Seminario Matematico e Fisico di Milano
https://www.mate.polimi.it/smf/index.php?settore=home&id_link=10
Monday June 21, 5pm
Link
zoom
Speaker: Jacopo De Simoi (University of Toronto)
Title: Dynamical rigidity of convex billiards
Abstract: Convex billiards are a classical topic in conservative
dynamics. Typically, their dynamics is qualitatively very intricate,
since it showcases a coexistence of hyperbolic dynamics and KAM
phenomena. Understanding long-term statistical properties of the
dynamics with the current technology is essentially an
intractable problem. Here I venture in the opposite direction and I will
discuss dynamical inverse problems: how much geometrical information can
be extracted from the dynamics? More precisely: what can be deduced
about the billiard table if one knows the lengths of all periodic
orbits? The quantum version of this question has been famously stated as
“Can one hear the shape of a drum?” In this talk I will review the
latest results and describe the next steps in this direction. This is a
joint project with Vadim Kaloshin.