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SUMMARY:On the inverse problem for isometry groups of norms - Emmanuel Bre
 uillard (University of Oxford)
DTSTART:20220728T080000Z
DTEND:20220728T085000Z
UID:TALK176567@talks.cam.ac.uk
DESCRIPTION:&nbsp\;We study the problem of determining when a compact grou
 p can be realized as the group of isometries of a norm on a finite dimensi
 onal real vector space V. &nbsp\;We give a geometric characterization of s
 uch groups in terms of their vector closure. Using factorizations of compa
 ct Lie groups as well as a new characterization of irreducible prehomogene
 ous spaces\, we prove that every compact connected subgroup of linear tran
 sformations can be realized as the connected component of the identity of 
 the isometry group of some norm on V\, except for an explicit list of exce
 ptions.&nbsp\;(joint work with Martin Liebeck\, Assaf Naor and Aluna Rizzo
 li)
LOCATION:Seminar Room 1\, Newton Institute
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