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SUMMARY:Gurbir Dhillon (Yale University)
DTSTART:20220914T200000Z
DTEND:20220914T210000Z
DTSTAMP:20260414T174102Z
UID:BUGeom/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BUGeom/38/">
 The log Kazhdan--Lusztig correspondence</a>\nby Gurbir Dhillon (Yale Unive
 rsity) as part of Boston University Geometry/Physics Seminar\n\nLecture he
 ld in Zoom meeting ID: 953 4652 9200.\n\nAbstract\nA landmark discovery of
  the 1980s\, due to many mathematicians and\nphysicists (Drinfeld\, Kohno\
 , Witten\, etc.)\, was the close relationship between quantum groups and a
 ffine Lie algebras. Kazhdan–Lusztig established a sharp form of\nthis in
  representation theory via an equivalence of braided tensor categories of 
 modules. The subtlest cases of their result occur when the quantum paramet
 er q is\na root of unity\, where one has to pick the right form of the qua
 ntum group (the\nso-called Lusztig\, or divided-powers form) in order for 
 the equivalence to hold. In\nthe mid-2000s\, Feigin–Gainutdinov–Semikh
 atov–Tipunin conjectured a similar ‘log\nKazhdan–Lusztig corresponde
 nce’ between representations of another version of the\nquantum group\, 
 the small quantum group\, and a vertex algebra known as the triplet\,\nat 
 certain roots of unity. After providing a survey of these influential work
 s for nonspecialists\, we will propose a conjecture extending that of Feig
 in et. al. to all roots\nof unity. Time permitting\, we will indicate a wa
 y to prove it conditional on some\nfoundational conjectures in quantum geo
 metric Langlands.\n
LOCATION:https://researchseminars.org/talk/BUGeom/38/
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