BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Selman Ipek (Bilkent University) DTSTART:20241118T103000Z DTEND:20241118T113000Z DTSTAMP:20260422T140000Z UID:BilTop/95 DESCRIPTION:Title: Simplicial distributions and polyhedral geometry\nby Selman Ipek (Bilk ent University) as part of Bilkent Topology Seminar\n\nLecture held in SA 141.\n\nAbstract\nSimplicial distributions are collections of probability distributions that satisfy certain compatibility conditions that can be en coded topologically using simplicial sets. For a simplicial scenario where the measurement space X and outcome space Y are finitely generated the sp ace sDist(X\,Y) of allowed simplicial distributions is a convex set\, in f act\, a convex polytope. By the Minskowski-Weyl theorem of polytope theory it is well-known that there are two equivalent descriptions of a convex p olytope as the intersection of finitely many half-space inequalities (H-re presentation) or as the convex hull of finitely many extreme points (V-rep resentation). In this talk we detail how one constructs the H-representati on of sDist(X\,Y) and discuss the conversion to its V-representation\, kno wn as the vertex enumeration problem. Time permitting\, we will also discu ss the Bell polytope\, which delineates the boundary between contextual an d noncontextual measurement statistics\, and is a subpolytope of sDist(X\, Y).\n\n(This talk is part of the reading seminar series on the theory and applications of simplicial distributions.)\n LOCATION:https://researchseminars.org/talk/BilTop/95/ END:VEVENT END:VCALENDAR