Mathematical results inspired by physics

Details Mathematical results inspired by physics Mathematical results inspired by physics

2003-04-28

arxiv.org/abs/math/0304460v1

Proceedings of the ICM, Beijing 2002, vol. 3, 457--466

Mathematics

Algebraic Geometry

Scientific paper

I will discuss results of three different types in geometry and topology. (1) General vanishing and rigidity theorems of elliptic genera proved by using modular forms, Kac-Moody algebras and vertex operator algebras. (2) The computations of intersection numbers of the moduli spaces of flat connections on a Riemann surface by using heat kernels. (3) The mirror principle about counting curves in Calabi-Yau and general projective manifolds by using hypergeometric series.

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