Homological Mirror Symmetry - Nikita Nekrasov

Explore a 56-minute lecture on homological mirror symmetry delivered by Nikita Nekrasov from the Simons Center at Stony Brook University. Delve into the construction of Lax operators for classical and quantum integrable systems of Garnier (Gaudin) and elliptic Calogero-Moser type, which are expected to capture the Seiberg-Witten geometry of A-type quiver N=2 gauge theories in four dimensions. Examine the intersection theory on the moduli space of framed parabolic sheaves on the projective plane and its relation to surface defects in Omega-deformed linear or cyclic quiver N=2 theory. Cover topics such as time evolution, spectral invariance, classical integrability, Garnier model, algebraic integral systems, four-dimensional theory, super partition functions, quiver gauge theories, algebraic geometry, and surface defects. Gain insights into the works of Nekrasov, I. Krichever, and A. Grekov in this advanced mathematical physics presentation.