Bounding cohomology

David Stewart (Newcastle)

Frank Adams 1,

A conjecture of Guralnick states that there is a universal upper bound on the dimension of the first cohomology group of a finite group with coefficients in a faithful irreducible module. While this conjecture is now regarded as very unlikely to be true, it has nonetheless inspired a lot of work on finding bounds for cohomology based either on the dimension of the module or something about the group. I'll give a broad overview of this area, including work with Brian Parshall and Len Scott, with Alison Parker and some work of my PhD Student John Rizkallah.

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