Bounding cohomology
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 David Stewart
 Wednesday 01 May 2013, 16:3017:30
 MR12.
If you have a question about this talk, please contact Christopher Brookes.
A lot of recent research has sprung out of work on a conjecture of
Guralnick: There is a constant c such that for any finite group G and
irreducible, faithful representation V for G, the dimension of H^1(G,V) is
less than c. This conjecture reduces to the case of simple groups. New
computer calculations of F. Lübeck and a student of L. Scott show that it is
likely that the conjecture is wrong, but if one fixes either the dimension
of V or the Lie rank of G then there do exist bounds. In the latter case the
results are due to Parshall—Scott (defining characteristic) and
Guralnick—Tiep (cross characteristic). The latter is explicit and the former has now been made explicit by some recent work of A. Parker and
myself. There are many more general results, however. I’ll give an overview of the area.
This talk is part of the Algebra and Representation Theory Seminar series.
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