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PRODID:-//Memento EPFL//
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SUMMARY:Cohomology of symmetric and alternating groups
DTSTART:20170509T101500
DTEND:20170509T113000
DTSTAMP:20260916T225603Z
UID:1f4954e4388be73049d4e96e4855e0e1d8ff65a0332c631c316bff9d
CATEGORIES:Conferences - Seminars
DESCRIPTION:Dev Sinha (Oregon)\n\n \nThe homology of symmetric groups has
  been well-known since Nakaoka’s seminal work in 1962 and then Cohen-Lad
 a-May’s reformulation and extension in 1974.  But the cup co-product st
 ructure of the latter relies on Adem relations\, and so has been of limite
 d value in applications\, for example providing no insight as to the numbe
 r of ring generators or existence of nilpotent elements.  For that reason
 \, mathematicians such Madsen\, Milgram\, Magannis\, Adem and ultimately F
 eshbach devoted considerable energy to understanding cup product structure
  in more detail\, building on its beautiful connection to invariant theory
 .\n\nWhat was missing\, from our perspective\, was an induction or transfe
 r product which along with known structures forms a Hopf ring\, first disc
 overed by Strickland and Turner in 1997. Using this\, Giusti\, Salvatore a
 nd myself have a “one-line” description of the mod-two cohomology of s
 ymmetric groups published in 2012\, and Giusti and I have just finished a 
 corresponding presentation for alternating groups\, which is substantially
  more technically challenging.   Such structure occurs for representation
 s of symmetric or alternating groups\, including at finite characteristic\
 , and would be interesting to utilize in that setting.   \n\nIn this tal
 k\, I will give a hands-on introduction to our calculation for symmetric g
 roups and then talk about the broader picture before discussing alternatin
 g groups.\n 
LOCATION:CM 113
STATUS:CONFIRMED
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