Speaker: Dr. 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.
Bio: George Stepaniants is an Assistant Professor in the Department of Applied Mathematics and Theoretical Physics at the University of Cambridge. Previously, he was an NSF Mathematical Sciences Postdoctoral Research Fellow in Computing and Mathematical Sciences at Caltech and received his PhD in Mathematics from MIT in 2024. His research spans applied analysis, inverse problems, optimal transport, and scientific machine learning.
In person attendance at this seminar is only open to Columbia University affiliates. External guests are welcome to attend remotely. Please contact [email protected] if you need the Zoom link for this seminar.