A∞ deformations of extended Khovanov arc algebras and Stroppel’s Conjecture
Extended Khovanov arc algebras are graded finite-dimensional algebras which appear at the confluence of representation theory, link homology and symplectic geometry. In this talk I will explain how to obtain explicit A∞ deformations of these algebras by presenting their Koszul duals as path algebras of quivers with relations and using a combinatorial method via reduction systems to determine their deformations. This settles a conjecture by Catharina Stroppel (ICM 2010) on the bigraded Hochschild cohomology groups of extended Khovanov arc algebras and produces explicit A∞ deformations of Fukaya-Seidel categories associated to Hilbert schemes of points on nilpotent slices of type A singularities constructed recently by Cheuk Yu Mak and Ivan Smith. This talk is based on https://arxiv.org/abs/2211.03354 joint with Zhengfang Wang.