BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander A. Trost (Ruhr University Bochum) DTSTART:20220525T111000Z DTEND:20220525T123000Z DTSTAMP:20260423T024648Z UID:GDS/60 DESCRIPTION:Title: Ele mentary bounded generation for global function fields and some application s\nby Alexander A. Trost (Ruhr University Bochum) as part of Geometry and Dynamics seminar\n\n\nAbstract\nBounded generation (and elementary bou nded generation) are essentially the \nability to write each element of a given group as products with factors from \na finite collection of ”simp le” subgroups of the group in question and with \na uniform bound on the number of factors needed. These somewhat technical \nproperties were init ially introduced in the study of the congruence subgroup \nproperty of ari thmetic groups\, but they traditionally also found applications \nin the r epresentation theory of these groups\, their subgroup growth and \nKazdhan ’s Property (T). Recently however\, there has been renewed interest in \ nthese properties from the area of geometric group theory as bounded eleme ntary \ngeneration appears naturally as a technical assumption in various results \nstudying arithmetic groups ranging from the study of conjugation -invariant \nnorms on\, say\, SLn as well as in the study of the first-ord er theories of \narithmetic groups. Classical results in this area were us ually concerned with \ngroups arising from number fields though and somewh at surprisingly there are \nfew such results for groups arising from globa l function fields. In this talk\, \nI will give a short introduction about the history of bounded generation in \ngeneral and then present a general bounded generation for split Chevalley \ngroups arising from global funct ion fields together with some applications \nif time allows.\n LOCATION:https://researchseminars.org/talk/GDS/60/ END:VEVENT END:VCALENDAR