Bartolomiej Zawalski (Kent State University)

Title: ON STAR-CONVEX BODIES WITH ROTATIONALLY INVARIANT SECTIONS

Abstract: We will outline the proof that an origin-symmetric star-convex body K with sufficiently smooth boundary and such that every hyperplane section of K passing through the origin is a body of affine revolution, is itself a body of affine revolution. This will give a positive answer to the question asked by G. Bor, L. Hernández-Lamoneda, V. Jiménez de Santiago, and L. Montejano-Peimbert in their recent paper on the isometric Banach’s conjecture, though with slightly different prerequisites. The theorem may be also seen as a high-dimensional variant of Bezdek’s conjecture. Our argument is built mainly upon the tools of differential geometry and linear algebra, but occasionally we will need to use some more involved facts from other fields like algebraic topology or commutative algebra

Where: Pavillion André-Aisenstadt, room 5183

Join Zoom Meeting

https://umontreal.zoom.us/j/89528730384?pwd=IF10Cg8C0YfogaBlL6F1NboPaQvAaV.1

Meeting ID: 895 2873 0384

Passcode: 077937