Localization and Conjectures from String Duality

Abstract

We describe the applications of localization methods, in particular the functorial localization formula, in the proofs of several conjectures from string theory. Functorial localization formula pushes the computations on complicated moduli spaces to simple moduli spaces. It is a key technique in the proof of the general mirror formulas, the proof of the Hori-Vafa formulas for explicit expressions of basic hypergeometric series of homogeneous manifolds, the proof of the Mariño-Vafa formula, its generalizations to two partition analogue. We will also discuss our development of the mathematical theory of topological vertex and simple localization proofs of the ELSV formula and Witten conjecture. This is my lecture on the 23rd International Conference of Differential Geometric Methods in Theoretical Physics Tianjin, 20 - 26 August, 2005.

Lecture on the 23rd International Conference of Differential Geometric Methods in Theoretical Physics Tianjin, 20 - 26 August, 2005

References in corpus (8)

• Hodge integrals, Hurwitz numbers, and Symmetric Groups
• A simple proof of Witten conjecture through localization
• A Conjecture on Hodge Integrals
• Topological String Partition Functions as Equivariant Indices
• Two Proofs of a Conjecture of Hori and Vafa
• Mathematical results inspired by physics
• Computing Hodge integrals with one lambda-class
• On A-twisted moduli stack for curves from Witten's gauged linear sigma models