Speaker: George Stepaniants (University of Cambridge)
Title: A Shortcake Counterexample to the Planar Pompeiu and Schiffer Conjectures
Abstract: The Pompeiu and Schiffer conjectures are longstanding problems in integral and spectral geometry with deep connections to the theory of deconvolution and overdetermined eigenvalue problems arising in scattering theory and incompressible flows. We present a computer-assisted construction of a noncircular planar domain with real-analytic boundary that provides a counterexample to both conjectures, and discuss the implications of this result.