Applied Math Colloquium with Dr. George Stepaniants, University of Cambridge

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.
 

Preprint:

https://arxiv.org/pdf/2608.01579
 

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.