Equidistribution of intersections with homogeneous subspaces

Seminar: 
Group Actions and Dynamics
Event time: 
Monday, November 8, 2021 - 10:15am
Location: 
Zoom
Speaker: 
Nicolas Tholozan
Speaker affiliation: 
École Normale Supérieure
Event description: 
I will discuss the following general problem in homogeneous dynamics: Let G be a semisimple Lie group, K a compact subgroup of G and Γ a lattice in G. Let On be an equidistributing sequence of locally homogeneous subspaces of ΓG/K. What is the distribution of the intersection of On with a fixed analytic subspace V?
 
In a joint work with Salim Tayou, we show that, under the correct hypotheses, this intersection equidistributes towards a certain G-invariant form on G/K. Determining this form leads to an interesting question about the cohomology of compact homogeneous spaces. This result has interesting applications in arithmetics and in Hodge theory, which I will mention briefly if time permits.