Mirror Symmetry and Big Algebras in the Hitchin System

Explore the intricate connections between mirror symmetry and big algebras in this advanced mathematics lecture. Discover how to model the Hitchin system on very stable upward flows using the spectrum of equivariant cohomology of a Grassmannian and its mirror through the spectrum of the Kirillov algebra of a minuscule representation of the Langlands dual group. Delve into the generalization of this concept to non-minuscule representations, employing a big commutative subalgebra of the Kirillov algebra and ringifying the equivariant intersection cohomology of affine Schubert varieties. Conclude with a visual exploration of the skeletons of big and medium algebras of the octet and decuplet of SL(3), providing a deeper understanding of these complex mathematical structures.