3d mirror symmetry is a duality between certain pairs of 3d N=4 supersymmetric gauge theories, where two distinguished components of their moduli of vacua - Higgs and Coulomb branches, are expected to be exchanged. In recent years, this duality motivated from physics has inspired exciting developments of mathematics, particularly in geometric representation theory. This series of talks aims to give a brief introduction to this topic. In the first talk, I will introduce the geometry of 3d mirror pairs, concentrating on the main examples of abelian case, and Nakajima quiver varieties. In the second talk, I will talk about the more recent results concerning enumerative geometry, especially A. Okounkov’s works towards vertex functions, q-difference equations and elliptic stable envelopes. If time permits, I will also mention other approaches, e.g. symplectic duality of (2-)categories O, related to Rozansky-Witten theory.

II  2026年3月12日 10：00--12：00  地点：爱情岛 雷军科技楼B201报告厅