BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Federico Ardila (San Francisco State University) DTSTART:20240306T170000Z DTEND:20240306T180000Z DTSTAMP:20260423T021344Z UID:CG-BLT/1 DESCRIPTION:Title: I ntersection theory of matroids: variations on a theme\nby Federico Ard ila (San Francisco State University) as part of Combinatorics and Geometry BLT Seminar\n\n\nAbstract\nChow rings of toric varieties\, which originat e in intersection theory\, feature a rich combinatorial structure of indep endent interest. We survey four different ways of computing in these rings \, due to Billera\, Brion\, Fulton–Sturmfels\, and Allermann–Rau. We i llustrate the beauty and power of these methods by sketching four proofs o f Huh and Huh–Katz’s formula µ^k (M) = deg(α^{r−k}β^k) for the co efficients of the reduced characteristic polynomial of a matroid M as the mixed intersection numbers of the hyperplane and reciprocal hyperplane cla sses α and β in the Chow ring of M. Each of these proofs sheds light on a different aspect of matroid combinatorics\, and provides a framework for further developments in the intersection theory of matroids. \n\nOur pres entation is combinatorial\, and does not assume previous knowledge of tori c varieties\, Chow rings\, or intersection theory.\n LOCATION:https://researchseminars.org/talk/CG-BLT/1/ END:VEVENT END:VCALENDAR