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SUMMARY:Adrian Diaconu
DTSTART:20260317T190000Z
DTEND:20260317T200000Z
DTSTAMP:20260419T152507Z
UID:BC-MIT/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/BC-MIT/31/">
 Moments of quadratic L-functions over function fields</a>\nby Adrian Diaco
 nu as part of BC-MIT number theory seminar\n\nLecture held in Maloney 560 
 at Boston College.\n\nAbstract\nIn 2001\, Conrey\, Farmer\, Keating\, Rubi
 nstein\, and Snaith developed a "recipe" utilizing heuristic arguments to 
 predict the asymptotics of moments of various families of $L$-functions. T
 his heuristic was later extended by Andrade and Keating to include moments
  and ratios of the family of $L$-functions associated to hyperelliptic cur
 ves of genus $g$ over a fixed finite field. In joint work with Bergström\
 , Petersen\, and Westerland\, we related the moment conjecture of Andrade 
 and Keating to the problem of understanding the homology of the braid grou
 p with symplectic coefficients. We computed the stable homology groups of 
 the braid groups with these coefficients\, together with their structure a
 s Galois representations\, and showed that the answer matches the number-t
 heoretic predictions. Our results\, combined with a recent homological sta
 bility theorem of Miller\, Patzt\, Petersen\, and Randal-Williams\, imply 
 the conjectured asymptotics for all moments in the function field case\, f
 or all large enough odd prime powers $q$.\n
LOCATION:https://researchseminars.org/talk/BC-MIT/31/
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