BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Luis Ferroni (KTH Royal Institute of Technology) DTSTART:20230328T190000Z DTEND:20230328T200000Z DTSTAMP:20260423T024612Z UID:Matroids/44 DESCRIPTION:Title: Ehrhart polynomials of matroid polytopes\nby Luis Ferroni (KTH Royal Institute of Technology) as part of Matroids - Combinatorics\, Algebra an d Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAb stract\nA fundamental invariant associated to a lattice polytope is its Eh rhart polynomial\, which encodes the number of lattice points inside all t he integer dilations of the polytope and much more arithmetic\, algebraic and combinatorial information. One may associate to any matroid two polyto pes called respectively the base polytope and the independence polytope\; both of these polytopes can be seen as part of the larger family of genera lized permutohedra. A conjecture of De Loera\, Haws and Köppe asserted th at the Ehrhart polynomials of base polytopes of matroids had positive coef ficients only\; more generally\, Castillo and Liu conjectured this was tru e for all generalized permutohedra (in particular\, also for independence polytopes). We will show how to construct counterexamples to these conject ures\; we will exhibit examples of matroids whose base and independence po lytopes attain negative Ehrhart coefficients. On the positive side\, we wi ll discuss about some families of matroids that satisfy Ehrhart positivity . Several open problems regarding Ehrhart polynomials of matroids will be stated.\n LOCATION:https://researchseminars.org/talk/Matroids/44/ END:VEVENT END:VCALENDAR