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SUMMARY:The Cohen–Lenstra moments for functions fields and stable homolo
 gy of Hurwitz spaces [MPIM]
DTSTART:20250120T130000Z
DTEND:20250120T140000Z
DTSTAMP:20260514T015400Z
UID:indico-event-197@math-events.uni-bonn.de
DESCRIPTION:Speakers: Ishan Levy (University of Copenhagen)\n\nMPIM Topolo
 gy Seminar\nThe Cohen--Lenstra heuristics predict the distribution of the 
 odd part of class groups of quadratic fields\, and are one of the driving 
 conjectures in arithmetic statistics. I will explain work with Aaron Lande
 sman\, where we compute the moments of the Cohen–Lenstra distribution fo
 r function fields\, when the size of the finite field is sufficiently larg
 e (depending on the moment). We follow an approach to this problem due to 
 Ellenberg–Venkatesh–Westerland\, and the key new input is the computat
 ion of the stable rational homology of Hurwitz spaces associated to certai
 n conjugacy classes in generalized dihedral groups. I will explain the ide
 as in our computation of the stable homology in the case of the dihedral g
 roup of order 6 with conjugacy class transpositions. \n \n\nhttps://math
 -events.uni-bonn.de/event/197/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/197/
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