Mathematical results inspired by physics

TL;DR

This paper explores mathematical results inspired by physics, including vanishing theorems, intersection number computations, and curve counting in Calabi-Yau manifolds, connecting geometry, topology, and theoretical physics.

Contribution

It introduces new results linking modular forms, algebraic structures, and geometric computations inspired by physical theories.

Findings

Proved vanishing and rigidity theorems of elliptic genera using modular forms and algebraic structures.

Computed intersection numbers of moduli spaces of flat connections via heat kernel methods.

Applied hypergeometric series to count curves in Calabi-Yau and projective manifolds.

Abstract

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.