# On Hikita-Nakajima conjecture for some quiver varieties and Slodowy slices

### APA

Krylov, V. (2023). On Hikita-Nakajima conjecture for some quiver varieties and Slodowy slices. Perimeter Institute. https://pirsa.org/23030118

### MLA

Krylov, Vasily. On Hikita-Nakajima conjecture for some quiver varieties and Slodowy slices. Perimeter Institute, Mar. 31, 2023, https://pirsa.org/23030118

### BibTex

@misc{ pirsa_PIRSA:23030118, doi = {10.48660/23030118}, url = {https://pirsa.org/23030118}, author = {Krylov, Vasily}, keywords = {Mathematical physics}, language = {en}, title = {On Hikita-Nakajima conjecture for some quiver varieties and Slodowy slices}, publisher = {Perimeter Institute}, year = {2023}, month = {mar}, note = {PIRSA:23030118 see, \url{https://pirsa.org}} }

Vasily Krylov Massachusetts Institute of Technology (MIT)

**Collection**

**Talk Type**Scientific Series

**Subject**

## Abstract

Symplectic duality predicts that symplectic singularities should come in pairs. For example, Nakajima quiver varieties are conjecturally dual to BFN Coulomb branches (of the corresponding quiver theories). Another family of potentially symplectically dual pairs was described recently in the works of Losev, Mason-Brown, and Matvieievskyi: they describe symplectically duals to Slodowy slices to nilpotent orbits.

In this talk, we will discuss the Hikita-Nakajima conjecture that relates the geometry of symplectically dual varieties. We will restrict to the cases of certain quiver varieties and Slodowy slices and discuss the picture in these cases.

Based on the joint work with Pavel Shlykov (arXiv:2202.09934) and the work in progress with Do Kien Hoang and Dmytro Matvieievskyi.

Zoom link: https://pitp.zoom.us/j/98651907502?pwd=ODA1K3NKVHFLdkp6TEtaSnJXdThVZz09