2-Associahedra and the velocity fan

Abstract: Associahedra are polytopes that encode homotopy associativity and allow for the definition of A-infinity categories. There are numerous polytopal realizations of associahedra, my favourite being due to Loday.

Nate Bottman introduced a family of abstract polytopes called 2-associahedra, that should stand behind the theory of (A-infinity,2)-categories. While an associahedron K(n) compactifies the moduli space of configurations of n points on a line, a 2-associahedron K(n_1, ... , n_k) compactifies the moduli space of configurations of k lines, with n_i points on the line number i. The combinatorics of this object is rather intricate, and the question of finding a polytopal realization is difficult.

In my talk, I will define 2-associahedra and tell about our recent construction of complete fans realizing these abstract polytopes. We are currently working to prove that these fans are projective. Some cases are settled, so there will be 3D pictures.

computational geometrydiscrete mathematicscommutative algebracombinatorics

Audience: researchers in the topic

Copenhagen-Jerusalem Combinatorics Seminar

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The password for the zoom room is 123456