BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Guillaume Laplante-Anfossi (University of Melbourne) DTSTART:20230518T141500Z DTEND:20230518T160000Z DTSTAMP:20260422T070056Z UID:CJCS/116 DESCRIPTION:Title: T he combinatorics of the permutahedron diagonals\nby Guillaume Laplante -Anfossi (University of Melbourne) as part of Copenhagen-Jerusalem Combina torics Seminar\n\n\nAbstract\nThe Fulton—Sturmfels formula (introduced i n 1997) gives a combinatorial-geometric way of defining the cup product on the Chow ring of toric varieties: one perturbs the normal fan of the asso ciated polytope in a generic direction and counts intersections of the res ulting complex. Starting with the Losev—Manin toric varieties (introduce d in 2000)\, associated to the permutahedron\, one is led to study generic ally translated copies of the braid arrangement. The combinatorics of the resulting hyperplane arrangements are quite interesting: one can obtain cl osed formulas for the number of facets and vertices\, and in the case of s pecific choices of perturbation that we call « operadic »\, find explici t bijections with some planar labelled bipartite trees. This allows us to recover the algebraic diagonal of Saneblidze—Umble (introduced in 2004)\ , and moreover prove by combinatorial means some purely (higher) algebraic results: for instance\, that there is exactly four universal tensor produ cts of homotopy associative algebras and morphisms. This is joint work wit h Bérénice Delcroix-Oger\, Matthieu Josuat-Vergès\, Vincent Pilaud and Kurt Stoeckl.\n LOCATION:https://researchseminars.org/talk/CJCS/116/ END:VEVENT END:VCALENDAR