Cohomology of the general linear group and values of the zeta function

21.11.2023 13:15 - 14:45

Francis Brown (U Oxford)

The subject of this talk lies at the intersection of many subjects, including the moduli spaces of tropical curves, abelian varieties, graph complexes and the symmetric space of the general linear group \(GL_n(\mathbb Z)\).

I will first recall some very classical constructions on quadratic forms due to Voronoi, volume integrals due to Minkowski, and the theory of invariant differential forms of Cartan. Then by constructing suitable algebro-geometric compactifications of the spaces mentioned above, one can exhibit infinitely many new cohomology classes in the unstable cohomology of \(SL_n(\mathbb Z), GL_n(\mathbb Z)\).


H. Grobner, A. Minguez-Espallargas, A. Mellit


BZ 2, 2. OG., OMP 1