Bernhard Keller (Université Paris Cité): On actions of braid groups on triangulated categories arising in cluster theory
We will present an approach to the construction of actions of braid groups on triangulated categories arising in the (additive) categorification of cluster algebras and varieties. The examples will be inspired by combinatorial braid group actions constructed by Fraser, Fock-Goncharov, Goncharov-Shen and others. The results we will present were obtained in several joint projects notably involving, in chronological order, Chris Fraser, Yilin Wu, Alessandro Contu, Miantao Liu, Haoyu Wang and Xiaofa Chen.
Cheuk Yu Mak (Sheffield): Khovanov algebra, Fukaya category and annulation
Khovanov algebra is a family of algebras which were introduced to study links in the three-sphere. Chen-Khovanov and Brundan-Stroppel generalise it to a family of algebras that have better homological properties, called the quasi-hereditary covers in the sense of Rouquier. We will describe these algebras, their properties, and their annular versions. Then we will give a symplectic geometric understanding of these algebras, followed by a discussion of some open problems. The talk is based on previous joint work with Kristen Hendricks and Ivan Smith.