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SUMMARY:Laura Schaposnik (University of Illinois at Chicago)
DTSTART:20211214T150000Z
DTEND:20211214T160000Z
DTSTAMP:20260423T021423Z
UID:ZAG/172
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/172/">Th
 e geometry of Generalized Hyperpolygons\, Hitchin systems and other scient
 ific advances</a>\nby Laura Schaposnik (University of Illinois at Chicago)
  as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstract\nIn this t
 alk we will introduce generalized hyperpolygons\, which arise as Nakajima-
 type representations of a comet-shaped quiver\, following recent work join
 t with Steven Rayan. After showing how to identify these representations w
 ith pairs of polygons\, we shall associate to the data an explicit meromor
 phic 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 d
 eveloped within that set up to study geometric properties of integrable sy
 stems and their dualities. Finally\, we shall conclude the talk mentioning
  other directions in which one can apply geometric insights to make scient
 ific advances.\n
LOCATION:https://researchseminars.org/talk/ZAG/172/
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