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SUMMARY:Tony Feng (MIT)
DTSTART:20211005T210000Z
DTEND:20211005T220000Z
DTSTAMP:20260423T024836Z
UID:UAANTS/24
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/24/">
 Higher arithmetic theta series</a>\nby Tony Feng (MIT) as part of Universi
 ty of Arizona Algebra and Number Theory Seminar\n\n\nAbstract\nArithmetic 
 theta series are incarnations of theta functions in arithmetic algebraic g
 eometry. The first examples were constructed by Kudla as generating series
  of special cycles on Shimura varieties. Their conjectural key features ar
 e (1) modularity of the generating series\, and (2) the arithmetic Siegel-
 Weil formula\, relating their enumerative geometry to the first derivative
  of Eisenstein series at special values. In joint work with Zhiwei Yun and
  Wei Zhang\, we construct "higher" arithmetic theta series on moduli space
 s of shtukas\, which we conjecture to also enjoy (1) modularity and (2) a 
 higher arithmetic Siegel-Weil formula relating their enumerative geometry 
 to all derivatives of Eisenstein series at special values. We prove severa
 l results towards these conjectures\, drawing upon ideas from Ngo's proof 
 of the Fundamental Lemma in addition to new ingredients from Springer theo
 ry and derived algebraic geometry.\n
LOCATION:https://researchseminars.org/talk/UAANTS/24/
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