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SUMMARY:Bounding cohomology - David Stewart
DTSTART:20130501T153000Z
DTEND:20130501T163000Z
UID:TALK45011@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:A lot of recent research has sprung out of work on a conjectur
 e of\nGuralnick: There is a constant c such that for any finite group G an
 d\nirreducible\, faithful representation V for G\, the dimension of H^1(G\
 ,V) is\nless than c. This conjecture reduces to the case of simple groups.
  New\ncomputer calculations of F. Lübeck and a student of L. Scott show t
 hat it is\nlikely that the conjecture is wrong\, but if one fixes either t
 he dimension\nof V or the Lie rank of G then there do exist bounds. In the
  latter case the\nresults are due to Parshall--Scott (defining characteris
 tic) and\nGuralnick--Tiep (cross characteristic). The latter is explicit a
 nd the former has now been made explicit by some recent work of A. Parker 
 and\nmyself. There are many more general results\, however. I'll give an o
 verview of the area.\n
LOCATION:MR12
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