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DTSTAMP:20260424T114318Z
UID:1701345600@ist.ac.at
DTSTART:20231130T130000
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DESCRIPTION:Speaker: Dan Petersen\nhosted by Tim Browning \nAbstract: This 
 is a report of joint work with Bergström-Diaconu-Westerland and Miller-Pa
 tzt-Randal-Williams. Based on random matrix theory\, Conrey-Farmer-Keatin
 g-Rubinstein-Snaith have conjectured precise asymptotics for moments of fa
 milies of quadratic L-functions over number fields. There is an extremely 
 similar function field analogue\, worked out by Andrade-Keating. I will ex
 plain that one can relate this problem to understanding the homology of 
 the braid group with symplectic coefficients. With Bergström-Diaconu-West
 erland we compute the stable homology groups of the braid groups with the
 se coefficients\, together with their structure as Galois representations.
  This may be thought of as a hyperelliptic analogue of the Mumford conjec
 ture (Madsen-Weiss theorem) with twisted coefficients. We moreover show 
 that the answer matches the number-theoretic predictions. With Miller-Pat
 zt-Randal-Williams we prove an improved range for homological stability w
 ith these coefficients. Together\, these results imply the conjectured asy
 mptotics for all moments in the function field case\, for all sufficien
 tly large (but fixed) q.
LOCATION:Heinzel Seminar Room (I21.EG.101)\, Office Building West\, ISTA\, 
 ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at 
SUMMARY:Dan Petersen: Moments of families of quadratic L-functions over fun
 ction fields via homotopy theory
URL:https://talks-calendar.ista.ac.at/events/4401
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