BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alon Dogon (Weizmann Institute) DTSTART:20230117T140000Z DTEND:20230117T160000Z DTSTAMP:20260423T023017Z UID:WienGAGT/33 DESCRIPTION:Title: Hyperlinearity versus flexible Hilbert Schmidt stability for property (T ) groups\nby Alon Dogon (Weizmann Institute) as part of Vienna Geometr y and Analysis on Groups Seminar\n\n\nAbstract\nIn these two talks\, we wi ll present and illustrate a phenomenon\, commonly termed "stability vs. ap proximation"\, that has been present in several works in recent years. \nO n the one hand\, consider the following classical question: Given two almo st commuting matrices/permutations\, are they necessarily close to a pair of commuting matrices/permutations? This turns out to be a typical stabili ty question for groups\, which was introduced by G.N. Arzhantseva and L. P aunescu\, and since then considered in different scenarios for general gro ups. \n\nOn the other hand\, the well known subject of approximation for g roups is of central interest. Various metric approximation properties for groups have been defined by different mathematicians (including M. Gromov\ , A. Connes\, F. Radulescu\, E. Kirchberg....)\, resulting in notions such as sofic and hyperlinear groups\, which have gained importance since thei r inception. Surprisingly\, no counterexamples for failing soficity or hyp erlinearity are known. A somewhat simple observation shows that a group th at is both stable and approximable is residually finite. This yielded a su ccessful strategy for constructing certain non-approximable groups by givi ng ones that are stable but not residually finite. \n\nIn the introductory lecture we will discuss these notions precisely\, and in the research par t we will present classical residually finite groups\, for which establish ing (flexible Hilbert Schmidt) stability would still give non hyperlinear groups.\nThe same phenomenon is also shown to be generic for random groups in certain models.\n LOCATION:https://researchseminars.org/talk/WienGAGT/33/ END:VEVENT END:VCALENDAR