MIT-Harvard-MSR Combinatorics Seminar
Wednesday, December 14, 2022 at 4:15pm to 5:15pm
MIT-Math Dept., /Room 2-132
Speaker: Darij Grinberg (Drexel)
Title: Noncommutative Birational rowmotion on Rectangles
Birational rowmotion is a (partial) map defined for any field and any finite poset, generalizing some combinatorial and geometric constructions.
Since 2015, it is known that for a rectangular poset of the form $[p] \times [q]$, this map 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 gives rise to some interesting problems (work in progress).
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