Speaker:	Yukiko Konishi (Kyoto University)
Title:	Local B-model and mixed Hodge structure
Date (JST):	Mon, Nov 22, 2010, 14:00 - 17:00
Place:	Seminar Room A
Abstract:	Given a two-dimensional reflexive polyhedron, we are able to construct: (i) three-dimensional fan and the associated noncomplete toric variety; (ii) Gelfand-Kapranov-Zelevinsky's hypergeometric system; and (iii) a family of Laurent polynomials whose Newton polyhedron is the given polyhedron and thus a family of affine curves in two-dimensional algebraic torus. The statement of the local mirror symmetry is that both (i) (the genus zero local Gromov-Witten invariants of the toric variety;the local A-model) and (iii)(the variation of mixed Hodge structures (VMHS) of the relative cohomology of the affine curve and its ambient space;the local B-model) are governed by (ii). I would like to talk about my joint work with Satoshi Minabe on a definition of the Yukawa coupling for the local B-model [Local B-model and Mixed Hodge Structure, arXiv:0907.4108]. In Part I, I will explain the VMHS. It has a description by a Jacobian ring due to Batyrev and Stienstra. In Part II, I will give our definition of the Yukawa coupling. If time permits, I would like to explain how to modify Bershadsky-Cecotti-Ooguri-Vafa's holomorphic anomaly equation to the local B-model.

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