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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:Craig Westerland\nUniversity of Minnesota\n\nAbstract: Question
s about the growth rate of zeta functions and L-functions are a central top
ic in analytic number theory. In 2005\, Conrey\, Farmer\, Keating\, Rubins
tein\, and Snaith posed a conjecture on the asymptotics of moments of quadr
atic L-functions. While these sorts of problems originate as questions abo
ut number fields\, they have a more geometric version when posed over funct
ion fields in positive characteristic. I’ll talk about how one can reinter
pret the central object in this conjecture in terms of the action of the Ga
lois group of a finite field on the cohomology of braid groups with certain
coefficients coming from the braid group’s interpretation as the hyperelli
ptic mapping class group. We will see the “arithmetic factor” in this conj
ecture appear in the part of this cohomology that is accessible through too
ls of homological stability. This is joint work with Jonas Bergström\, Adr
ian Diaconu\, and Dan Petersen.
DTEND:20230426T233000Z
DTSTAMP:20240724T234917Z
DTSTART:20230426T223000Z
GEO:34.022409;-118.291027
LOCATION:Kaprielian Hall (KAP)\, 414
SEQUENCE:0
SUMMARY:Mathematics Colloquium: Moments of L-functions via the homology of
braid groups
UID:tag:localist.com\,2008:EventInstance_42977239120923
URL:https://calendar.usc.edu/event/mathematics_colloquium_moments_of_l-func
tions_via_the_homology_of_braid_groups
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