Bảo Châu NgôCollège de FranceFormes automorphes (chaire internationale)Année 2022-2023Théorie géométrique des représentationsSéminaire - Tamas Hausel : Mirror Symmetry and Big AlgebrasRésuméFirst we recall the mirror symmetry identification of the coordinate ring of certain very stable upward flows in the Hitchin system and the Kirillov algebra for the minuscule representation of the Langlands dual group via the equivariant cohomology of the cominuscule flag variety (e.g. complex Grassmannian). In turn we discuss a conjectural extension of this picture to non-very stable upward flows in terms of a big commutative subalgebra of the Kirillov algebra, which also ringifies the equivariant intersection cohomology of the corresponding affine Schubert variety.Tamas Hausel, IST Austria 1998 : PhD University of Cambridge 1998-1999 : Post-doctoral member IAS Princeton 1999-2002 : Miller Research Fellow, UC Berkeley 2002-2007 : Assistant and Associate Professor, UT Austin 2005-2012 : Royal Society URF, Oxford 2012-2016 : Chair of Geometry, EPF Lausanne 2016- : Hausel group, IST Austria