BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Anton Zeitlin (Louisiana State University)
DTSTART;VALUE=DATE-TIME:20200608T191000Z
DTEND;VALUE=DATE-TIME:20200608T204000Z
DTSTAMP;VALUE=DATE-TIME:20200812T040055Z
UID:BerkeleyStringMathe/3
DESCRIPTION:Title: Geometry of Bethe Equations and q-Opers\nby Anton Zeitl
in (Louisiana State University) as part of Informal string-math seminar\n\
n\nAbstract\nIntegrable models are known to keep reemerging over time in
various mathematical incarnations. Recently\, such models based on quantu
m groups naturally appeared in the framework of enumerative geometry. In t
his context the so-called Bethe ansatz equations\, instrumental for findin
g the spectrum of the XXZ model Hamiltonian\, naturally show up as constra
ints for the quantum K-theory ring of quiver varieties. \n\nIn this talk I
will describe another geometric interpretation of Bethe ansatz equations\
, which is indirectly related to the above. I will introduce the notion of
(G\,q)-opers\, the difference analogue of oper connections for simply con
nected group G. I will explain the one-to-one correspondence between (G\,q
)-opers of specific kind and Bethe equations for XXZ models. The key eleme
nt in this identification is the so-called QQ-system\, which has previousl
y appeared in the study of ODE/IM correspondence and the Grothendieck ring
of the category O of the relevant quantum algebras. \nI will speculate o
n how that fits into recently proposed quantum q-Langlands correspondence
by M. AganŠ°gic\, E. Frenkel and A. Okounkov.\n\nThe talk is based on join
t work with E. Frenkel\, P. Koroteev and D. Sage ( arXiv:1811.09937\, arXi
v:2002.07344)\n\nzoom link: https://berkeley.zoom.us/j/93328405860?pwd=Um1
GbHBCSUJMdUlWWnd0ZVMxQmwwdz09\n
END:VEVENT
END:VCALENDAR