BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Spencer Backman (University of Vermont) DTSTART:20230330T190000Z DTEND:20230330T200000Z DTSTAMP:20260423T024654Z UID:Matroids/45 DESCRIPTION:Title: Higher Categorical Associahedra\nby Spencer Backman (University of V ermont) as part of Matroids - Combinatorics\, Algebra and Geometry Seminar \n\nLecture held in Room 210 The Fields Institute.\n\nAbstract\nThe associ ahedron is a well-known poset with connections to many different areas of combinatorics\, algebra\, geometry\, topology\, and physics. The associahe dron has several different realizations as the face poset of a convex poly tope and one realization\, due to Loday\, is a generalized permutahedron\, i.e. a polymatroid. From the perspective of symplectic geometry\, the ass ociahedron encodes the combinatorics of morphisms in the Fukaya category o f a symplectic manifold. In 2017\, Bottman introduced a family of posets c alled 2-associahedra which encode the combinatorics of functors between Fu kaya categories\, and he conjectured that they can be realized as the face posets of convex polytopes. In this talk we will introduce categorical n- associahedra as a natural extension of associahedra and 2-associahedra\, a nd we will produce a family of complete polyhedral fans called velocity fa ns whose face posets are the categorical n-associahedra. Categorical n-ass ociahedra cannot be realized by generalized permutahedra or any of their k nown extensions. On the other hand\, our velocity fan specializes to the n ormal fan of Loday’s associahedron suggesting a new extension of general ized permutahedra. This is joint work with Nathaniel Bottman and Daria Pol iakova.\n LOCATION:https://researchseminars.org/talk/Matroids/45/ END:VEVENT END:VCALENDAR