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SUMMARY:Andrey Smirnov (University of North Carolina at Chapel Hill)
DTSTART:20201001T185000Z
DTEND:20201001T195000Z
DTSTAMP:20260423T005802Z
UID:GPRTatNU/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GPRTatNU/4/"
 >Quantum difference equations\, monodromies and mirror symmetry</a>\nby An
 drey Smirnov (University of North Carolina at Chapel Hill) as part of Geom
 etry\, Physics\, and Representation Theory Seminar\n\n\nAbstract\nAn impor
 tant enumerative invariant of a symplectic variety $X$ is its vertex funct
 ion. The vertex function is the analog of J-function in Gromov-Witten theo
 ry: it is the generating function for the numbers of rational curves in $X
 $.\n\nIn representation theory these functions feature as solutions of var
 ious $q$-difference and differential equations associated with $X$\, with 
 examples including qKZ and quantum dynamical equations for quantum loop gr
 oups\, Casimir connections for Yangians and other objects.\n\nIn this talk
  I explain how these equations can be extracted from algebraic topology of
  symplectic dual variety $X^!$\, also known as $3D$-mirror of $X$. This ca
 n be summarized as "identity"\n$$\n\\text{Enumerative geometry of }X = \\t
 ext{algebraic topology of }X^!\n$$\nThe talk is based on work in progress 
 with Y.Kononov arXiv:2004.07862\; arXiv:2008.06309.\n
LOCATION:https://researchseminars.org/talk/GPRTatNU/4/
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