Explore enhanced mirror symmetry for Langlands dual Hitchin systems in this 47-minute lecture by Tamas Hausel, presented by the International Mathematical Union. Delve into advanced mathematical concepts, beginning with an introduction to SYZ mirror symmetry for Hitchin systems. Progress through topological mirror symmetry and the classical limit of homological mirror symmetry. Examine enhanced mirror symmetry in the classical limit and investigate Lagrangian upward flows in M. Study examples of very stable Higgs bundles and learn how the Hitchin map functions as a spectrum of equivariant cohomology. Conclude by exploring the universal bundle of Kirillov algebras and understanding how the mirror of equivariant cohomology relates to Kirillov algebra.