BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mario Sanchez (Cornell University) DTSTART:20221117T200000Z DTEND:20221117T210000Z DTSTAMP:20260423T024614Z UID:Matroids/14 DESCRIPTION:Title: Valuations and Hopf Monoid of Generalized Permutahedra\nby Mario San chez (Cornell University) as part of Matroids - Combinatorics\, Algebra an d Geometry Seminar\n\nLecture held in Room 210 The Fields Institute.\n\nAb stract\nMany combinatorial objects\, such as matroids\, graphs\, and poset s\, can be realized as generalized permutahedra - a beautiful family of po lytopes. These realizations respect the natural multiplication of these ob jects as well as natural "breaking" operations. Surprisingly many of the i mportant invariants of these objects\, when viewed as functions on polytop es are valuations\, that is\, they satisfy an inclusion-exclusion formula with respect to subdivisions. In this talk\, I will discuss work with Fede rico Ardila that describes the relationship between the algebraic structur e on generalized permutahedra and valuations. Our main contribution is a n ew easy-to-apply method that converts simple valuations into more complica ted ones. New examples of valuations coming from this method include the K azhdan-Lustzig polynomials of matroids and the motivic zeta functions of m atroids.\n LOCATION:https://researchseminars.org/talk/Matroids/14/ END:VEVENT END:VCALENDAR