On generalized hyperpolygons

Speaker: 
Laura Schaposnik
Date: 
Thu, Jun 25, 2020
Location: 
Zoom
Conference: 
Qolloquium: A One-Day Conference on Quivers, Representations, Resolutions
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 (arXiv:2001.06911). 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. Time permitting, we shall conclude the talk by mentioning some partial results on current work on the construction of triple branes (in the sense of Kapustin-Witten mirror symmetry), and dualities between tame and wild Hitchin systems (in the sense of Painlevé transcendents).

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