PIRSA:21020032

On generalized hyperpolygons

APA

Schaposnik, L. (2021). On generalized hyperpolygons. Perimeter Institute. https://pirsa.org/21020032

MLA

Schaposnik, Laura. On generalized hyperpolygons. Perimeter Institute, Feb. 23, 2021, https://pirsa.org/21020032

BibTex

          @misc{ pirsa_21020032,
            doi = {10.48660/21020032},
            url = {https://pirsa.org/21020032},
            author = {Schaposnik, Laura},
            keywords = {Mathematical physics},
            language = {en},
            title = {On generalized hyperpolygons},
            publisher = {Perimeter Institute},
            year = {2021},
            month = {feb},
            note = {PIRSA:21020032 see, \url{https://pirsa.org}}
          }
          

Laura Schaposnik University of Illinois at Urbana-Champaign (UIUC)

Abstract

In this talk we will introduce generalized hyperpolygons, which arise as Nakajima-type representations of a comet-shaped quiver, following recent work joint 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.