BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Theo Douvropoulos (University of Massachusetts at Amherst) DTSTART:20230508T130000Z DTEND:20230508T140000Z DTSTAMP:20260423T021334Z UID:GANT/28 DESCRIPTION:Title: Re cursions and Proofs in Coxeter-Catalan combinatorics\nby Theo Douvropo ulos (University of Massachusetts at Amherst) as part of Greek Algebra & N umber Theory Seminar\n\n\nAbstract\nIn a significant --yet absolutely unde rstandable-- deviation from traditions of logic\, secularism\, and platoni c dialectic\, combinatorialists the world around have celebrated Catalan o bjects with a reverence better suited to mystical\, preternatural endeavor s. Various sects have been formed through the years by mathematicians who study particular aspects of the Catalan doctrine\, including the Coxeter-C atalan sect of which the speaker might be a member.\n\nOne of the central objects in Coxeter-Catalan combinatorics is the noncrossing partition latt ice $NC(W)$ associated to a finite Coxeter group $W$ and its sibling objec t\, the cluster complex $Y(W)$. These two objects encode much of the geome tric group theory\, combinatorics\, and representation theory of $W$\, and they have fascinating stuctural and enumerative properties\; in particula r\, the zeta polynomials of certain intervals in $NC(W)$ and the (almost) colored $f$-vectors of $Y(W)$ all have product formulas given in terms of invariants of $W$ (generalizing formulas of Kreweras and Loday for the sym metric group case). A central open problem in the area since at least the early 2000's has been to give case-free proofs of these product formulas\, i.e. proofs that do not depend on the classification of finite Coxeter gr oups. In this talk\, I will present the first such proof\, in collaboratio n with Matthieu Josuat-Verges\, solving the more general Fuss version of t he problem\; in our approach\, we develop a collection of recursions that are shown to be satisfied by both the combinatorial objects and the produc t formulas.\n LOCATION:https://researchseminars.org/talk/GANT/28/ END:VEVENT END:VCALENDAR