Algebra/topology seminar

Speaker: Anssi Lahtinen (Hamburg)

Title: Modular characteristic classes for representations over finite fields

Abstract: While the cohomology groups of the general linear group GL_n(F) over a
finite field F of characteristic p have been completely computed by
Quillen with coefficients in a field of characteristic different from
p, little is known about the cohomology groups of GL_n(F) in the
modular case where the coefficient field is also of characteristic p.
In this talk, I will report on joint work in progress with David
Sprehn which sheds light on these modular cohomology groups by
constructing a new system of characteristic classes for
representations over finite fields. In particular, our work provides
explicit nontrivial elements in the cohomology of GL_n(F) in degrees
linear in n, in contrast with the lowest-dimensional non-trivial
elements known so far, which reside in degrees exponential in n.