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Group , Algebra and Topology team (GAT)

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The team is mainly concerned with representation theory and group theory, algebraic topology, related categorical aspects, and interactions with other areas of mathematics :

  • Finite reductive groups and their representations, Coxeter groups, complex reflection groups, root systems, Hecke algebras, Garside groups and Garside categories, Kac-Moody groups.
  • Braid groups and their representations, knot invariants, centralizing algebras and diagram algebras (Temperley-Lieb, BMW, ...), cubic Hecke algebras, infinitesimal Hecke algebras, Grothendieck-Teichmüller group, geometric Galois actions.
  • Representations of algebras, quivers, derived categories, stable categories, cluster algebras and cluster categories, and equivalences of these categories. Hochschild (co)homology and geometric representations. Categorifications of cluster algebras, Calabi-Yau triangulated categories, orbit categories, and their links with combinatorics.
  • Categories associated to groups and bisets, and similar structures. Associated functors, Mackey functors, cohomological Mackey functors, Burnside rings, fusion systems. Applications to block theory.
  • Quantum groups, crystal bases, combinatorics, cryptography.
  • Algebraic topology, homotopical algebra, operads, higher categories, topology of manifolds, algebraic varieties and stratified spaces.

The group theory seminar takes place once a week. A weekly working group is also organized on various themes in algebra. The group theory team is part of the GDR "Théorie de Lie Algébrique et Géométrique", of the GDR "Tresses", and of the GDR "Topologie Algébrique et Applications" of the CNRS. Its members are in charge of the Master 2 "Algèbre, Théorie des Nombres et Applications", jointly with Université de Paris.

Members list