BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Skenderi (UW Madison) DTSTART:20260205T171500Z DTEND:20260205T183000Z DTSTAMP:20260423T021931Z UID:NEDNT/100 DESCRIPTION:Title: Asymptotically large free semigroups in Zariski dense discrete subgroups o f Lie groups\nby Alexander Skenderi (UW Madison) as part of New Englan d Dynamics and Number Theory Seminar\n\nLecture held in Online.\n\nAbstrac t\nAn important quantity in the study of discrete groups of isometries of Riemannian manifolds\, Gromov hyperbolic spaces\, and other interesting ge ometric objects is the critical exponent. For a discrete subgroup of isome tries of the quaternionic hyperbolic space or octonionic projective plane\ , Kevin Corlette established in 1990 that the critical exponent detects wh ether a discrete subgroup is a lattice or has infinite covolume. Precisely \, either the critical exponent equals the volume entropy\, in which case the discrete subgroup is a lattice\, or the critical exponent is less than the volume entropy by some definite amount\, in which case the discrete s ubgroup has infinite covolume. In 2003\, Leuzinger extended this gap theor em for the critical exponent to any discrete subgroup of a Lie group havin g Kazhdan’s property (T) (for instance\, a discrete subgroup of SL(n\,R) \, where n is at least 3).\nIn this talk\, I will present a result which s hows that no such gap phenomenon holds for discrete semigroups of Lie grou ps. More precisely\, for any Zariski dense discrete subgroup of a Lie grou p\, there exist free\, finitely generated\, Zariski dense subsemigroups wh ose critical exponents are arbitrarily close to that of the ambient discre te subgroup.\nAs an application\, we show that the critical exponent is lo wer semicontinuous in the Chabauty topology whenever the Chabauty limit of a sequence of Zariski dense discrete subgroups is itself a Zariski dense discrete subgroup.\n LOCATION:https://researchseminars.org/talk/NEDNT/100/ END:VEVENT END:VCALENDAR