The inverse spectral problem for strictly convex domains
Recent developments in microlocal analysis October 14, 2019 - October 18, 2019
Location: MSRI: Simons Auditorium
In this talk I will discuss the recent developments in the inverse spectral theory of bounded planner domains with strictly convex smooth boundaries. I will first present a joint work with Steve Zelditch in which we prove ellipses of small eccentricity are spectrally unique among all smooth domains. I will then discuss an inverse spectral result for nearly circular domains with an axial symmetry. A linearized version of this problem was studied by De Simoi, Kaloshin, and Wei. The non-linear problem is more interesting and uses second variations of the length functions and also some techniques of Avila, De Simoi, and Kaloshin
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