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SUMMARY:Siddarth Sankaran (University of Manitoba)
DTSTART:20211126T200000Z
DTEND:20211126T210000Z
DTSTAMP:20260423T053048Z
UID:ANTULaval/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTULaval/6/
 ">Green forms\, special cycles and modular forms</a>\nby Siddarth Sankaran
  (University of Manitoba) as part of Algebra and Number Theory Seminars at
  Université Laval\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 abundance of “special” cycles. These cycles are at the centre of a 
 conjectural program proposed by Kudla\; roughly speaking\, Kudla’s conje
 ctures suggest that upon passing to an (arithmetic) Chow group\, the speci
 al cycles behave like the Fourier coefficients of automorphic forms. These
  conjectures also include more precise identities\; for example\, the arit
 hmetic Siegel-Weil formula relates arithmetic heights of special cycles to
  derivatives of Eisenstein series. In this talk\, I’ll describe a constr
 uction (in 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 Kudl
 a’s conjectures.\n
LOCATION:https://researchseminars.org/talk/ANTULaval/6/
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