Gromov--Witten invariants and quantum cohomology

TL;DR

This paper introduces quantum cohomology using Gromov--Witten invariants, explaining the concepts to a broad audience and highlighting their significance in modern geometry and mathematical physics.

Contribution

It provides an accessible exposition of quantum cohomology based on Gromov--Witten invariants, aimed at a general audience and prospective researchers.

Findings

Overview of Gromov--Witten invariants and quantum cohomology

Connections between quantum cohomology and operator theory

Foundational ideas for future research in the field

Abstract

This article is an elaboration of a talk given at an international conference on Operator Theory, Quantum Probability, and Noncommutative Geometry held during December~20--23, 2004, at the Indian Statistical Institute, Kolkata. The lecture was meant for a general audience, and also prospective research students, the idea of the quantum cohomology based on the Gromov--Witten invariants. Of course there are many important aspects that are not discussed here.