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

Explore an advanced lecture on non-holomorphic deformations of Landau-Ginzburg models in the context of homological mirror symmetry. Delve into the intricate world of complex geometry as Maxim Kontsevich from the Institut des Hautes Etudes Scientifiques discusses the association of a sheaf of differential graded Lie algebras with a non-singular complex variety and holomorphic function. Examine the conditions for smoothness and finite-dimensionality of the formal germ of the derived moduli space. Investigate the interpretation of part of the derived moduli space as moduli of holomorphic deformations and its significance in describing genus 0 Gromov-Witten invariants for general symplectic manifolds. Gain insights into Fukaya-theoretic and Hodge-theoretic aspects of non-holomorphically deformed LG models, including a generalization of the theory of spectra for isolated singularities.