Tian-Todorov theorem for varieties with potentials

by Prof. Tony Pantev (University of Pennsylvania, USA)

Monday 12 May 2014, 16:00 → 17:00 Asia/Kolkata

AG-77 (Colaba Campus)

 I will report on a recent joint work with L. Katzarkov and
M. Kontsevich on the deformation theory of varieties equipped with
holomorphic functions. I will discuss various generalizations of the
unobstructedness
theorem for deformations of compact Calabi-Yau manifolds. In
particular I will explain  a Tian-Todorov theorem for the deformations
of Landau-Ginzburg models and will explain the new Hodge theoretic
statements needed in the proof. I will also discuss the various
definitions of Hodge numbers for non-commutative
Hodge structures of Landau-Ginzburg type and the role they play in
mirror symmetry.