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SUMMARY:Siddharth Sankaran (U. Manitoba)
DTSTART:20210413T160000Z
DTEND:20210413T170000Z
DTSTAMP:20260423T024513Z
UID:GNTRT/11
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GNTRT/11/">G
 reen forms\, special cycles and modular forms.</a>\nby Siddharth Sankaran 
 (U. Manitoba) as part of Geometry\, Number Theory and Representation Theor
 y Seminar\n\n\nAbstract\nShimura varieties attached to orthogonal groups (
 of which modular curves are examples) are interesting objects of study for
  many reasons\, not least of which is the fact that they possess an abunda
 nce of “special” cycles. These cycles are at the centre of a conjectur
 al program proposed by Kudla\; roughly speaking\, Kudla’s conjectures su
 ggest that upon passing to an (arithmetic) Chow group\, the special cycles
  behave like the Fourier coefficients of automorphic forms. These conjectu
 res also include more precise identities\; for example\, the arithmetic Si
 egel-Weil formula relates arithmetic heights of special cycles to derivati
 ves of Eisenstein series. In this talk\, I’ll describe a construction (i
 n joint work with Luis Garcia) of Green currents for these cycles\, which 
 are an essential ingredient in the “Archimedean” part of the story\; I
 ’ll also sketch a few applications of this construction to Kudla’s con
 jectures.\n
LOCATION:https://researchseminars.org/talk/GNTRT/11/
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