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SUMMARY:Dimers\, double-dimers\, and the PT / DT correspondence
DTSTART:20210129T093000Z
DTEND:20210129T103000Z
DTSTAMP:20230925T122300Z
UID:indico-event-6489@indico.math.cnrs.fr
DESCRIPTION:Speakers: Helen Jenne\n\nThe dimer model is the study of the s
et of dimer configurations (or perfect matchings) of a graph. In this talk
\, I will begin with an overview of the combinatorics of the dimer model\,
highlighting surprising connections between the dimer model and other are
as of math such as algebraic geometry.\n\nI will then present joint work w
ith Ben Young and Gautam Webb which uses the dimer model and the less well
-studied double-dimer model to resolve an open conjecture from enumerative
geometry. To do so\, we prove that two generating functions for plane par
tition-like objects (the "box-counting" formulae for the Calabi-Yau topolo
gical vertices in Donaldson-Thomas theory and Pandharipande-Thomas theory)
are equal up to a factor of MacMahon's generating function for plane part
itions. Our proof is combinatorial\, and no prior knowledge of enumerative
geometry (or the dimer model) is required to understand the talk.\n\n \n
\nhttps://indico.math.cnrs.fr/event/6489/
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URL:https://indico.math.cnrs.fr/event/6489/
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