Videos and slides of minicourse in Madrid available

Conference: The Hitchin system, Langlands duality and mirror symmetry, ICMAT Madrid, April 2023

Minicourse: Mirror symmetry and big algebras

After surveying some mirror symmetry phenomena in the geometry of Langlands dual Hitchin systems, we will model the Hitchin system on cominuscule upward flows by the equivariant cohomology of cominuscule flag varieties like the Grassmannian. Then we will explain how mirror symmetry implies a synthetic BNR correspondence. To generalise to the non-minuscule case we will construct a big commutative subalgebra of the Kirillov algebra to model the mirror of the universal principal bundle in an irreducible representation. We finish with an overview of results and conjectures on involutions on big algebras induced from quasi-split real forms.

Lecture 1. Mirror symmetry for Hitchin systems, Lecture 1. slides, Lecture 1. video

Lecture 2. Equivariant cohomology, Kirillov algebras and BNR correspondence, Lecture 2. slides, Lecture 2. video

Lecture 3. Big algebras and real forms, Lecture 3. slides, Lecture 3. video