On Banach's isometric subspace problem

• 主讲人：Sergey Ivanov (St. Petersburg Department of Steklov Mathematical Institute)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2023-04-27 20:00 - 2023-04-27 21:00
• 地点： online

Recording: https://disk.pku.edu.cn:443/link/C7DCC1DD2C9C640F862DE94FD472BFC5
Valid Until: 2027-05-31 23:59

 

Abstract: An old problem by Banach asks whether a finite-dimensional Banach space V is necessarily Euclidean if all its hyperplanes are isometric to one another. An equivalent formulation is whether a centered  convex body is necessarily an ellipsoid if all its central cross-sections are affine equivalent. The problem has been solved in some dimensions but the general case remains open. We will discuss a differential geometric approach to the problem, its connections to Finsler geometry, and a recent solution of the case dim V=4, obtained jointly with D.Mamaev and A.Nordskova.

 

Bio: Sergei Ivanov is a Principal Research Fellow at St. Petersburg Department of Steklov Math Institute and the Dean of the Mathematics and Computer Science Department of St.Petersburg State University. He graduated from St.Petersburg State University in 1994, got his PhD in 1996 and Habilitation in 2009. His main research interests are in geometry and dynamical systems. He is a corresponding member of the Russian Academy of Sciences since 2011. He was an invited speaker at the ICM 2010 in Hyderabad. In 2014, he and his co-authors D.Burago and Yu.burago received the Leroy P. Steele Prize from the A.M.S. for their book "A Course in Metric Geometry".