# On generalized hyperpolygons, Higgs bundles and branes

### APA

Schaposnik, L. (2021). On generalized hyperpolygons, Higgs bundles and branes. Perimeter Institute. https://pirsa.org/21100011

### MLA

Schaposnik, Laura. On generalized hyperpolygons, Higgs bundles and branes. Perimeter Institute, Oct. 01, 2021, https://pirsa.org/21100011

### BibTex

@misc{ pirsa_PIRSA:21100011, doi = {10.48660/21100011}, url = {https://pirsa.org/21100011}, author = {Schaposnik, Laura}, keywords = {Mathematical physics}, language = {en}, title = {On generalized hyperpolygons, Higgs bundles and branes}, publisher = {Perimeter Institute}, year = {2021}, month = {oct}, note = {PIRSA:21100011 see, \url{https://pirsa.org}} }

Laura Schaposnik University of Illinois at Chicago

**Collection**

**Talk Type**Scientific Series

**Subject**

## Abstract

In this talk we will introduce generalized hyperpolygons, which arise as Nakajima-type representations of a comet-shaped quiver, following recent work with Steven Rayan. After showing how to identify these representations with pairs of polygons, we shall associate to the data an explicit meromorphic Higgs bundle on a

genus-g Riemann surface, where g is the number of loops in the comet. We shall see that, under certain assumptions on flag types, the moduli space of generalized hyperpolygons admits the structure of a completely integrable Hamiltonian system. Finally, we shall look into the appearance of branes within the moduli space of generalized hyperpolygons as well as of Higgs bundles, and consider mirror symmetry for such branes. Time permitting, we will mention some other recent results in various areas of science.

Zoom Link: https://pitp.zoom.us/j/91592778202?pwd=WnM2VS9pS2c0QVIxVWFOdGhFMTdEdz09