20/06/17  Seminario  14:30  15:30  1201 Dal Passo  Livia Corsi  Georgia Tech (Atlanta, USA)  Billiards and rigid rotations
Probably one of the most famous open problems concerning billiard systems is the Birkhoff conjecture: "If a billiard map is integrabile than the boundary of the billiard table is an ellipse". Recently Treschev conjectured that there might exist analytic billiards, different from ellipses, for which the dynamics in the neighborhood of the period2 orbit is conjugated to a rigid rotation, suggesting a very interesting example of local integrability for billiard tables different from ellipses. However the result of Treschev is only formal in the sense that he finds only a formal power series. Our aim is to prove the convergence of such series.
This is a joint work (in progress) with M. Procesi.

20/06/17  Seminario  11:00  13:00  1201 Dal Passo  Rick Miranda  Colorado State University  Matrix reduction approaches to interpolation problems: a review with remarks
About ten years ago M Dumnicki developed some techniques for interpolation problems related to a careful study of the rank of the matrices involved. Using these techniques he was able to extend the state of the art at the time, bringing certain problems into the range of computer analyses; this enabled him to prove that linear systems in the plane satisfied the SGHH conjecture for homogeneous multiplicities up to 42, the record then. We'll review the method, and consider some refinements, and applications to systems with ten points. The talk should be accessible to nonexperts.
