Olivier Taïbi: Unimodular lattices and the cuspidal cohomology of GL_n(Z)

Abstract: 

I will explain the relation between the classification of unimodular euclidean lattices (and other genera) and the computation of the cuspidal cohomology of \(\mathrm{GL}_n(\mathbb{Z})\), motivated by the following open problem: what is the smallest integer \(n\) such that \(H_{\mathrm{cusp}}^*(\mathrm{GL}_n(\mathbb{Z}), \mathbb{Q})\) is non-zero? I will present recent progress on these questions (joint work with Gaëtan Chenevier).