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Groups, representations and applications: new perspectives

Participation in INI programmes is by invitation only. Anyone wishing to apply to participate in the associated workshop(s) should use the relevant workshop application form.

6th January 2020 to 30th June 2020
Martin Liebeck Imperial College London
Kay Magaard University of Birmingham
Colva Mary Roney-Dougal University of St Andrews
Britta Späth Bergische Universität Wuppertal
Pham Tiep Rutgers, The State University of New Jersey

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)

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons