On the crossroads of enumerative geometry and geometric representation theory

TL;DR

This paper explores the deep connections between enumerative geometry and geometric representation theory, illustrating key ideas through the example of HilbpC2, nq to inspire further interdisciplinary research.

Contribution

It provides an accessible exposition of the interplay between enumerative geometry and geometric representation theory using a specific illustrative example.

Findings

Deep connections between the subjects are illustrated through HilbpC2, nq

The paper aims to inspire applications across various fields

Provides foundational ideas for further research

Abstract

The subjects in the title are interwoven in many different and very deep ways. I recently wrote several expository accounts [64-66] that reflect a certain range of developments, but even in their totality they cannot be taken as a comprehensive survey. In the format of a 30-page contribution aimed at a general mathematical audience, I have decided to illustrate some of the basic ideas in one very interesting example - that of HilbpC2, nq, hoping to spark the curiosity of colleagues in those numerous fields of study where one should expect applications.