Dienstag, 29. Juni 2021 (organisiert von Prof. Dr. Max Horn):
      • 16:00-16:45 Uhr: Andrea Thevis (RWTH Aachen und Universität des Saarlands): Square-tiled surfaces, normal covers, and cylinder decompositions Abstract

       

      Organisatoren Jun.-Prof. Dr. Caroline Lassueur und  Dr. Lucas Ruhstorfer

      Termin: kein regelmäßiger Termin. Zur Anmeldung als externer Gast verwenden Sie bitte diesen Link.

       

      • Donnerstag, 14. Januar 2021:
        • 16:00-16:45 Uhr: Nadia Mazza (Lancaster, University): Endotrivial modules for finite groups of Lie type Abstract
        • 17:00-17:45 Uhr: Matthew Gelvin: Dade groups and relative syzygies for finite groups Abstract
      • Donnerstag, 28. Januar 2021:
        • 16:00-16:45 Uhr: Jay Taylor (University of Southern California):  Rationality Properties of Kawanaka Characters Abstract
        • 17:00-17:45 Uhr: Mandi A. Schaeffer Fry (MSU Denver): The inductive McKay-Navarro Conditions in Type C for the Prime 2 Abstract
      • Donnerstag, 4. Februar 2021:
        • 16:00-16:45 Uhr: Cesare Ardito (City, University of London): Classification of blocks and open conjectures Abstract
        • 17:00-17:45 Uhr: Patrick Serwene (City, University of London): Exotic and block-exotic fusion systems Abstract

         

        Organisatoren:Dr. Niamh Farrell, Jun.-Prof. Dr. Caroline Lassueur und  Lucas Ruhstorfer

        Termin: Donnerstags 17:00-18:00, Raum 48-436

        • Donnerstag, 31. Oktober 2019: Julian Brough (Bergische Universität Wuppertal)
          • Titel: A criterion for the inductive Alperin weight condition [Abstract]

            Many of the local-global conjectures have been reduced to so called inductive conditions on simple groups. Moreover Späth has been successful in verifying the inductive McKay condition for most families of simple groups by considering an alternative criterion on a larger group with some additional information about the corresponding Clifford theory. In this talk I will discuss a joint work with Späth, in which we have provided an analogous criterion for the Alperin weight conjecture.

        • Donnerstag, 7. November 2019: Paul Wedrich (MPI Bonn)
          • Titel: Quivers for SL(2) tilting modules [Abstract]

            I will explain how diagrammatic algebra can be used to give an explicit generators-and-relations presentation of all morphisms between indecomposable tilting modules for SL(2) over an algebraically closed field of positive characteristic. The result takes the form of a path algebra of an infinite, fractal-like quiver with relations, which can be considered as the (semi-infinite) Ringel dual of SL(2). Joint work with Daniel Tubbenhauer.

        • Donnerstag, 14. November 2019: kein Seminar
        • Donnerstag, 21. November 2019: Jens Eberhardt (UCLA, 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.

        • Donnerstag, 28. November 2019: Ivo Dell'Ambrogio (Université de Lille)
          • Titel: The Green correspondence in algebra and topology [Abstract]

            The Green correspondence, a classic and basic result of modular representation theory, describes a bijection between indecomposable H-modules and indecomposable G-modules having the same vertex Q, provided H is a subgroup of G containing the normaliser of Q. Already in the 70's, Green himself noticed that the correspondence can be strengthened to an equivalence of categories between certain additive sub-quotients of G-modules and H-modules. I will explain how the latter Green equivalence can be proved and clarified in the general setting of "Mackey 2-functors", and how one can make sense of it also in situations where the Krull-Schmidt theorem does not hold (where indecomposable objects are not helpful). For example, and perhaps most notably, there follows a version of the Green equivalence for equivariant stable homotopy theory. This is joint work with Paul Balmer.

        • Donnerstag, 5. Dezember 2019: kein Seminar (Nikolaus Conference)
        • Donnerstag, 19. Dezember 2019: Ellen Henke (University of Aberdeen)
          • Titel: A generalisation of a theorem by Camina-Herzog [Abstract]

            An old theorem of Camina—Herzog states that a finite group has abelian Sylow 2-subgroups if the centralizer of any 2-element is of odd index. After an introduction to the theory of fusion systems, I will present a generalization of this theorem to fusion systems together with a very short and elementary proof. As a corollary, one obtains a theorem about 2-blocks of finite groups which was conjectured by Külshammer, Sambale and Tiep.

        • Donnerstag, 9. Januar 2020: kein Seminar
        • Donnerstag, 16. Januar 2020: kein Seminar (canceled)
        • Donnerstag, 23. Januar 2020: Jenny August (MPI Bonn)
          • Titel: Contraction Algebras in the Homological Minimal Model Programme [Abstract]

            In this talk, I will give an introduction to a class of symmetric, finite dimensional algebras, known as contraction algebras, which are one of the main tools used in the Homological Minimal Model Programme. This program aims to use noncommutative algebra to answer questions in algebraic geometry and my goal for the talk is to not only convince you that the contraction algebras are very useful for this purpose, but to also show you that they have some very interesting algebraic properties.

        • Donnerstag, 30. Januar2020: Vincent Beck (Université de Tours/ Université d'Orléans)
          • Titel: Cohomological computations for reflection groups and their braid groups and application to the determination of the finite subgroups of B/[P,P] [Abstract]

            In 2015, Guaschi, Goncalves and Ocampos started to study the finite subgroups of $B_n/[P_n,P_n]$ where $B_n$ is the standard braid group on $n$ strands and $P_n$ the pure braid group. They exhibited cyclic and abelian subgroup and even a non abelian subgroup of $B_7/[P_7,P_7]$. Their constructions were generalized to complex reflection groups by Marin. Finally, using cohomological methods, in a joint work with Marin, we were able to give a complete description of the finite subgroups of $B/[P,P]$ for every complex reflection groups $W$ (where $B$ is the braid group of $W$ and $P$ its pure braid group). I will present these results and how the cohomological description of the exact sequence 1-> P/[P,P] -> B/[P,P] -> W -> 1 has led to our classification of finite subgroups of B/[P,P].

        • Donnerstag, 6. Februar 2020: Maike Gruchot (RWTH Aachen)
          • Titel: On a relative version of complete reducibility [Abstract]

            In this talk we discuss a relative version of Serre’s notion of complete reducibility introduced by Bate, Martin, Röhrle and Rudolf. In the first part of the talk I introduce Serre’s notion of complete reducibility. In the second part, we introduce the relative version and discuss a characterization of relative G-complete reducibility which directly generalizes equivalent formulations of complete reducibility in representation theory. In the last part of the talk, we consider the case of a subgroup of G which normalizes the identity component K^0 of K, it turns that such a subgroup is relatively G-completely reducible with respect to K if and only if its image in the automorphism group of K^0 is completely reducible. This allows us to generalize a number of fundamental results from the absolute to the relative setting.

        • Donnerstag, 13. Februar 2020: kein Seminar

         

        Organisatoren: Dr. Niamh Farrell  und Dr. Alessandro Paolini

        Termin: Donnerstags 17:00-18:00, Raum 48-436

        • Montag(!), 15. April 2019, 15:45 Uhr: Bernhard Böhmler [TU Kaiserslautern]
          • Titel: On a counter-example to a conjecture about Morita algebras [Abstract]

          This is joint work with René Marczinzik. We give an example of a Morita algebra A with a tilting module T such that the endomorphism algebra End(T) over A has dominant dimension at least two, but is not a Morita algebra. This provides a counter-example to a conjecture by Hongxing Chen and Changchang Xi.

        • Donnerstag, 25. April 2019: Sophiane Yahiatene [Universität Bielefeld]
          • Titel: Hurwitz action and extended Weyl groups [Abstract]

          In the talk we will investigate the so-called extended Weyl groups which can be seen as a extention of a family of Coxeter groups. In these groups we will consider a class of distinguished elements, called Coxeter transformations and define a group action on certain factorizations of them. The action is called Hurwitz action and appears in the study of hereditary abelian categories. It serves as a helpful tool in understanding the lattice of thick subcategories. (j.w. B. Baumeister and P. Wegener)

        • Donnerstag, 2. Mai 2019: Jonas Hetz [Universität Stuttgart]
          • Titel: On the values of unipotent characters of finite groups of Lie type [Abstract]
        • Donnerstag, 9. Mai 2019: Martin Hofer [LMU München]
          • Titel: Construction of elliptic p-units [Abstract]

          Special values of elliptic functions have been studied since the 19th century, an example being the elliptic units defined by G. Robert in the 1970s. Interest in elliptic units has reemerged in the more recent past as they have proven to be quite useful in Iwasawa theory in cases where the base field k is imaginary quadratic. In this talk we present a construction of certain p-units with the help of classical elliptic units and compute their valuation when a rational prime p is non-split in k. This result, which can be used in Iwasawa theory, is an extension of the work done in the split case by W. Bley and a natural analogue of the cyclotomic situation proved by D. Solomon. In particular, we want to present how we collected numerical evidence for our theorem before proving it. Most parts of this project are joint work with W. Bley.

        • Donnerstag, 16. Mai 2019: Kein Seminar.
        • Donnerstag, 23. Mai 2019: Patrick Wegener [TU Kaiserslautern]
          • Titel: An invitation to Coxeter and Artin groups [Abstract]

          In this talk I will shortly review the definitions of Coxeter and Artin groups. Then I will explain and state some of the open problems and open conjectures in the theory of Coxeter and Artin groups. Furthermore I will explain how some of my results and my research are (or might be) related to these problems and conjectures.

        • Donnerstag, 30. Mai 2019: Kein Seminar (Christi Himmelfahrt).
        • Donnerstag, 6. Juni 2019: Thomas Weigel [Universita' di Milano-Bicocca] CANCELED!
          • Titel: tba
        • Donnerstag, 20. Juni 2019: Kein Seminar (Fronleichnam).
        • Montag, 24. Juni 2019: Michael Livesey [Universität Jena]
          • Titel: On Donovan's conjecture for abelian defect groups and strong Frobenius numbers [Abstract]

          Donovan's conjecture states that for a fixed p-group P there are only finitely many blocks (up to Morita equivalence) with defect group isomorphic to P. In this talk I will talk about recent progress made on this question for P abelian. The main tool used is the strong Frobenius number of a block. I will also talk about the corresponding results over an appropriately defined complete, discrete valuation ring. This is joint work with Charles Eaton and Florian Eisele.

        • Donnerstag, 27. Juni 2019: Giovanni De Franceschi [University of Auckland]
          • Titel: Centralizers and conjugacy classes in finite classical groups [Abstract]

          In computational group theory, solving problems on finite simple groups allows to solve problems in general, since there is plenty of literature on how to extend solutions to extensions of groups and products of groups. Groups of matrices are one of the best known classes of finite simple groups, so studying classical groups (groups of isometries for non-degenerate forms on vector spaces) is the first step to get solutions of many problems. In this talk I show three strictly correlated problems: list conjugacy classes, describe explicitely a conjugacy element, describe the group structure of the centralizer of an arbitrary element. During my PhD at University of Auckland I integrated the pre-existing results for some particular cases and extended them to subgroups of isometry groups (special and Omega groups). I will also show the results of the algorithmic study run parallel to the theoretical research.

        • Donnerstag, 4. Juli 2019: Eugenio Giannelli [Università degli Studi di Firenze]
          • Titel: Character correspondences for symmetric and complex reflection groups [Abstract]
        • Montag, 8. Juli 2019, 15:30 (Raum 48-438): Shigeo Koshitani [Chiba University]
          • Title: Equivalences of blocks algebras

          Donovan's conjecture states that for a fixed p-group P there are only finitely many blocks (up to Morita equivalence) with defect group isomorphic to P. In this talk I will talk about recent progress made on this question for P abelian. The main tool used is the strong Frobenius number of a block. I will also talk about the corresponding results over an appropriately defined complete, discrete valuation ring. This is joint work with Charles Eaton and Florian Eisele.

        • Donnerstag, 11. Juli 2019, 16:15-17:15 (!): Leo Margolis [Vrije Universiteit Brussel]
          • Titel: Blocks of defect 1 and units in integral group rings [Abstract]
        • Donnerstag, 18. Juli 2019: Vortrag im Oberseminar

         

        Organisatoren: Dr. Niamh Farrell  und Dr. Alessandro Paolini

        Termin: Donnerstags 17:15-18:15, Raum 48-436

        • Donnerstag, 25. Oktober 2018: Melissa Lee [Imperial College London],
          •  Titel: Bases of almost quasisimple groups and Pyber's conjecture [Abstract]
        • Donnerstag, 1. November 2018: Kein Seminar (Allerheiligen)
        • Donnerstag, 8. November 2018: Yann Palu [LAMFA, Amiens]
          • Titel: From cluster algebras to cluster categories [Abstract]

            The classification of cluster algebras with finitely many clusters shares some similarities with Gabriel's theorem on the classification of finite dimensional algebras (or quivers) of finite representation type. The link between cluster algebras and representation theory of quivers, first studied by Marsh-Reineke-Zelevinsky, was made more precise by Buan-Marsh-Reineke-Reiten-Todorov (see also Caldero-Chapoton-Schiffler for type A) by using the so-called cluster categories. This talk will be an introduction to the representation theory of quivers and to cluster categories. We will mainly focus on the example of quivers of Dynkin type A.

        • Donnerstag, 15. November 2018:Stacey Law [University of Cambridge]
          • Titel: Linear characters of Sylow subgroups of the symmetric group [Abstract]

            Let p be an odd prime and n a natural number. We determine the irreducible constituents of the permutation module induced by the action of the symmetric group S_n on the cosets of a Sylow p-subgroup P_n . In the course of this work, we also prove a symmetric group analogue of a well-known result of Navarro for p-solvable groups on a conjugacy action of N_G(P ). Before describing some consequences of these results, we will give an overview of the background and recent related results in the area.

        • Mittwoch(!), 21. November 2018, 17:15-18:15:Theodosios Douvropoulos [Institut de Recherche en Informatique Fontamentale]
          • Titel: Coxeter numbers: From fake degree palindromicity to the enumeration of reflection factorizations of regular elements [Abstract]

            A famous theorem of Cayley states that there are n^{n-2} vertex-labeled trees on n vertices. A different interpretation of this number, due to Hurwitz, is that it counts smallest length factorizations of the Coxeter element (12...n) of S_n in transpositions. As with many fascinating theorems for the Symmetric group, this statement is the shadow of a result that holds for all reflection groups. Bessis has shown after case-by-case calculations that: The number of smallest length reflection factorizations of a Coxeter element c of W is equal to h^n*n!/|W|, where h is the order of the Coxeter element and n the rank of W. We will present in this talk a uniform argument for this statement (that however relies on the BMR-freeness theorem) and partial generalizations of it that hold for arbitrary regular elements and arbitrary length factorizations. A classical approach due to Frobenius translates the above problem into a series of character evaluations. In the absence of a uniform construction of the characters $\chi$ of complex reflection groups, our method first groups the characters together with respect to an invariant called the Coxeter number $c_{\chi}$. It proceeds by making use of a Galois action on the corresponding Hecke algebra characters which was first considered by Malle to prove a palindromicity phenomenon on the fake degrees of W.

        • Donnerstag, 29. November 2018: Lleonard Rubio y Degrassi [University of Leicester]
          • Titel: On the Lie structure of $HH^1$ of tame blocks [Abstract]

            Blocks are usually classified by Morita or derived equivalence or by stable equivalence of Morita type. Stable equivalences of Morita type are the most general and frequent in modular representation theory but also the least understood. The main reason is that we do not know if many of the invariants for Morita and derived equivalences are still invariants for stable equivalences of Morita type.
            In this context, Hochschild cohomology records crucial information about a block $B$: its first degree component, denoted by $HH^1(B)$ is a Lie algebra and it is invariant under stable equivalences of Morita type. However, there are very few families of blocks for which the Lie algebra structure of $HH^1$ has been calculated. Therefore it is essential to extend these calculations to further families of examples.
            In this talk I will show that if $B$ is a block with tame representation type, then $HH^1(B)$ is a solvable Lie algebra. This is joint work with Sibylle Schroll and Andrea Solotar.

        • Donnerstag, 6. Dezember 2018: Kein Seminar (Nikolaus Conference)
        • Donnerstag, 13. Dezember 2018: Ruwen Hollenbach [TU Kaiserslautern]
          • Titel: Quasi-Isolated Blocks of Finite Groups of Lie Type [Abstract]

            In a recent paper G. Malle and G. Robinson proposed a modular analogue to the k(B)-conjecture. If B is a p-block with defect group D, then they conjecture that l(B) \leq p^r, where r is the sectional p-rank of D. I will talk about recent progress on this conjecture for finite groups of Lie type.

        • Dienstag(!), 18. Dezember 2018, 17:15-18:15 (Raum: 48-208):Jesua Chavez [Institut de Mathématiques de Jussieu-Paris Rive Gauche]
          • Titel: Howe correspondence between Harish-Chandra series[Abstract]
        • Donnerstag, 3. Januar 2019: kein Seminar
        • Donnerstag, 17. Januar 2019: David Stewart [Newcastle]
          • Titel: Gröbner bases, smooth centralisers and the Lefschetz principle  [Abstract]

            (Joint with Ben Martin and Lewis Topley). In a paper in the now defunct LMS Journal of Computation I used GAP to compute the Lie-theoretic centralisers in the exceptional groups of elements in their minimal modules in all characteristics, establishing when the centralisers in the groups were smooth. Non-smoothness was only found in very small characteristics, even where there are infinitely many orbits. This led to a question on when all centralisers of elements in a Z-defined representation would be smooth if the characteristic were large enough. With my co-authors we managed to prove this using the Lefschetz principle from model theory applied to Gröbner bases, which gave rise to what we call ‘d-bounded Hopf quadruples’. I’ll explain some of this.

        • Donnerstag, 24. Januar 2019: Tung Le [University of Pretoria]
          • Titel: On Characters of a Sylow p-subgroup of a Chevalley group G(p^f)[Abstract]
        • Donnerstag, 31. Januar 2019:Simon Goodwin [University of Birmingham]
          • Titel: Representations of reduced enveloping algebras for gl_n and restricted Yangians[Abstract]
        • Donnerstag, 7. Februar 2019: kein Seminar
        • Donnerstag, 14. Februar 2019, 17:00 Uhr(!): Arezoo Aslizadeh [TU Kaiserslautern/ Shahid Beheshti University, Tehran]
          • Titel: The nilpotent multipliers of the direct sum of Lie algebras [Abstract]

        Organisatoren: Dr. Niamh Farrell and Dr. Alessandro Paolini

        • Donnerstag, 12. April 2018: Kein Seminar.
        • Donnerstag, 19. April 2018: Kein Seminar.
        • Donnerstag, 26. April 2018: Kein Seminar.
        • Donnerstag, 3. Mai 2018: Keivan Mallahi-Karai [Jacobs University, Bremen]
          • Titel: Kirillov's orbit method and the polynomiality of the essential dimension of p-groups
        • Montag, 7. Mai 2018: Thomas Gobet [University of Sydney]
          • Titel: Dual and classical generators of Artin groups of spherical type
        • Donnerstag, 17. Mai 2018: Zhicheng Feng [TU Kaiserslautern]
          • Titel: On the inductive blockwise Alperin weight condition for special linear and unitary groups
        • Donnerstag, 24. Mai 2018: Keine Seminar
        • Donnerstag, 31. Mai 2018: Kein Seminar (Fronleichnam)
        • Donnerstag, 7. Juni 2018: two seminars.
          • 16.30-17.30: İpek Tuvay [Mimar Sinan Fine Arts University, Istanbul]
            • Titel: Brauer indecomposability of Scott modules for the quadratic group Qd(p)
          • 17.30-18.30: Kivanc Ersoy [Freie Universität Berlin]
            • Titel: Groups with certain conditions on fixed points of automorphisms
        • Donnerstag, 14. Juni 2018: Iulian Simion [Babes-Bolyai University, Cluj]
          • Titel: Minimal realizations of finite groups of isometries
        • Donnerstag, 21. Juni 2018: Alex Malcolm [Heilbronn Institute for Mathematics, Bristol]
          • Titel: Strong reality in finite simple groups: on products of classes and characters
        • Donnerstag, 28. Juni 2018: Kein Seminar
        • Donnerstag, 05. Juli 2018: Kein Seminar
        • Donnerstag, 12. Juli 2018: Madeleine Whybrow [TU Kaiserslautern]
          • Titel: Constructing Majorana representations

        Organisatoren: Jun.-Prof. Dr. Caroline Lassueur and Dr. Alessandro Paolini

        • Donnerstag, 26. Oktober 2017: Andrew Mathas [University of Sydney]
          • Titel: Jantzen filtrations and graded Specht modules  

            The Jantzen sum formula is a classical result in the representation theory of the symmetric and general linear groups that describes a natural filtration of the Specht modules over any field. Analogues of this result exist for many algebras including the cyclotomic Hecke algebras of type A. Quite remarkably, the cyclotomic Hecke algebras of type A are now know to admit a Z-grading because they are isomorphic to cyclotomic KLR algebras. I will explain how to give an easy proof, and stronger formulation, of Jantzen sum formula for the cyclotomic Hecke algebras of type A using the KLR grading. I will discuss some consequences and applications of this approach.     

          • Donnerstag, 02. November 2017: Caroline Lassueur [TU Kaiserslautern]
            • Titel: Lifting Morita equivalences with an endo-permutation source
          • Donnerstag, 09. November 2017: Kein Seminar
          • Donnerstag, 16. November 2017: Olivier Dudas [Université Paris Diderot - Paris 7]
            • Titel: On the unitriangular shape of decomposition matrices for finite reductive groups
          • Donnerstag, 23. November 2017: Reda Chaneb [Université Paris Diderot - Paris 7]
            • Titel: Basic sets for unipotent blocks of finite reductive groups
          • Donnerstag, 7. December 2017, Oberseminar Representation Theory : Emil Rotilio [TU Kaiserslautern]
            • Titel: Lie superalgebras in Physics  

              The current understanding of nature finds in the „Standard Model“ the most complete and verified theory (for now). The mathematics it involves heavily relies on Lie theory (Lie groups and Lie algebras). To better describe the universe, phisicists have come up with a „Supersymmetry“ theory (among others). This theory is described in terms of Lie superalgebras. The goal of this talk is to give an overview of which Lie algebras/superalgebras are used in Physics and why they help describing nature.
                             

          • Donnerstag, 14. December 2017: Stefano Sannella [University of Birmingham]       
            • Titel: Broué's conjecture and perverse equivalences                  

              The representation theory of a finite group G over a field F of positive characteristic carries many questions that have not been answered yet. Most of them can be stated as global/local conjectures: in various forms, they state that the representation theory of G is somehow controlled by its p-local subgroups. Here we will mostly focus on one of these conjectures, Broué's Abelian Defect Group Conjecture, which might be considered as an attempt to give a structural explanation of what is actually connecting G and its local p-subgroups in the abelian defect case. In particular, we explain how the strategy of looking for a perverse equivalence (a specific type of derived equivalence) works successfully in some cases and how this procedure is related to some Deligne-Lusztig varieties.
                             

          • Donnerstag, 21. December 2017: Patrick Wegener [TU Kaiserslautern]
            • Titel: Hurwitz action in elliptic Weyl groups and coherent sheaves on a weighted projective line                  

              Since 2000 the poset of noncrossing partitions attached to a Coxeter
              group (independently introduced by Bessis and Brady-Watt) has gained a
              lot of attention from different areas of mathematics. In 2010 Igusa,
              Schiffler and Thomas showed that there exists an order preserving
              bijection between this poset and the set of thick subcategories in the
              derived category of mod(A) generated by an exceptional sequence, where
              A is a hereditary Artin algebra. Following Happel's classification of
              hereditary categories, it seems natural to ask if there is an analogous
              statement when replacing mod(A) by the category of coherent sheaves on a
              weighted projective line. I will give a short summary on hereditary
              categories, explain how elliptic Weyl groups show up in this context and
              then generalize the result of Igusa-Schiffler-Thomas to tubular weighted
              projective lines. (This is joint work with B. Baumeister and S. Yahiatene.)

          • Donnerstag, 11. Januar 2018: Kein Seminar.
          • Donnerstag, 18. Januar 2018: Florian Eisele [City, University of London]
            • Titel: A counterexample to the first Zassenhaus conjecture                  

              There are many interesting problems surrounding the unit group U(RG) of the ring RG,
              where R is a commutative ring and G is a finite group. Of particular interest are the finite subgroups of
              U(RG). In the seventies, Zassenhaus conjectured that any u in U(ZG) is conjugate, in the group U(QG),
              to an element of the form +/-g, where g is an element of the group G. This came to be known as the "Zassenhaus conjecture".

              In recent joint work with L. Margolis, we were able to construct a
              counterexample to this conjecture. In this talk I will give an introduction to the various conjectures surrounding finite subgroups of U(RG),
              and how they can be reinterpreted as questions on the (non-)existence of certain R(GxH)-modules, where H is another finite group.
              This establishes a link with the representation theory of finite groups, and I will explain how, p-locally, our example is made up of certain p-permutation modules.   

          • Donnerstag, 25. Januar 2018: Petra Schwer [Karlsruher Institut für Technologie] 
            • Titel: Reflection length in affine Coxeter groups                

              Affine Coxeter groups have a natural presentation as reflection groups on some
              affine space. Hence the set R of all its reflections, that is all conjugates of its
              standard generators, is a natural (infinite) set of generators. Computing the reflection
              length of an element in an affine Coxeter group means that one wants to determine
              the length of a minimal presentation of this element with respect to R.
              In joint work with Joel Brewster Lewis, Jon McCammond and T. Kyle Petersen we were
              able to provide a simple formula that computes the reflection length of any element
              in any affine Coxeter group. In this talk I would like to explain this formula, give
              its simple uniform proof and allude to the geometric intuition behind it. 

          • Donnerstag, 1. Februar 2018: Kein Seminar
          • Donnerstag, 8. Februar 2018: Kein Seminar

          Organisator: Dr. Alessandro Paolini

          • Donnerstag, 20. April 2017: Kein Seminar
          • Donnerstag, 27. April 2017: Kivanç Ersoy [TU Kaiserslautern]
            • Titel: Locally finite groups with small centralizers
          • Donnerstag, 4. Mai 2017: Emily Norton [Max Planck Institute Bonn]
            • Titel: The \mathfrak{sl}_\infty-crystal combinatorics of higher level Fock spaces
          • Donnerstag, 11. Mai 2017: Andreas Bächle [Vrije Universiteit Brussel]
            • Titel: Rationality of groups and centers of integral group rings
          • Donnerstag, 18. Mai 2017: Kein Seminar
          • Donnerstag, 25. Mai 2017: Kein Seminar
          • Donnerstag, 1. Juni 2017: Kein Seminar                         
          • Donnerstag, 08. Juni 2017: William Wong [TU Kaiserslautern]
            • Titel: A phenomenon in the representation of SL(2,q) in defining characteristics             
          • Donnerstag, 13. Juni 2017: Wolfgang Willems [Otto-von-Guericke-Universität Magdeburg]
            • Titel: On quasi-projective Brauer characters
          • Donnerstag, 22. Juni 2017: Baptiste Rognerud [IRMA, Straßburg]
            • Titel: A Morita theory for permutation modules                 
          • Donnerstag, 29. Juni 2017: Julian Külshammer [Universität Stuttgart]
            • Titel: Ringel duality as a special case of Koszul duality                
          • Donnerstag, 05. Juli 2017: Tung Le [University of Pretoria]
            • Titel: On the automorphisms of designs constructed from finite simple groups
          • Donnerstag, 13. Juli 2017: Kein Seminar ("Representation Theory in Kaiserslautern" Konferenz)
          • Donnerstag, 20. Juli 2017: Yujiao Sun [Universität Stuttgart]
            • Titel: Supercharacter theories for Sylow p-subgroups of finite exceptional groups of Lie type
          • *Freitag, 25. August 2017, 14:00-15:00*: Shigeo Koshitani [University of Chiba]
            • Titel: Brauer indecomposability of Alperin-Scott modules for finite non-abelian 2-groups

          Organisatoren: Dr. Julian Brough und Jun.-Prof. Dr. Caroline Lassueur

          • Donnerstag, 3. November 2016, : Yanjun Liu [TU Kaiserslautern]
            • Titel: Principal and defect-zero blocks of finite groups
          • Donnerstag, 24. November 2016, : Niamh Farrell [TU Kaiserslautern/City, University of London]
            • Titel: The rationality of blocks of quasi-simple finite groups
          • Donnerstag, 25. November 2016: Jesper Grodal [Københavns Universitet]
            • Titel: Endotrivial modules via homotopy theory
          • Donnerstag, 1. Dezember 2016: Emilio Pierro [Universität Bielefeld]
            • Titel: Quantities associated to the subgroup lattice
          • Donnerstag, 8. Dezember 2016: Kein Seminar: 9.-10. Dez. Nikolauskonferenz
          • Donnerstag, 15. Dezember 2016: Kein Seminar: Konferenz "Finite simple groups, their fusion systems and representations", EPFL
          • Donnerstag, 12. Januar 2017: Kein Seminar: 12.-14. Jan. Permutation Konferenz, Bielefeld University   
          • Donnerstag, 19. Januar 2017: Iris Köster [Universität Stuttgart]
            • Titel: Sylow Numbers in Character Tables and Integral Group Rings             
          • Donnerstag, 26. Januar 2017: Kein Seminar: 27.-28. Jan. Darstellungstheorietage 2016
          • Donnerstag, 6. Februar 2017: Magdalena Boos [RUHR- Universtität Bochum]
            • Titel: Using quiver representations to prove finiteness criteria                 
          • Donnerstag, 9. Februar 2017: Charles Eaton [University of Manchester]
            • Titel: Loewy lengths of blocks                
          • Donnerstag, 8. März 2017: Micheal Geline [Northern Illinois University]
            • Titel: Some quantitative and qualitative aspects of Knörr lattices

          Organisatoren: Dr. Thomas Gobet und Dr. Caroline Lassueur

          • Donnerstag, 21. April 2016, 15:30-16:30, Raum 48-582: Paul Balmer (UCLA, Bielefeld)
            • Titel: A quick tour of tensor triangular geometry
          • Donnerstag, 28. April 2016, 17:00-18:00: Jitendra Bajpai (MPI Bonn) - canceled
            • Titel: Introduction to the theory of hypergeometric groups
          • Donnerstag, 5. Mai 2016: no talk (Christi Himmelfahrt)
          • Mittwoch, 11. Mai 2016, 17:00-18:00, Raum 48-436: Jay Taylor (Padova)
            • Titel: Sums of Skew Characters of Symmetric Groups
          • Donnerstag, 12. May 2016, 17:00-18:00, Raum 48-436: Christopher Voll (Bielefeld)
            • Title: Representation growth of finitely generated nilpotent groups
          • Donnerstag, 19. Juni 2016: no talk because of workshop "Branching problems for reductive groups" at IML
          • Donnerstag, 26. Juni 2016: no talk because of Fronleichnam   
          • Donnerstag, 2. Juni 2016, 17:00-18:00, Raum 48-436: René Reichenbach (Jena)
            • Title: The Broué-Puig *-construction and some applications to 2-blocks           
          • Donnerstag, 26. Januar 2017: Kein Seminar: 27.-28. Jan. Darstellungstheorietage 2016
          • Donnerstag, 6. Februar 2017: Magdalena Boos [RUHR- Universtität Bochum]
            • Titel: Using quiver representations to prove finiteness criteria                 
          • Donnerstag, 9. Februar 2017: Charles Eaton [University of Manchester]
            • Titel: Loewy lengths of blocks                
          • Donnerstag, 8. März 2017: Micheal Geline [Northern Illinois University]
            • Titel: Some quantitative and qualitative aspects of Knörr lattices

          Organisatoren: Dr. Thomas Gobet und Dr. Caroline Lassueur

          • Donnerstag, 15. Oktober 2015, 16:00-17:00, Raum 48-436: Mikaël Cavallin [EPFL, Ecublens, CH]
            • Titel: Restriction of irreducibles and structure of Weyl modules
          • Donnerstag, 29. Oktober 2015: Philipp Perepelitsky [TU Kaiserslautern]
            • Titel: p-permutation equivalences between blocks of finite groups
          • Donnerstag, 5. November 2015: Benjamin Sambale [TU Kaiserslautern]
            • Titel: Broué's Conjecture for sporadic groups
          • Donnerstag, 12. November 2015: Neil Saunders [EPFL, Ecublens, CH]
            • Titel: Irreducible Components of Springer Fibres
          • Donnerstag, 19. November 2015: Thomas Gobet [TU Kaiserslautern]
            • Titel: On twisted filtrations on Soergel bimodules and linear Rouquier complexes
          • Mittwoch, 25. November 2015: Olivier Dudas [University Paris Diderot - Paris 7, FR]
            • Titel: On the unitriangular shape of decomposition matrices for finite reductive groups
          • Donnerstag, 26. November 2015: Chris Bowman [City University, London, UK]
            • Titel: The co-Pieri rule for Kronecker coefficients
          • Donnerstag, 3. Dezember 2015: Benedetta Lancellotti [Università degli Studi di Milano-Bicocca, IT]
            • Titel: Trivial source lattices and a strong form of McKay conjecture
          • Mittwoch, 9. Dezember 2015, 16:00-17:00, Raum 48-582: Patrick Wegener [Universität Bielefeld]
            • Titel: Hurwitz action in Coxeter Groups
          • Donnerstag, 17. Dezember 2015: Oberseminar Complex Reflection Groups
          • Donnerstag, 14. Januar 2016: Alessandro Paolini [University of Birmingham, UK]
            • Titel: A reduction of characters of Sylow p-subgroups of finite groups of Lie type
          • Donnerstag, 28. Januar 2016: Oliver Goodbourn [Ruhr-Universität Bochum]
            • Titel: Reductive pairs from representations of algebraic groups
          • Donnerstag, 4. Februar 2016: Julian Brough [TU Kaiserslautern]
            • Titel: Determining finite group structure from the size of the conjugacy classes
          • Donnerstag, 11. Februar 2016: John Murray [Maynooth University, IR]
            • Titel: Strong and weak reality and principal indecomposable modules in characteristic 2

          Organisatorinnen: Dr. habil. Britta Späth und Dr. Caroline Lassueur

          • Donnerstag, 23. April, 15:30-16:30, Raum 48-582: Ulrike Faltings [TU Kaiserslautern]
            • Titel: On the decomposition numbers of F_4(q) for q even
          • Donnerstag, 30. April, 15:30-16:30, Raum 48-582: Carolina Vallejo [Universitat de València]
            • Titel: Coprime action and Brauer characters
          • Dienstag, 12. Mai, 15:30-16:30, Raum 48-436: Danny Neftin [University of Michigan, Ann Arbor]
            • Titel: Monodromy groups of rational functions
          • Donnerstag, 21. Mai, 15:30-16:30, Raum 48-519: Vivien Ripoll [Universität Wien]
            • Titel: Coxeter elements in well-generated complex reflection groups
          • Donnerstag, 4. Juni: Kein Seminar (Fronleichnam)
          • Donnerstag, 15:30-16-30, 11. Juni: Amanda Schaeffer Fry [Metropolitan State University Denver]
            • Titel: Finite groups with an irreducible character of large degree
          • Donnerstag, 18. Juni, 17:00-18:00, Raum 48-436: Thomas Gerber [RWTH Aachen]
            • Titel: Weak Harish-Chandra theory for finite unitary groups
          • Donnerstag, 25. Juni, 15:30-16:15: Matthias Klupsch [RWTH Aachen]
            • Titel: Supercuspidal modules of finite reductive groups
          • Donnerstag, 16. Juli, 17:00-18:00, Seminarraum 48-436: Oksana Yakimova [Friedrich-Schiller-Universität Jena]
            • Titel: On symmetric invariants of semi-direct products
          • Donnerstag, 23. Juli: Kein Seminar

          Organisatorinnen: Dr. habil. Britta Späth und Dr. Caroline Lassueur

          • Donnerstag, 2. Oktober: Shigeo Koshitani [University of Chiba]
            • Titel: Remarks on the Loewy length of a block algebra
          • Donnerstag, 30. Oktober: Attila Maróti [TU Kaiserslautern]
            • Titel: Groups equal to a product of three conjugate proper subgroups
          • Donnerstag, 27. November: Imke Toborg [Universität Koblenz-Landau]
            • Titel: Local methods need some representation theory to prove Z_3^* results
          • Donnerstag, 18. Dezember: Sebastian Herpel [Ruhr-Universität Bochum]
            • Titel: Maximal subalgebras of Cartan Type in the exceptional Lie algebras
          • Donnerstag, 8. Januar: Tommy Hofmann [TU Kaiserslautern]
            • Titel: Integrality of Representations of Finite Groups
          • Donnerstag, 5. Februar, 17:00 Raum 48-436: Eirini Chavli [Université Paris Diderot - Paris 7]
            • Titel: The BMR freeness conjecture: the exceptional groups of rank 2         
          • Donnerstag, 19. Februar, 17:00 Raum 48-436: Barbara Baumeister [Universität Bielefeld]
            • Titel: Moufang twin buildings and Kac-Moody groups

           

           

           

           

           

           

           

           

          Organisatoren: Britta Späth und Jay Taylor

          • 24.04.2014, 17:00-18:00 (Room 48-436): Simon Schmider
            • Titel: On Auslander-Reiten components for Hecke algebras of type A
          • 08.05.2014, 17:00-18:00 (Room 48-436): Frank Himstedt [TU München]
            • Titel: On the decomposition numbers of the groups $\rm SO_7(q)$ and
              $\rm Sp_6(q)$
          • 22.05.2014, 17:00-18:00 (Room 48-436): Erwan Biland [Sherbrooke University, Kanada]
            • Titel: Stable equivalences related to the Z*p-theorem
          • 28.05.2014, 17:00-18:00 (Room 48-436): Pablo Luka
            • Titel: Vertex-bounded defects
          • 05.06.2014, 15:45-16:45 (Room 48-582): Eugenio Gianelli [Royal Holloway University of London]
            • Titel: On permutation modules and decomposition numbers of the symmetric group
          • 05.06.2014, 17:00-18:00 (Room 48-436): Hung P. Tong-Viet [Universität Bielefeld]
            • Titel: Some results on Brauer character degrees of finite groups
          • 12.06.2014, 17:00-18:00 (Room 48-436): Martino Garonzi [Università di Padova]
            • Titel: Factorizing a group with conjugate subgroups
          • 03.07.2014, 16:00-17:00 (Room 48-582): Giovanna Carnovale [Università di Padova]
            • Titel: Conjugacy classes in finite simple groups and pointed Hopf algebras        
          • 17.07.2014, 17:00-18:00 (Room 48-436): Martina Lanini [FAU Erlangen-Nürnberg]
            • Titel: Finite dimensional representations of rational Cherednik algebras

           

           

           

           

           

           

           

           

          Organisatorin: Britta Späth

          • 07.11.2013, 15:30-16:030 (Room 48-436): Philipp Perepelitsky
            • Titel: $p$-permutation equivalences between blocks of finite groups
          • 14.11.2013, 15:30-16:30 (Room 48-436): Iulian Simion
            • Titel: Refining the Bruhat decomposition
          • 21.11.2013: no talk
            • Baer Kolloqium (23.11.2013)
          • 28.11.2013, 15:30-16:30 (Room 48-436): Fuat Erdem
            • Titel: On the generating graph of a finite group
          • 05.12.2013: no talk
            • Titel: Darstellungstheorietage und Nikolauskonferenz
          • 12.12.2013, 16:00-17:00 (Room 48-436): Jürgen Müller
            • Titel: The Abelian Defect Group Conjecture for sporadic simple groups
          • 19.12.2013, 15:30-16:30 (Room 48-436): Olivier Dudas
            • Titel: Ordering conjugacy classes in Weyl groups
          • 09.01.2014, 15:30-16:30 (Room 48-436): Caroline Lassueur
            • Titel: The position of endo-$p$-permutation modules and relatives in the Auslander-Reiten quiver        
          • 16.01.2014, 17:00-18:00 (Room 48-436): Serge Bouc
            • Titel: The poset of posets
          • 23.01.2014, 15:30-16:30 (Room 48-436): Elisabeth Schulte
            • Titel: Alperin's Weight Conjecture - On Inductive Conditions for $G_2(q)$
          • 30.01.2014, 15:30-16:30 (Room 48-436): Burkhard Külshammer
            • Titel: Some questions in block theory
          • 10.02.2014, 15:30-16:30 (Room 48-436): Alessandro Paolini [University of Birmingham]
            • Titel: A Basis of the Gelfand-Graev Algebra of a Chevalley Group
          • 06.03.2014, 10:30-11:30 (Room 48-436): Michel Enguehard [Institut de Mathematique de Jussiue]
            • Titel: Towards a Jordan decomposition of blocks of finite reductive groups