# Mathematics Colloquia and Seminars

### Schur-Weyl duality and diagrammatics for (double affine) Hecke algebras and $\mathbb{A}_q$ algebra
In the first part of this talk, I will give an overview of some recent results on the interplay between the representation theory of (double affine) Hecke algebras and the representation of quantum groups. I will explain how these results allow us to understand the diagrammatic description of such algebras as tangle algebras. In the second part of the talk, I will describe some new expected results for the $\mathbb{A}_q$ algebra, namely, a Schur-Weyl duality result and a model for the diagrammatic description of the algebra. This is based on joint work with L. Bittmann and A. Mellit.