Assoc. prof. dr. Kenny De Commer, Vrije Universiteit Brussel: The braid equation and the reflection equation

In data de 3 noiembrie 2022, ora 10:30, sala „pi” din clădirea Mathematica, va avea loc prelegerea invitată cu titlul:

The braid equation and the reflection equation

susținută de Dr. Kenny De Commer, associate professor at VUB, department of Mathematics and Data Science, Bruxelles, Belgia.

Abstract: There is currently a lot of interest in algebraic structures which can mimic topological operations. One particular such operation is braiding: take the ends of two strands which are hanging down, and turn around 180 degrees. If we replace each strand by a set X, one mimics the braiding operation by an invertible map r from the Cartesian square X² to itself. The crucial requirement of this map is that it satisfies the braid equation (also known as Yang-Baxter equation). It turns out that such a map r leads to a wealth of interesting algebraic structures. We will give an overview of the different incarnations of these structures, and their surprising relation with other well-known areas of algebra (Galois theory, radical rings, ...) We then look at a closely related topological operation: take the ends of two strands and turn around 360 degrees! Transferring this operation to the set-theoretic world, we are now looking at maps satisfying a different equation, known as the reflection equation. As our own small contribution to this area, we will comment on some algebraic structures associated to this equation.