Seminar series

Date

Mon, 29 May 2023

14:15

14:15

Location

L4

Speaker

Thibaut Mazuir

Organisation

Humboldt Universität zu Berlin

In this talk, I will introduce the notion of $n$-morphisms between two $A_\infty$-algebras. These higher morphisms are such that 0-morphisms correspond to standard $A_\infty$-morphisms and 1-morphisms correspond to $A_\infty$-homotopies. Their combinatorics are encoded by new families of polytopes, which I call the $n$-multiplihedra and which generalize the standard multiplihedra.

Elaborating on works by Abouzaid and Mescher, I will then explain how this higher algebra of $A_\infty$-algebras naturally arises in the context of Morse theory, using moduli spaces of perturbed Morse gradient trees.