The geometry of Generalized Hyperpolygons, Hitchin systems and other scientific advances

Laura Schaposnik (University of Illinois at Chicago)

14-Dec-2021, 15:00-16:00 (2 years ago)

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. Having made the connection to Hitchin moduli spaces, we will consider different geometric methods developed within that set up to study geometric properties of integrable systems and their dualities. Finally, we shall conclude the talk mentioning other directions in which one can apply geometric insights to make scientific advances.

algebraic geometry

Audience: researchers in the topic


ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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Organizers: Jesus Martinez Garcia*, Ivan Cheltsov*, Jungkai Chen, Jérémy Blanc, Ernesto Lupercio, Yuji Odaka, Zsolt Patakfalvi, Julius Ross, Cristiano Spotti, Chenyang Xu
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