BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Prof. Alex Lubotzky (Einstein Institute of Mathematics\, Hebrew Un iversity) DTSTART:20210113T123000Z DTEND:20210113T133000Z DTSTAMP:20260423T005726Z UID:tmc-dls/7 DESCRIPTION:Title: Stability\, non-approximate groups\, and high dimensional expanders\nb y Prof. Alex Lubotzky (Einstein Institute of Mathematics\, Hebrew Universi ty) as part of TMC Distinguished Lecture Series\n\n\nAbstract\nSeveral wel l-known open questions (such as: are all groups sofic or hyperlinear?) hav e a common form: can all groups be approximated by asymptotic homomorphism s into the symmetric groups Sym(n) (in the sofic case) or the unitary grou ps U(n) (in the hyperlinear case)?\nIn the case of U(n)\, the question can be asked with respect to different metrics and norms. We answer\, for the first time\, one of these versions\, showing that there exist finitely pr esented groups which are not approximated by U(n) with respect to the Frob enius (=L2) norm.\nThe strategy is via the notion of 'stability': some hi gher dimensional cohomology vanishing phenomena is proven to imply stabili ty and using higher dimensional expanders\, it is shown that some non-resi dually finite groups (central extensions of some lattices in p-adic Lie gr oups) are Frobenious stable and hence cannot be Frobenius approximated.\nA ll notions will be explained. Joint work with M. De Chiffre\, L. Glebsky a nd A. Thom.\n LOCATION:https://researchseminars.org/talk/tmc-dls/7/ END:VEVENT END:VCALENDAR