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DTSTART;TZID=America/New_York:20261116T163000
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DTSTAMP:20261013T151243Z
CREATED:20260729T200924Z
LAST-MODIFIED:20261013T151243Z
UID:10004033-1794846600-1794850200@live-hu-cmsa-222.pantheonsite.io
SUMMARY:Snake graphs and q-deformed real numbers
DESCRIPTION:Colloquium \nSpeaker: James Propp (UMass Lowell) \nTitle: Snake graphs and q-deformed real numbers \nAbstract: I’ll present a statistical-mechanical construction of q-deformed real numbers [[x]]_q\, inspired by the q-deformed rational numbers [x]_q of Morier-Genoud and Ovsienko. The new construction admits two equivalent formulations: one in terms of random filters in snake posets and the other in terms of random dimer covers of snake graphs. \nI’ll begin with a combinatorial approach to Stern’s diatomic series and the Calkin–Wilf bijection via finite snake graphs\, and then construct q-deformed rational numbers by introducing an activity parameter q into the model. I extend from q-deformed rationals to q-deformed reals by passing from finite to infinite snake graphs; the main technical step is to show that the associated limiting probability measures are well defined. \nThe resulting q-deformation [[x]]_q satisfies [[x]]_1 = x for all x>0. There’s evidence that\, wherever both [x]_q and [[x]]_q are defined\, [[x]]_q = q [x]_q. For more details\, see arXiv:2607.14332. \n  \n\nTo subscribe or unsubscribe to the colloquium mailing list\, please visit this link.
URL:https://live-hu-cmsa-222.pantheonsite.io/event/colloquium-111626/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
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