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SUMMARY:Tony Feng (MIT)
DTSTART:20210416T220000Z
DTEND:20210416T230000Z
DTSTAMP:20260423T024738Z
UID:UCSBsga/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSBsga/19/"
 >Higher Siegel-Weil formulas over function fields</a>\nby Tony Feng (MIT) 
 as part of UCSB Seminar on Geometry and Arithmetic\n\n\nAbstract\nThe Sieg
 el-Weil formula relates the integral of a theta function along a classical
  group H to a special value of a Siegel-Eisenstein series on another group
  G. Kudla proposed an "arithmetic analogue" of the Siegel-Weil formula\, r
 elating intersection numbers of special cycles on Shimura varieties for H 
 to the first derivative at a special value of a Siegel-Eisenstein series o
 n G. We study a function field analogue of this problem in joint work with
  Zhiwei Yun and Wei Zhang. We define special cycles on moduli stacks of un
 itary shtukas\, construct associated virtual fundamental classes\, and rel
 ate their degrees to the derivatives to *all* orders of Siegel-Eisenstein 
 series. The results can be seen as “higher derivative” analogues of th
 e Kudla-Rapoport Conjecture. A key to the proof is a categorification of l
 ocal density formulas for Fourier coefficients of Eisenstein series\, and 
 a parallel categorification of the degrees of virtual fundamental classes 
 of special cycles\, in terms of a global variant of Springer theory.\n
LOCATION:https://researchseminars.org/talk/UCSBsga/19/
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