Homological Mirror Symmetry - Non-Holomorphic Deformations of Landau-Ginzburg

Explore a 54-minute lecture on non-holomorphic deformations of Landau-Ginzburg models presented by Maxim Kontsevich from the Institut des Hautes Etudes Scientifiques. Delve into the intricate world of complex geometry, examining how a sheaf of differential graded Lie algebras can be associated with a non-singular complex variety and a holomorphic function. Discover the conditions under which the formal germ of the derived moduli space becomes smooth and finite-dimensional. Investigate the interpretation of part of the derived moduli space as moduli of holomorphic deformations, and learn why the entire space lacks a direct holomorphic interpretation. Gain insights into the weakened Frobenius manifold structure of these spaces and their expected role in describing genus 0 Gromov-Witten invariants for general symplectic manifolds. Examine Fukaya-theoretic and Hodge-theoretic aspects of non-holomorphically deformed Landau-Ginzburg models, including an extension of the theory of spectra for isolated singularities, based on ongoing joint work with D. Auroux and L. Katzarkov.