Counting conjectures and beyond

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Workshop theme

The fascinating survey on the representation theory of finite groups written by R. Brauer in 1963 starts in the following way: "It has been said by E. T. Bell that “wherever groups disclosed themselves or could be introduced, simplicity crystallized out of comparative chaos.” This may often be true, but, strangely enough, it does not apply to group theory itself, not even when we restrict ourselves to groups of finite order.” Much has been achieved since the publication of this survey, for example, the Classification of Finite Simple Groups was completed, but still we do not know, for instance, if the number of irreducible characters in a Brauer p-block is bounded by the size of its defect group. Stated as Problem 20 in Brauer’s survey, this is now known as the k(B)-conjecture. Also, we still do not know if a block with only height zero characters has an abelian defect group (that is, one implication of the height zero conjecture, Problem 23 in Brauer’s list, is still open).

The announcement of the McKay conjecture in 1971 is the origin of a different kind of counting conjectures of finite groups. These include several refinements of the McKay conjecture, the Alperin weight conjecture and the Dade-Robinson conjectures. In a few words, they assert that important information of a finite group, as the number of irreducible complex characters of degree not divisible by a given prime p, can be calculated locally, namely in a much smaller group with restricted normal structure. It is believed that an explanation for all these phenomena might involve derived categories (as in Broué’s conjecture), methods in algebraic topology and working over the field of p-adic numbers. In the meantime, all these conjectures (but not the k(B)-conjecture) have been reduced to questions on simple groups, in the hope that a better understanding of the representation theory of (quasi-)simple groups can provide proofs for them ultimately using the Classification of Finite Simple Groups. This has happened with the McKay conjecture for the prime p = 2. The purpose of this meeting is to gather relevant mathematicians working on counting conjectures and related global-local problems in order to discuss the state of the art and the new developments in the area. In particular, this workshop will celebrate the great influence of Gunter Malle on those developments

Speakers list:

Geoffrey Robinson (University of Aberdeen)
Lucas Ruhstorfer (Technische Universität Kaiserslautern)
Thomas Keller (Texas State University)
Raphaël Rouquier (University of California, Los Angeles)
Donna Testerman (EPFL - Ecole Polytechnique Fédérale de Lausanne)
Benjamin Sambale ( Leibniz Universität Hannover)
Pham Huu Tiep (Rutgers, The State University of New Jersey)
Alexander Kleshchev (University of Oregon)
Michael Livesey (University of Manchester)
Britta Späth (Bergische Universität Wuppertal)
Damiano Rossi (Bergische Universität Wuppertal)
Jason Semeraro (University of Leicester)
Mandi Schaeffer Fry (Metropolitan State University of Denver)
Eugenio Giannelli (Università di Firenze)
Noelia Rizo (Universidad de Oviedo)
Stacey Law (University of Cambridge)
Jay Taylor (University of Manchester)
George Lusztig (Massachusetts Institute of Technology)
Radha Kessar (University of London)
Michel Broué (Université Paris 7 - Denis-Diderot)
Olivier Dudas (Université Denis Diderot)
Alexander Moretó (Universitat de València)
Jesper Grodal (Københavns Universitet (University of Copenhagen)
Charles Eaton (University of Manchester)
Caroline Lassueur (Technische Universität Kaiserslautern)
Niamh Farrell (Leibniz Universität Hannover)

Fees

Registration Only

Registration Package: £208
Student Registration Package: £158

The Registration Package includes admission to all seminars, lunches and refreshments on the days that lectures take place (Monday - Friday), wine reception and formal dinner, but does not include other meals or accommodation.

Formal Dinner Only

Formal Dinner: £55

Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event. For all remaining participants who would like to attend, such as programme participants, the above charge will apply.

Accommodation

Unfortunately we do not have any accommodation to offer so all successful applicants will need to source their own accommodation.

Please see the Hotels Combined website for a list of local hotels and guesthouses.

Meals

Lunch Lunch timings and location will be confirmed with timetable.

Evening Meal Participants are free to make their own arrangements for dinner.

Formal Dinner The Formal Dinner location and date is to be confirmed.

Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event.

Timetable

Monday 9th May 2022
09:00 to 09:55	Registration	No Room Required
09:55 to 10:00	Ulrike Tillmann University of Oxford Welcome Talk	No Room Required
10:00 to 10:50	Geoffrey Robinson University of Aberdeen Chair: Markus Linckelmann Counting conjectures and auxiliary questions	Room 1
10:50 to 11:20	Morning Coffee	No Room Required
11:20 to 11:50	Donna Testerman EPFL - Ecole Polytechnique Fédérale de Lausanne Chair: Markus Linckelmann Eigenvalue multiplicities in representations of simple algebraic groups	Room 1
11:50 to 12:20	Noelia Rizo Universidad de Oviedo Chair: Markus Linckelmann On blocks with few irreducible characters	Room 1
12:20 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:20	Raphael Rouquier University of California, Los Angeles Chair: Martin Liebeck Beyond Broué's conjecture	Room 1
14:20 to 14:30	Break	No Room Required
14:30 to 15:20	Michael Livesey University of Manchester Chair: Martin Liebeck RoCK blocks for double covers of symmetric groups	Room 1
15:20 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:50	Pham Tiep Rutgers, The State University of New Jersey Chair: Martin Liebeck Character bounds for finite groups of Lie type	Room 1
16:50 to 18:00	Welcome Wine Reception at INI	No Room Required

Tuesday 10th May 2022
09:00 to 09:50	Charles Eaton University of Manchester Chair: John Murray Counting blocks	Room 1
09:50 to 10:00	Break	No Room Required
10:00 to 10:50	Britta Späth Bergische Universität Wuppertal Chair: John Murray Counting extensions of Characters of Spin groups, equivariant Jordan decomposition and the McKay Conjecture	Room 1
10:50 to 11:20	Morning Coffee	No Room Required
11:20 to 11:50	Thomas Keller Texas State University Chair: John Murray Large orbits in finite group actions	Room 1
11:50 to 12:20	Damiano Rossi City, University of London Chair: John Murray Inductive local-global conditions and generalized Harish-Chandra theory	Room 1
12:20 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:20	Mandi Schaeffer Fry Metropolitan State University of Denver Chair: Carolina Vallejo The inductive McKay—Navarro conditions for the prime 2 and some groups of Lie type.	Room 1
14:20 to 14:30	Break	No Room Required
14:30 to 15:20	Eugenio Giannelli Università di Firenze Chair: Carolina Vallejo On Restriction of Characters to Sylow Subgroups	Room 1
15:20 to 16:00	Afternoon Tea	No Room Required
16:00 to 17:00	Poster Session	Room 1

Wednesday 11th May 2022
09:00 to 09:50	Michel Broué Université Paris 7 - Denis-Diderot Chair: Jean Michel Gunter is sixty something	Room 1
09:50 to 10:00	Break	No Room Required
10:00 to 10:50	Olivier Dudas Université Denis Diderot Chair: Jean Michel Counting unipotent representations in transverse characteristic	Room 1
10:50 to 11:20	Morning Coffee	No Room Required
11:20 to 11:50	Jason Semeraro University of Leicester; University of Bristol Chair: Jean Michel Counting conjectures for fusion systems	Room 1
11:50 to 12:20	Jesper Grodal Københavns Universitet (University of Copenhagen) Chair: Jean Michel Integral endotrivial modules	Room 1
12:20 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 16:50	Free Afternoon	No Room Required
19:30 to 22:00	Formal Dinner, Murray Edward	No Room Required

Thursday 12th May 2022
09:00 to 09:50	Radha Kessar University of London Chair: Marc Cabanes The principal block of a Z_l-spets.	Room 1
09:50 to 10:00	Break	No Room Required
10:00 to 10:50	Alexander Moreto Universitat de València Chair: Marc Cabanes Prime divisors and the number of conjugacy classes of finite groups	Room 1
10:50 to 11:20	Morning Coffee	No Room Required
11:20 to 11:50	Stacey Law University of Cambridge Chair: Marc Cabanes On plethysms and Sylow branching coefficients	Room 1
11:50 to 12:20	Niamh Farrell Leibniz Universität Hannover Chair: Marc Cabanes Oriented Temperley-Lieb algebras and $p$-Kazhdan-Lusztig theory	Room 1
12:20 to 13:30	Lunch at Churchill College	No Room Required
13:30 to 14:20	Benjamin Sambale Leibniz Universität Hannover Chair: Peter Webb Another characterization of nilpotent blocks	Room 1
14:20 to 14:30	Break	No Room Required
14:30 to 15:20	Caroline Lassueur Technische Universität Kaiserslautern; RWTH Aachen University Chair: Peter Webb On p-permutation modules	Room 1
15:20 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:50	George Lusztig Massachusetts Institute of Technology Chair: Peter Webb A parametrization of unipotent representations	Room 1

Friday 13th May 2022
09:00 to 09:50	Alexander Kleshchev University of Oregon Chair: Gunter Malle On RoCK blocks and Broue’s Conjecture for double covers of symmetric groups	Room 1
09:50 to 10:00	Break	No Room Required
10:00 to 10:50	Jay Taylor University of Manchester Chair: Gunter Malle Rationality Questions for Finite Reductive Groups	Room 1
10:50 to 11:20	Morning Coffee	No Room Required
11:20 to 12:10	Lucas Ruhstorfer Technische Universität Kaiserslautern Chair: Gunter Malle Quasi-isolated blocks and the Alperin-McKay conjecture	Room 1
12:10 to 12:15	Chair: Gunter Malle Close	Room 1
12:15 to 13:30	Lunch at Churchill College	No Room Required

Groups, representations and applications: new perspectives

Organisers

Gabriel Navarro Universitat de València
Britta Späth Bergische Universität Wuppertal
Carolina Vallejo Universidad Autonoma de Madrid

Speakers

Michel Broué Université Paris 7 - Denis-Diderot
Olivier Dudas Université Denis Diderot
Charles Eaton University of Manchester
Niamh Farrell Technische Universität Kaiserslautern
Eugenio Giannelli Università di Firenze
Jesper Grodal Københavns Universitet (University of Copenhagen)
Thomas Keller Texas State University
Radha Kessar University of London
Alexander Kleshchev University of Oregon
Caroline Lassueur Technische Universität Kaiserslautern
Stacey Law University of Cambridge
Michael Livesey University of Manchester
George Lusztig Massachusetts Institute of Technology
Alexander Moreto Universitat de València
Noelia Rizo
Geoffrey Robinson University of Aberdeen
Damiano Rossi Bergische Universität Wuppertal
Raphael Rouquier University of Oxford
Lucas Ruhstorfer Technische Universität Kaiserslautern
Benjamin Sambale
Mandi Schaeffer Fry Metropolitan State University of Denver
Jason Semeraro University of Leicester; University of Bristol
Britta Späth Bergische Universität Wuppertal
Jay Taylor University of Southern California
Donna Testerman EPFL - Ecole Polytechnique Fédérale de Lausanne
Pham Tiep Rutgers, The State University of New Jersey

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Participants

Lorenzo Bonazzi Università degli Studi di Firenze; Università degli Studi di Ferrara
Julian Brough Bergische Universität Wuppertal
Michel Broué Université Paris 7 - Denis-Diderot
Marc Cabanes Institut de Mathématiques de Jussieu; CNRS (Centre national de la recherche scientifique)
Peter Cameron University of St Andrews; Queen Mary University of London
Rachel Camina University of Cambridge
Sergio Cia Sorbonne Université
Alice Dell'Arciprete University of East Anglia
Olivier Dudas Université Denis Diderot
Charles Eaton University of Manchester
Niamh Farrell Leibniz Universität Hannover
Meinolf Geck Universität Stuttgart
Eugenio Giannelli Università di Firenze
Jesper Grodal Københavns Universitet (University of Copenhagen)
Pierre Guillot University of Strasbourg
Jonas Hetz Universität Stuttgart
Geoffrey Janssens Vrije Universiteit Brussel; Université Catholique de Louvain
Urban Jezernik University of Ljubljana
Birte Johansson Technische Universität Kaiserslautern
Thomas Keller Texas State University
Radha Kessar University of London
Alexander Kleshchev University of Oregon
Mikko Korhonen University of Manchester
Caroline Lassueur Technische Universität Kaiserslautern; RWTH Aachen University
Stacey Law University of Cambridge
Martin Liebeck Imperial College London
Markus Linckelmann City University, London
Michael Livesey University of Manchester
George Lusztig Massachusetts Institute of Technology
Gunter Malle Technische Universität Kaiserslautern
Stuart Martin University of Cambridge
J. Miquel Martínez Universitat de València
Jamie Mason University of Birmingham
Jean Michel Institut de Mathématiques de Jussieu; Université Paris 7 - Denis-Diderot
Alexander Moreto Universitat de València
John Murray National University of Ireland, Maynooth
Gabriel Navarro Universitat de València
Miriam Norris King's College London; Imperial College London
Richard Parker None / Other
Chris Parker University of Birmingham
Amrutha Parola None / Other
Sonia Petschick Bergische Universität Wuppertal
Lorenzo Putignano Università degli Studi di Firenze
Kamilla Rekvenyi Imperial College London
Noelia Rizo Universidad de Oviedo
Aluna Rizzoli University of Cambridge
Geoffrey Robinson University of Aberdeen
Colva Roney-Dougal University of St Andrews
Damiano Rossi City, University of London
Raphael Rouquier University of California, Los Angeles
Lucas Ruhstorfer Technische Universität Kaiserslautern
Benjamin Sambale Leibniz Universität Hannover
Mandi Schaeffer Fry Metropolitan State University of Denver
Jason Semeraro University of Leicester; University of Bristol
Britta Späth Bergische Universität Wuppertal
Jay Taylor University of Manchester
Doryan Temmerman Universiteit Hasselt
Donna Testerman EPFL - Ecole Polytechnique Fédérale de Lausanne
Ulrich Thiel University of Kaiserslautern
Pham Tiep Rutgers, The State University of New Jersey
Carolina Vallejo Universidad Autonoma de Madrid; ICMAT
Laura Voggesberger Technische Universität Kaiserslautern
Giada Volpato Università degli Studi di Firenze
Peter Webb University of Minnesota
Emine Yildirim Isaac Newton Institute; University of Cambridge