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Landau-Ginzburg model via L^2-Hodge theory

Author:    Publicsh date:2019-05-16    Clicks:
Title:Landau-Ginzburg model via L^2-Hodge theorySpeaker: 文豪 清华大学丘成桐数学中心博士后Time: 2019.5月22日 下午三点到五点Location: Center for Mathematical Sciences, Room 813Abstract:Given a non-compact Calabi-Yau manifold X and a holomorphic function f on it with only compact critical locus, I will describe an L^2 theoretic approach to study the deformation theory of this Landau-Ginzburg mode...

Title:Landau-Ginzburg model via L^2-Hodge theory

Speaker: 文豪 清华大学丘成桐数学中心博士后

Time: 2019.5月22日 下午三点到五点

Location: Center for Mathematical Sciences, Room 813


Abstract:

Given a non-compact Calabi-Yau manifold X and a holomorphic function f on it with only compact critical locus, I will describe an L^2 theoretic approach to study the deformation theory of this Landau-Ginzburg model. Concretely, the notion of f-twisted Sobolev spaces is introduced when f satisfies an asymptotic condition and it is then used to prove the Hodge-to-de Rham degeneration property. This leads to a Frobenius manifold structure via the Barannikov-Kontsevich construction and unifies the Landau-Ginzburg and Calabi-Yau geometry.