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SUMMARY:Jethro van Ekeren (Instituto de Matemática Pura e Aplicada (IMPA)
 )
DTSTART:20230816T070000Z
DTEND:20230816T083000Z
DTSTAMP:20260422T161058Z
UID:HKUST-AG/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HKUST-AG/11/
 ">Chiral homology\, the Zhu algebra\, and Rogers-Ramanujan</a>\nby Jethro 
 van Ekeren (Instituto de Matemática Pura e Aplicada (IMPA)) as part of Al
 gebra and Geometry Seminar @ HKUST\n\nLecture held in Room 5506.\n\nAbstra
 ct\nGraded dimensions of rational vertex algebras are modular functions. T
 he proof of this celebrated theorem by Y. Zhu centres on geometric objects
  attached to elliptic curves known as conformal blocks\, and their behavio
 ur in the limit as the underlying curve becomes singular. In this limit\, 
 roughly speaking\, conformal blocks pass to the degree zero Hochschild hom
 ology of Zhu's associative algebra. On the other hand\, conformal blocks h
 ave been interpreted by Beilinson and Drinfeld as the degree zero componen
 t of a theory of chiral homology. It is therefore natural to wonder if the
  relationship extends to higher homological degrees. We are indeed able to
  extend this story to homological degree 1 for classically free vertex alg
 ebras\, and in the process we discover relations with objects of number th
 eory such as the Rogers-Ramanujan identity and its generalisations. This i
 s joint work with R. Heluani and G. Andrews.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/11/
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