Title: Bow varieties: geometry, curve counts, and mirror symmetry

Abstract: In physics, 3d mirror symmetry is a duality for pairs of theories whose Higgs and Coulomb branches are interchanged. In mathematics, it descends to a number of conjectures relating enumerative and topological invariants attached to the dual sides. In this talk, I will first explain how to use brane diagrams and Cherkis bow varieties to describe both branches of an affine type A gauge theory. Then, I will discuss the current understanding of mirror symmetry for bow varieties. The talk is based on joint work with Richard Rimanyi and Hunter Dinkins.