Symplectic resolutions, symplectic duality, and Coulomb branches

TL;DR

This paper surveys recent advances in symplectic resolutions, focusing on symplectic duality and Coulomb branches, with applications to ADE quiver varieties and affine Grassmannian slices.

Contribution

It provides a comprehensive overview of recent developments in symplectic duality, Coulomb branch constructions, and their applications in representation theory.

Findings

Identification of dual pairs of symplectic resolutions

Development of Coulomb branch techniques for studying duality

Connections to quantization, categorification, and enumerative geometry

Abstract

Symplectic resolutions are an exciting new frontier of research in representation theory. One of the most fascinating aspects of this study is symplectic duality: the observation that these resolutions come in pairs with matching properties. The Coulomb branch construction allows us to produce and study many of these dual pairs. These notes survey much recent work in this area including quantization, categorification, and enumerative geometry. We particularly focus on ADE quiver varieties and affine Grassmannian slices.