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UID:49b5e8e2-c32d-432b-9c12-6e18cc5b91b0@nexttoyou
DTSTAMP:20261106T174211Z
DTSTART:20261118T201500Z
DTEND:20261118T211500Z
SUMMARY:Richard P. Stanley Seminar in Combinatorics
LOCATION:Harvard Science Center 232
DESCRIPTION:Speaker: Jim Propp (UMass Lowell and Radcliffe Institute)\n\nT
 itle: Snake graphs and q-deformed real numbers\n\nAbstract: I'll present 
 a statistical-mechanical construction of q-deformed real numbers\, inspir
 ed by the q-deformed rational numbers [x]_q of Morier-Genoud and Ovsienko
 . The new construction admits two equivalent formulations: one in terms o
 f random filters in snake posets and the other in terms of random dimer c
 overs of snake graphs.\n\nI'll begin with a combinatorial approach to Ste
 rn's diatomic series and the Calkin–Wilf bijection via finite snake graph
 s\, and then construct q-deformed rational numbers by introducing an acti
 vity parameter q into the model. For irrational values of x\, the constru
 ction requires passing from finite to infinite snake graphs\; the main te
 chnical step is to show that the associated limiting probability measures
  are well defined.\n\nThe resulting q-deformation satisfies [[x]]_1 = x f
 or all x>0. There's evidence that\, wherever both [x]_q and [[x]]_q are d
 efined\, [[x]]_q = q [x]_q. For more details\, see arXiv:2607.14332.\n\nh
 ttp://next-to-u.app/events/49b5e8e2-c32d-432b-9c12-6e18cc5b91b0
URL:http://next-to-u.app/events/49b5e8e2-c32d-432b-9c12-6e18cc5b91b0
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