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SUMMARY:Adrian Ioana (UCSD)
DTSTART:20220315T140000Z
DTEND:20220315T160000Z
DTSTAMP:20260423T041009Z
UID:WienGAGT/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WienGAGT/10/
 ">Almost commuting matrices and stability for product groups</a>\nby Adria
 n Ioana (UCSD) as part of Vienna Geometry and Analysis on Groups Seminar\n
 \n\nAbstract\nI will present a result showing that the direct product grou
 p \\(G=\\mathbb F_2\\times\\mathbb F_2\\)\, where \\(\\mathbb F_2\\) is th
 e free group on two generators\, is not Hilbert-Schmidt stable. This means
  that \\(G\\) admits a sequence of asymptotic homomorphisms (with respect 
 to the normalized Hilbert-Schmidt norm) which are not perturbations of gen
 uine homomorphisms.  While this result concerns unitary matrices\, its pro
 of relies on techniques and ideas from the theory of von Neumann algebras.
  I will also explain how this result can be used to settle in the negative
  a natural version of an old question of Rosenthal concerning almost commu
 ting matrices. More precisely\, we derive the existence of contraction mat
 rices \\(A\,B\\) such that \\(A\\) almost commutes with \\(B\\) and \\(B^*
 \\) (in the normalized Hilbert-Schmidt norm)\, but there are no matrices \
 \(A’\,B’\\) close to \\(A\,B\\) such that \\(A’\\) commutes with \\(
 B’\\) and \\(B’*\\).\n
LOCATION:https://researchseminars.org/talk/WienGAGT/10/
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