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DTSTART:20190331T030000
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DTSTAMP:20190821T141529Z
UID:5c3337d55851b553917812@ist.ac.at
DTSTART:20190124T133000
DTEND:20190124T153000
DESCRIPTION:Speaker: Will Sawin\nhosted by Timothy Browning\nAbstract: Deli
gne proved the Ramanujan conjecture bounding the Hecke eigenvalues of modu
lar forms by constructing two-dimensional Galois representations associate
d to them. The same strategy was used by Laurent Lafforgue to prove the Ra
manujan conjecture for automorphic forms on GL_n over function fields as a
corollary of his proof of the Langlands correspondence\, building on idea
s of Drinfeld who handled the GL_2 case. With Nicolas Templier\, we have a
different approach to proving the Ramanujan conjecture over function fiel
ds\, based on estimating the trace of the Hecke operator on a whole family
of automorphic forms at once. Our main tools are from geometry\, but a di
fferent sort of geometry than the proofs of Drinfeld and Lafforgue - we us
e the moduli space of G-bundles\, rather than the moduli space of shtukas.
We can prove the conjecture under two conditions (one local condition and
one assumption about cyclic base change).
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
T Austria
ORGANIZER:lmarr@ist.ac.at
SUMMARY:On the Ramanujan conjecture over function fields
URL:https://talks-calendar.app.ist.ac.at/events/1764
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