## Meetings

### Simple groups: New perspectives and applications

In August 2018 I am co-organising a three-day meeting on Simple groups: New perspectives and applications at the University of Bristol. See the conference website for further details.

Main speakers:

• Inna Capdeboscq, University of Warwick
• Pierre-Emmanuel Caprace, Université catholique de Louvain
• David Craven, University of Birmingham
• Tom De Medts, Ghent University
• Robert Guralnick, University of Southern California
• Martin Liebeck, Imperial College
• Gunter Malle, TU Kaiserslautern
• Ben Martin, University of Aberdeen
• Eamonn O'Brien, University of Auckland
• Gerhard Röhrle, Ruhr-Universität Bochum
• Colva Roney-Dougal, University of St Andrews
• Aner Shalev, Hebrew University of Jerusalem
• Donna Testerman, EPFL (TBC)
• Pham Tiep, Rutgers

### Groups and their applications

In February 2018 I am organising a one-day meeting in Bristol as part of the LMS-funded series Groups and their applications.

Speakers:

• Nick Gill, University of South Wales
• Carlisle King, Imperial College
• Stacey Law, University of Cambridge

### Groups and their applications

In May 2017 I organised a one-day meeting in Bristol as part of the LMS-funded series Groups and their applications.

Speakers:

• Joanna Fawcett, University of Cambridge
• Melissa Lee, Imperial College
• Simon Smith, University of Lincoln

### Permutation groups: Methods and applications

In January 2017 I co-organised a workshop on Permutation groups: Methods and applications at Bielefeld University. See the conference website for further details.

Main speakers:

• Michael Giudici, University of Western Australia
• Thomas Gobet, TU Kaiserslautern
• Martin Liebeck, Imperial College
• Kay Magaard, University of Birmingham
• Gunter Malle, TU Kaiserslautern
• Attila Maróti, Rényi Institute
• Alice Niemeyer, RWTH Aachen
• Benjamin Nill, Magdeburg University
• Cheryl Praeger, University of Western Australia
• Laci Pyber, Rényi Institute
• Colva Roney-Dougal, University of St Andrews
• Aner Shalev, Hebrew University of Jerusalem
• Donna Testerman, EPFL
• Gareth Tracey, University of Warwick

### Groups and their applications

In June 2016 I organised a one-day meeting in Bristol as part of the LMS-funded series Groups and their applications.

Speakers:

• Barbara Baumeister, Bielefeld University
• Peter Cameron, University of St Andrews
• Gareth Tracey, University of Warwick

### Branching problems for reductive groups

In May 2016 I co-organised a workshop on Branching problems for reductive groups at the Institut Mittag-Leffler in Stockholm.

### Algebra workshop, British Mathematical Colloquium

In March 2016, the University of Bristol hosted the British Mathematical Colloquium, which is the largest Pure Mathematics conference to be held annually in the UK. The meeting included several workshops on different themes - Jeremy Rickard and I organised the algebra workshop.

Workshop speakers:

• Chris Bowman, City University
• Sinéad Lyle, University of East Anglia
• Alex Malcolm, Imperial College
• Tom de Medts, Ghent University
• Vanessa Miemietz, University of East Anglia
• Nikolay Nikolov, University of Oxford
• David Pauksztello, University of Manchester
• Susanne Pumpluen, University of Nottingham

### Simple groups, representations and related topics

In July 2015 I co-organised a conference on Simple groups, representations and related topics at the Centre for Mathematical Sciences in Cambridge.

This meeting celebrated the hugely influential work of Martin Liebeck and Jan Saxl. A conference banquet was held at Gonville and Caius College on July 14th.

Speakers:

• Michael Aschbacher, California Institute of Technology
• Jon Brundan, University of Oregon
• Joanna Fawcett, University of Western Australia
• Nick Gill, University of South Wales
• Bob Guralnick, University of Southern California
• Alastair Litterick, University of Auckland
• Gunter Malle, TU Kaiserslautern
• Ben Martin, University of Aberdeen
• Peter Neumann, University of Oxford
• Eamonn O'Brien, University of Auckland
• Cheryl Praeger, University of Western Australia
• Laci Pyber, Rényi Institute, Budapest
• Aner Shalev, Hebrew University of Jerusalem
• Donna Testerman, EPFL Lausanne
• John Thompson, University of Florida
• Pham Tiep, University of Arizona

### Groups and their applications

In May 2015 I organised a one-day meeting in Bristol as part of the LMS-funded series Groups and their applications. This followed earlier meetings in 2014/15 at Birkbeck, Birmingham and Manchester.

Programme:

14:00 - 15:00: Adam Thomas (University of Cambridge)

Title: Complete reducibility in exceptional algebraic groups

Abstract: The notion of complete reducibility was introduced by J.-P. Serre in 1998. It generalises the notion of a completely reducible module in classical representation theory. After giving an introduction to complete reducibility for algebraic groups, we discuss recent work with A. Litterick on classifying the subgroups of exceptional algebraic groups that are not completely reducible. The techniques used are a mix of standard representation theory, non-abelian cohomology and computational group theory.

15:00 - 15:30: Tea and coffee in the common room

15:30 - 16:30: Michael Bate (University of York)

Title: Representation varieties, reductive pairs and a question of Külshammer

Abstract: Let $\Gamma$ be a finite group. A natural and interesting way to think about the representation theory of $\Gamma$ over an algebraically closed field $k$ is to study the representation varieties $\mathrm{Hom}(\Gamma,\mathrm{GL}_n(k))$ for different $n$. These sets carry the structure of an affine variety, and the algebraic group $\mathrm{GL}_n(k)$ acts naturally. Understanding the orbit structure of this action allows one to use techniques from Geometric Invariant Theory to study representation-theoretic questions. For example, the closed orbits correspond to isomorphism classes of $n$-dimensional semisimple representations of $\Gamma$.

More generally, one can study the variety $\mathrm{Hom}(\Gamma, G)$ for any reductive group $G$. In this talk I'll give a survey of some of the basic results in this area, including results of Richardson and Slodowy which allow one to relate the structure of $\mathrm{Hom}(\Gamma, G)$ to that of $\mathrm{Hom}(\Gamma, \mathrm{GL}_n(k))$, given an embedding $G \subseteq \mathrm{GL}_n(k)$. Some of my own work has explored the limitations of Richardson's techniques; in this vein I'll also present an example which answers a question of Külshammer.

16:30 - 17:30: Martin Liebeck (Imperial College)

Title: Multiplicity-free representations of algebraic groups

Abstract: A finite-dimensional representation of a group is said to be multiplicity-free if every irreducible representation appears at most once as a composition factor. I shall talk about the problem of classifying irreducible representations of simple algebraic groups for which the restriction to some proper subgroup is multiplicity-free. There are many interesting examples of such representations, and under suitable assumptions there is some hope of classifying them. There are also some nice connections with other aspects of algebraic group theory - for example, invariant theory and unipotent classes.