Event № 222
In this talk I will describe some new arithmetic invariants for pairs of torus orbits on inner forms of PGLn and SLn. These invariants generalize a work of Linnik in rank one and allow us to significantly strengthen results towards the equidistribution of packets of periodic torus orbits on higher rank S-arithmetic quotients. An important aspect of our method is that it applies to packets of periodic orbits of maximal tori which are only partially split.
Packets of periodic torus orbits are natural collections of torus orbits coming from a single rational adelic torus and are closely related to class groups of number fields. This is a generalization due to Einsiedler, Lindenstrauss, Michel and Venkatesh of the natural grouping of periodic geodesics and Hecke points on the modular surface by their discriminant.
A novel aspect of our method is that we are able to utilize the action of the Galois group of the splitting field of the torus.