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University of Cambridge > Talks.cam > Junior Geometry Seminar > On Banach’s isometric subspaces problem

## On Banach’s isometric subspaces problemAdd to your list(s) Download to your calendar using vCal - Daniil Mamaev, PDMI RAS and LSGNT
- Wednesday 24 May 2023, 16:00-17:00
- MR13.
If you have a question about this talk, please contact aj616. Is a normed vector space V whose n-dimensional linear subspaces are all isometric, for a fixed 2 <= n < dim V, necessarily Euclidean? This question was asked in 1932 by S. Banach and in the known cases the answer is always affirmative. In a joint work with S. Ivanov and A. Nordskova we handle `the smallest’ previously unresolved case n = 3, but the problem remains open for n 1 = dim V = 4k >= 8 and n 1= dim V = 134. I will start by formulating the problem in a couple equivalent ways, then give an overview of previous partial results, and proceed by sketching the proof in the case n = 3. If time permits, I will also discuss the local (stronger) version of the problem and its application to Finsler geometry. This talk is part of the Junior Geometry Seminar series. ## This talk is included in these lists:- All CMS events
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