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SUMMARY:Noncommutative Birational Rowmotion on Rectangles (Remote)
DTSTART;VALUE=DATE-TIME:20211130T130000Z
DTEND;VALUE=DATE-TIME:20211130T135000Z
DTSTAMP;VALUE=DATE-TIME:20220810T084051Z
UID:indico-contribution-5961@indico.math.cnrs.fr
DESCRIPTION:Speakers: Darij Grinberg (Drexel University)\nThe operation of
birational rowmotion on a finite poset has been a mainstay in dynamical a
lgebraic combinatorics for the last 8 years.\nSince 2015\, it is known tha
t for a rectangular poset of the form $[p] \\times [q]$\, this operation i
s periodic with period $p + q$. (This result\, as has been observed by Max
Glick\, is equivalent to Zamolodchikovâ€™s periodicity conjecture in type
AA\, proved by Volkov.)\nIn this talk\, I will outline a proof (joint wor
k with Tom Roby) of a noncommutative generalization of this result. The ge
neralization does not quite extend to the full generality one could hope f
or it covers noncommutative rings\, but not semirings\; however\, the proo
f is novel and simpler than the original commutative one. Extending this t
o semirings and to other posets is work in progress.\n\nhttps://indico.mat
h.cnrs.fr/event/7040/contributions/5961/
LOCATION:Le Bois-Marie Centre de confĂ©rences Marilyn et James Simons
URL:https://indico.math.cnrs.fr/event/7040/contributions/5961/
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