Mirror Symmetry and Big Algebras

Explore mirror symmetry and big algebras in this comprehensive lecture by Tamas Hausel. Delve into the mirror symmetry identification of coordinate rings in Hitchin systems and Kirillov algebras for minuscule representations of Langlands dual groups. Examine the connection to equivariant cohomology of cominuscule flag varieties, such as complex Grassmannians. Investigate a conjectural extension to non-very stable upward flows, involving a big commutative subalgebra of the Kirillov algebra and its relation to equivariant intersection cohomology of affine Schubert varieties. Cover key topics including introduction, motivation, fundamental modifications, pglnfix, aging map, universal bundle, and big algebra throughout this in-depth mathematical exploration.