# Combinatorics and Arithmetic for Physics: special days

30 November 2021 to 2 December 2021
Le Bois-Marie
Europe/Paris timezone

## Noncommutative Birational Rowmotion on Rectangles (Remote)

30 Nov 2021, 14:00
50m
Centre de conférences Marilyn et James Simons (Le Bois-Marie)

### Centre de conférences Marilyn et James Simons

#### Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette

### Speaker

Darij Grinberg (Drexel University)

### Description

The operation of birational rowmotion on a finite poset has been a mainstay in dynamical algebraic combinatorics for the last 8 years.
Since 2015, it is known that for a rectangular poset of the form $[p] \times [q]$, this operation is periodic with period $p + q$. (This result, as has been observed by Max Glick, is equivalent to Zamolodchikov’s periodicity conjecture in type AA, proved by Volkov.)
In this talk, I will outline a proof (joint work with Tom Roby) of a noncommutative generalization of this result. The generalization does not quite extend to the full generality one could hope for it covers noncommutative rings, but not semirings; however, the proof is novel and simpler than the original commutative one. Extending this to semirings and to other posets is work in progress.

### Presentation Materials

 cap2021-Grinberg.pdf Vidéo