# Action Now Seminar: Menny Aka (ETH), "On rational planes in four-dimensional space and their associated lattices"

To any two-dimensional rational plane in four-dimensional space, one can naturally attach a point in the Grassmannian $\operatorname{Gr}(2,4)$ and four lattices of rank two (each corresponding to a point on the modular surface). Here, the first two originate from the lattice of integer points in the plane and its orthogonal complement and the second two essentially arise from the accidental local isomorphism between $\operatorname{SO}(4)$ and $\operatorname{SU}(2)^2$.

We prove the simultaneous equidistribution of all of these objects, which is an application of a recent result of Einsiedler and Lindenstrauss on algebraicity of joinings on the product of rank one groups.
I will explain the natural construction of these associated four lattices of rank 2, formulate an equivalent equidistribution statement in homogeneous dynamics and explain how the latter follows from Einsiedler-Lindenstrauss result.

This is a joint work with Manfred Einsiedler and Andreas Wieser.

## Date:

Tue, 30/01/2018 - 16:00 to 17:00

## Location:

IIAS, HUJI, Feldman Building, Room 130