Abstract: Let G be a group and let H*(G,Fp) denote the cohomology algebra of G in mod p coefficients. One of the most important theorems about the algebra structure of H*(G,F2) is Serre's theorem of 1965 where he states that if G is not an elementary abelian group, then there exists nontrivial one dimensional classes x1,...,xm in the first cohomology group such that B(x1)B(x2)...B(xm)=0 in the cohomology algebra of G.
I will explain some of the consequences of this theorem in group cohomology and discuss a variation of it for 2-groups.
All necessary definitions will be given so the talk will be accessible to a general audience of algebraic geometers.
 J. P. Serre, Sur la dimension cohomologique des groups profinis, Topology 3 (1965) 413-420.
 J.P. Serre, Une relation dans la cohomologie des p-groups, C.R. Acad. Sci. Paris 304 (1987) 587-590
Place: Bilkent, Mathematics Seminar Room SA-141
Tea and cookies will be served before the talk.