CCMI Seminar – George Stepaniants (University of Cambridge)

George Stepaniants is coming to the Huxley Building on Tuesday 20 October, as part of the CCMI seminar series. He's over from the University of Cambridge, and the talk is titled 'A Shortcake Counterexample to the Planar Pompeiu and Schiffer Conjectures'. It runs from 14:00 to 15:00 in Room 144, on the South Kensington Campus.

If those conjectures sound like a mouthful, here's the gist. The Pompeiu and Schiffer conjectures are long-standing problems in geometry that essentially ask whether a shape can be uniquely identified by certain measurements — like the integrals of functions over its translates and rotates, or the way it vibrates. For a long time, the circle was the only known shape that fit the bill, and the conjectures suggested it might be the only one. Stepaniants is presenting a counterexample: a noncircular planar domain with a real-analytic boundary that breaks both conjectures at once. He calls it a 'shortcake' counterexample, and he built it with computer assistance.

It's not just a mathematical curiosity, either. During the talk, he'll walk through what this result actually means for integral and spectral geometry, and how it touches on the theory of deconvolution and overdetermined eigenvalue problems. Those might sound like niche interests, but they crop up in scattering theory and incompressible flows — the kind of physics that deals with how waves move and how fluids flow. So, while the starting point is a question about shapes, the implications reach into some very practical areas of science.

It's a free session, first come first served, so if you're planning to go, it's worth getting there a bit early to bag a seat. That's Room 144 in the Huxley Building, South Kensington Campus, on Tuesday 20 October from 14:00 to 15:00.