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SUMMARY:Nicholas Ovenhouse (Yale)
DTSTART:20221108T210000Z
DTEND:20221108T220000Z
DTSTAMP:20260423T005823Z
UID:UAANTS/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/49/">
 Super Ptolemy Relation and Double Dimer Covers</a>\nby Nicholas Ovenhouse 
 (Yale) as part of University of Arizona Algebra and Number Theory Seminar\
 n\nLecture held in ENR2-S395.\n\nAbstract\nGiven a quadrilateral inscribed
  in a circle\, Ptolemy's Theorem relates the lengths of the diagonals and 
 sides. In general\, for an inscribed polygon\, Ptolemy's relation allows o
 ne to write the length of any diagonal as a Laurent polynomial in terms of
  the lengths of the diagonals coming from some fixed triangulation. Schiff
 ler and Musiker showed that these Laurent polynomials can be written in te
 rms of perfect matchings (or "dimer covers") of some planar graph. Recentl
 y\, Penner and Zeitlin defined a super-symmetric version of Ptolemy's rela
 tion\, involving anti-commuting variables. In recent work with Musiker and
  Zhang\, we showed that iterated applications of the super Ptolemy relatio
 n gives a sum over double dimer covers of the same planar graph.\n
LOCATION:https://researchseminars.org/talk/UAANTS/49/
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