Groups, representations and applications: new perspectives
GRA2
3 May 2022 to 29 July 2022
Programme theme
Group Theory is essentially the theory of symmetry for mathematical and physical systems, and underpins much of modern mathematics. Born more than two centuries ago in the work of Evariste Galois, it achieved a major milestone when the Classification of Finite Simple Groups was completed. Since then, important and deep connections to areas as varied as topology, algebraic geometry, Lie theory, homological algebra, and mathematical physics, have been discovered and exploited. Still, the area abounds with basic problems and conjectures, some of which have been open for decades.Recent breakthroughs hold out the prospect of finally solving some venerable open problems. In turn, recent results in group- and representation theory have led to substantial progress in a vast number of applications in Lie theory, number theory, algebraic geometry, combinatorics and semigroup theory, to name a few.
All this wealth of new results and directions will be in the focus of the programme, which includes the following themes: -- Reductive groups: Representations, subgroup structure, and cohomology
-- Local-global conjectures in representation theory of finite groups
-- Fusion systems, local group theory, and revision projects
-- Modern algorithmic and computational methods
-- Connections with other areas of mathematics
There will be five one-week workshops, with the first one to provide participants with an overview of the programme's themes and how they fit together. The programme will bring together the leading experts in group and representation theory, on the one hand, and from several key other parts of mathematics on the other, with the aim of solving some of the main open problems, and taking the many connections between group theory and other areas of mathematics to the next level.
(programme image by Ivan Andrus)
Click here to download the programme's final scientific report
GRA programme: interview with organisers Martin Liebeck and Colva Roney-Dougal
Preprints
| Title | Year | Programme | |
|---|---|---|---|
Classifying spaces of finite groups of tame representation typeAuthors: David Benson |
2021 | GRA2 | 20 July 2022 |
Enhanced power graphs of groups are weakly perfectAuthors: Peter Cameron, Veronica Phan |
2021 | GRA2 | 19 July 2022 |
Recognizing the Commuting graph of a finite groupAuthors: V Arvind, Peter Cameron |
2021 | GRA2 | 19 July 2022 |
Workshops
Counting conjectures and beyond
9 May 2022 to 13 May 2022
Simple groups, representations and applications
25 July 2022 to 29 July 2022
Seminars
| Thursday 5th May 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Gabriel Navarro Universitat de València |
Room 2 | 
|
| Tuesday 17th May 2022 | |||
|---|---|---|---|
| 11:15 to 12:15 |
Carolina Vallejo Universidad Autonoma de Madrid; ICMAT |
Room 2 | |
| 11:45 to 12:45 | Telecommunications Room | ||
| Thursday 19th May 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Jonas Hetz Universität Stuttgart |
Room 2 | |
| Tuesday 24th May 2022 | |||
|---|---|---|---|
| 11:15 to 12:15 |
Gunter Malle Technische Universität Kaiserslautern |
Room 2 | |
| Thursday 26th May 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Markus Linckelmann City University, London |
Room 2 |
|
| Tuesday 31st May 2022 | |||
|---|---|---|---|
| 11:15 to 12:15 |
Patrick Serwene Technische Universität Dresden |
Room 2 |
|
| Thursday 2nd June 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Harald Helfgott CNRS (Centre national de la recherche scientifique); Georg-August-Universität Göttingen |
Room 1 | |
| Tuesday 7th June 2022 | |||
|---|---|---|---|
| 11:15 to 12:15 |
Nick Gill The Open University |
Room 2 |
|
| Thursday 9th June 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Emmanuel Breuillard University of Oxford |
Room 2 |
|
| Friday 10th June 2022 | |||
|---|---|---|---|
| 13:00 to 14:00 |
Valentina Grazian Università degli Studi di Milano - Bicocca |
Room 2 |
|
| 14:10 to 15:10 |
Lucia Morotti Leibniz Universität Hannover |
Room 2 |
|
| 15:50 to 16:50 |
Gareth Tracey University of Oxford |
Room 2 |
|
| Tuesday 14th June 2022 | |||
|---|---|---|---|
| 11:15 to 12:15 |
Frank Lübeck RWTH Aachen University |
Room 2 | |
| Thursday 16th June 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Cheryl Praeger University of Western Australia |
Room 2 |
|
| Tuesday 21st June 2022 | |||
|---|---|---|---|
| 11:15 to 12:15 |
Attila Maróti Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences |
Room 2 |
|
| Thursday 23rd June 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
David Benson University of Aberdeen |
Room 2 |
|
| Tuesday 28th June 2022 | |||
|---|---|---|---|
| 11:15 to 12:15 |
Michael Zieve University of Michigan |
Room 2 | |
| Thursday 30th June 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Laszlo Pyber Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences |
Room 1 |
|
| Tuesday 5th July 2022 | |||
|---|---|---|---|
| 11:15 to 12:15 |
Tim Burness University of Bristol |
Room 2 | |
| Thursday 7th July 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Alexandre Zalesski University of East Anglia |
Room 2 | |
| Tuesday 12th July 2022 | |||
|---|---|---|---|
| 11:15 to 12:15 |
Stacey Law University of Cambridge |
Room 2 | |
| Thursday 14th July 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Ellen Henke Technische Universität Dresden |
Room 2 | |
| Tuesday 19th July 2022 | |||
|---|---|---|---|
| 10:15 to 11:15 |
Chris Parker University of Birmingham |
Room 2 |
|
| Thursday 21st July 2022 | |||
|---|---|---|---|
| 16:00 to 17:00 |
Eamonn O'Brien University of Auckland |
Room 2 |
|
| Friday 22nd July 2022 | |||
|---|---|---|---|
| 09:00 to 10:00 | No Room Required | ||
| 10:00 to 10:30 |
Cheryl Praeger University of Western Australia |
Centre for Mathematical Sciences |
|
| 10:40 to 11:10 |
Nick Gill The Open University |
Centre for Mathematical Sciences |
|
| 11:40 to 12:10 |
Peter Cameron University of St Andrews; Queen Mary University of London |
Centre for Mathematical Sciences |
|
| 14:00 to 14:30 |
Pham Tiep Rutgers, The State University of New Jersey |
Centre for Mathematical Sciences |
|
| 14:40 to 15:10 |
Martin Liebeck Imperial College London |
Centre for Mathematical Sciences |
|
| 15:20 to 15:50 |
Robert Guralnick University of Southern California |
Centre for Mathematical Sciences |
|
| 16:15 to 17:15 |
Jan Saxl Memorial Day: Wine Reception: Isaac Newton Institute |
No Room Required | |
| Tuesday 26th July 2022 | |||
|---|---|---|---|
| 17:00 to 18:00 |
Robert Guralnick University of Southern California |
Room 1 |
|
Organisers
- Martin Liebeck Imperial College London
- Kay Magaard University of Arizona
- Colva Roney-Dougal University of St Andrews
- Britta Späth Bergische Universität Wuppertal
- Pham Tiep Rutgers, The State University of New Jersey
Speakers
- David Benson University of Aberdeen
- Emmanuel Breuillard University of Oxford
- Tim Burness University of Bristol
- Peter Cameron University of St Andrews; Queen Mary University of London
- Nick Gill The Open University
- Valentina Grazian Università degli Studi di Milano - Bicocca
- Robert Guralnick University of Southern California
- Harald Helfgott CNRS (Centre national de la recherche scientifique); Georg-August-Universität Göttingen
- Ellen Henke Technische Universität Dresden
- Jonas Hetz Universität Stuttgart
- Stacey Law University of Cambridge
- Martin Liebeck Imperial College London
- Markus Linckelmann City University, London
- Frank Lübeck RWTH Aachen University
- Gunter Malle Technische Universität Kaiserslautern
- Attila Maróti Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences
- Lucia Morotti Leibniz Universität Hannover
- Gabriel Navarro Universitat de València
- Eamonn O'Brien University of Auckland
- Chris Parker University of Birmingham
- Cheryl Praeger University of Western Australia
- Laszlo Pyber Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences
- Patrick Serwene Technische Universität Dresden
- Pham Tiep Rutgers, The State University of New Jersey
- Gareth Tracey University of Oxford
- Carolina Vallejo Universidad Autonoma de Madrid; ICMAT
- Alexandre Zalesski University of East Anglia
- Michael Zieve University of Michigan
Participants
- Michael Aschbacher CALTECH (California Institute of Technology)
- David Benson University of Aberdeen
- Michel Broué Université Paris 7 - Denis-Diderot
- Tim Burness University of Bristol
- 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
- Inna Capdeboscq University of Warwick
- Pierre-Emmanuel Caprace Université Catholique de Louvain
- Persi Diaconis Stanford University
- Stephen Doty Loyola University Chicago
- Olivier Dudas Université Denis Diderot
- Charles Eaton University of Manchester
- Saul Freedman University of St Andrews
- Daniele Garzoni Tel Aviv University
- Eugenio Giannelli Università di Firenze
- Nick Gill The Open University
- George Glauberman University of Chicago
- Valentina Grazian Università degli Studi di Milano - Bicocca
- Robert Guralnick University of Southern California
- Scott Harper University of Bristol
- Harald Helfgott CNRS (Centre national de la recherche scientifique); Georg-August-Universität Göttingen
- Ellen Henke Technische Universität Dresden
- Jonas Hetz Universität Stuttgart
- Ruwen Hollenbach Leibniz Universität Hannover
- Derek Holt University of Warwick
- Alexander Ivanov Imperial College London
- Urban Jezernik University of Ljubljana
- Birte Johansson Technische Universität Kaiserslautern
- Martin Kassabov Cornell University
- Nick Katz Princeton University
- Veronica Kelsey University of Manchester
- Radha Kessar University of London
- Alexander Kleshchev University of Oregon
- Mikko Korhonen University of Manchester
- Caroline Lassueur Technische Universität Kaiserslautern
- Stacey Law University of Cambridge
- Tung Le University of Pretoria
- Tae Young Lee Rutgers, The State University of New Jersey
- Martin Liebeck Imperial College London
- Markus Linckelmann City University, London
- Alastair Litterick University of Essex
- Michael Livesey University of Manchester
- Justin Lynd University of Louisiana at Lafayette
- Richard Lyons Rutgers, The State University of New Jersey
- Frank Lübeck RWTH Aachen University
- Gunter Malle Technische Universität Kaiserslautern
- Benjamin Martin University of Aberdeen
- Stuart Martin University of Cambridge
- Attila Maróti Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences
- Nadia Mazza Lancaster University
- Eilidh McKemmie Rutgers, The State University of New Jersey
- Jean Michel Institut de Mathématiques de Jussieu; Université Paris 7 - Denis-Diderot
- Alexander Moreto Universitat de València
- Lucia Morotti Leibniz Universität Hannover
- Gabriel Navarro Universitat de València
- Miriam Norris King's College London; Imperial College London
- Eamonn O'Brien University of Auckland
- Robert Oliver Université Paris 13
- Richard Parker None / Other
- Chris Parker University of Birmingham
- Sonia Petschick Bergische Universität Wuppertal
- Cheryl Praeger University of Western Australia
- Laszlo Pyber Alfréd Rényi Institute of Mathematics,Hungarian Academy of Sciences
- Kamilla Rekvenyi Imperial College London
- Noelia Rizo Universidad de Oviedo
- Aluna Rizzoli University of Cambridge
- Geoffrey Robinson University of Aberdeen
- Bernardo Rodrigues University of Pretoria; University of KwaZulu-Natal
- Colva Roney-Dougal University of St Andrews
- Damiano Rossi City, University of London
- Lucas Ruhstorfer Technische Universität Kaiserslautern
- Benjamin Sambale Leibniz Universität Hannover
- Mandi Schaeffer Fry Metropolitan State University of Denver
- Gary Seitz University of Oregon
- Jason Semeraro University of Leicester; University of Bristol
- Patrick Serwene Technische Universität Dresden
- Aner Shalev Hebrew University of Jerusalem
- Pablo Spiga Università degli Studi di Milano - Bicocca
- Britta Späth Bergische Universität Wuppertal
- David Stewart University of Newcastle upon Tyne
- Gernot Stroth Martin-Luther-Universität Halle-Wittenberg
- Jay Taylor University of Manchester
- Donna Testerman EPFL - Ecole Polytechnique Fédérale de Lausanne
- Adam Thomas University of Warwick
- Pham Tiep Rutgers, The State University of New Jersey
- Lewis Topley University of Bath
- Gareth Tracey University of Oxford
- Carolina Vallejo Universidad Autonoma de Madrid; ICMAT
- Martin van Beek University of Birmingham
- Laura Voggesberger Technische Universität Kaiserslautern
- Peiran Wu University of St Andrews
- Alexandre Zalesski University of East Anglia
- Michael Zieve University of Michigan
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