Geometry Seminar: D. Faifman (Tel Aviv)
Geometry Seminar
Speaker: Dmitry Faifman (Tel Aviv)
Title: From uncertainty to rigidity in integral geometry.
Abstract: The Radon and cosine transforms are central to convex and integral geometry, in particular in geometric tomography and convex valuation theory. The range of those operators has been described by Gelfand-Graev-Rosu and Alesker-Bernstein in representation-theoretic terms, and - for the Radon transform - also through a PDE by John, Grinberg, Gonzalez and Kakehi.
Speaker: Dmitry Faifman (Tel Aviv)
Title: From uncertainty to rigidity in integral geometry.
Abstract: The Radon and cosine transforms are central to convex and integral geometry, in particular in geometric tomography and convex valuation theory. The range of those operators has been described by Gelfand-Graev-Rosu and Alesker-Bernstein in representation-theoretic terms, and - for the Radon transform - also through a PDE by John, Grinberg, Gonzalez and Kakehi.
We will discuss a rigidity phenomenon imposed on functions in these ranges, realized through restrictions on their support, or more precisely, a quasianalyticity property of those ranges in the sense of Kazdan. This will lead to the strengthening of classical theorems of Aleksandrov and Funk in geometric tomography, and of Klain and Schneider in convex valuation theory. The results are based on a novel support-type uncertainty principle on grassmannians.