Emil Verkama: Promotion, rotation, webs, and other fancy words: An introduction to dynamical algebraic combinatorics

The purpose of this talk is to introduce the audience to some popular topics in dynamical algebraic combinatorics — the study of actions on combinatorial objects. Whereas a typical combinatorialist might be satisfied with counting the objects, a dynamical-algebraic-combinatorialist will also want to know about the orbit structure, order, and fixed points of the action.

The punchline is that, in many important cases, complicated-looking actions, such as promotion on linear extensions of posets, become simple rotations after passing to a different but bijectively related model. If time permits, we will discuss a recent, exciting instance of this phenomenon: the development of rotation-invariant SL_4-web bases due to Gaetz, Pechenik, Pfannerer, Striker, and Swanson.