Localization and conjectures from string duality

Kefeng Liu

Mathematical Physics mathscidoc:1912.43112

63-105, 2006
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 Mario-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.
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  title={Localization and conjectures from string duality},
  author={Kefeng Liu},
Kefeng Liu. Localization and conjectures from string duality. 2006. pp.63-105. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221111621998549672.
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