BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Anton Zeitlin (Louisiana State University) DTSTART:20200608T191000Z DTEND:20200608T204000Z DTSTAMP:20260521T001952Z UID:BerkeleyStringMathe/3 DESCRIPTION:Title: Geometry of Bethe Equations and q-Opers\nby Anton Zeitlin (Louisiana State University) as part of Informal string-math seminar\n\n\n Abstract\nIntegrable models are known to keep reemerging over time in var ious mathematical incarnations. Recently\, such models based on quantum g roups naturally appeared in the framework of enumerative geometry. In this context the so-called Bethe ansatz equations\, instrumental for finding t he spectrum of the XXZ model Hamiltonian\, naturally show up as constraint s for the quantum K-theory ring of quiver varieties. \n\nIn this talk I wi ll describe another geometric interpretation of Bethe ansatz equations\, w hich is indirectly related to the above. I will introduce the notion of (G \,q)-opers\, the difference analogue of oper connections for simply connec ted group G. I will explain the one-to-one correspondence between (G\,q)-o pers of specific kind and Bethe equations for XXZ models. The key element in this identification is the so-called QQ-system\, which has previously a ppeared in the study of ODE/IM correspondence and the Grothendieck ring of the category O of the relevant quantum algebras. \nI will speculate on h ow that fits into recently proposed quantum q-Langlands correspondence by M. AganŠ°gic\, E. Frenkel and A. Okounkov.\n\nThe talk is based on joint w ork with E. Frenkel\, P. Koroteev and D. Sage ( arXiv:1811.09937\, arXiv:2 002.07344)\n\nzoom link: https://berkeley.zoom.us/j/93328405860?pwd=Um1GbH BCSUJMdUlWWnd0ZVMxQmwwdz09\n LOCATION:https://researchseminars.org/talk/BerkeleyStringMathe/3/ END:VEVENT END:VCALENDAR