To Join Zoom Meeting:
Abstract: I will speak about classical results, problems, and recent developments on characterizations of Euclidean spaces among finite-dimensional Banach spaces. I will concentrate on an old problem asking whether an n-dimensional Banach space is necessarily Euclidean if, for some fixed 1 < k < n, all k-dimensional linear subspaces are isometric. Equivalently, the question asks whether an n-dimensional centered convex body all whose k-dimensional central cross-sections are linearly equivalent is necessarily an ellipsoid. The answer is known to be affirmative in some dimensions and unknown in others. Among other things, I will announce a solution (joint with D.Mamaev and A.Nordskova) for n = 4 and k = 3.
The talk is based on a joint work in progress with Florian Naef and Muze Ren.
Bio: Dr. Sergey V. Ivanov is the Chief Scientific Researcher at the St. Petersburg Department of Steklov Mathematical Institute. He is also the Dean and Professor at the Faculty of Mathematics and Computer Sciences, Saint Petersburg State University.
*This talk is a part of the International Conference "GEOMETRY, GROUPS, OPERATOR ALGEBRAS, AND INTEGRABILITY 2022", supported by the Moscow Center of Fundamental and Applied Mathematics