Speaker
Description
The central object of this talk is the braid group. I will recall some combinatorial structures revolving around this group. First two of its generalizations : on one hand virtual braid groups and on the other Artin groups. I will give a construction combining them, namely virtual Artin groups, and review some of its properties.
Then I will turn to the Hecke algebra and one of its categorical incarnation Soergel bimodules. I will present a gentle overview of the category of Soergel bimodules and of its importance in (higher) representation theory and knot theory. I will sketch the construction of a similar category but set in a slightly larger scope. In a very special case, I will give a complete description of this category and show how it then gives rise to an algebra related to the affine Hecke algebra. If time permits explain how, in the general case, one could hope to get a better understanding of this category through virtual Hecke-like algebras.