Joined Equidistribution of Arithmetic Objects associated to Planes in Indefinite Quaternary Quadratic Space
Vortrag von Konstantin Andritsch
Datum: 30.04.25 Zeit: 13.30 - 14.30 Raum: ETH HG G 19.1
Recent advances in the understanding of higher-rank diagonalizable actions on homogeneous spaces by Einsiedler and Lindenstrauss have opened the door to natural couplings of distributions of objects like periodic geodesics or complex multiplication points on the modular surface, or the distribution of integer points on large spheres. In this talk we will discuss such a natural coupling by considering an indefinite quaternary quadratic vector space (V, Q). To each rational plane in V one can naturally attach three arithmetic objects which are associated to quadratic forms. The first two objects arise from the plane and its orthogonal complements with respect to Q, the third (accidental) object is constructed via the Clifford algebra of (V, Q). These arithmetic objects lead to tuples consisting of three geodesics and a point. We discuss their constructions and simultaneous equidistribution using the joining classification result of Einsiedler and Lindenstrauss under a splitting condition. This is joint work with Menny Aka and Andreas Wieser.