Wed 19 Feb 2020, 14:00 (Paris time)
Location: École Normale Supérieure -- Salle W
David Cimasoni (Genève)
Dimers on the Klein bottle
The dimer model on graphs embedded in the torus (or equivalently,
doubly-periodic planar graphs) is very well understood thanks to the classical
work of Kasteleyn, Kenyon, Okounkov, Sheffield, and many others. In this talk,
I will report on ongoing work about the dimer model on graphs embedded in the
Klein bottle (or equivalently, periodic-antiperiodic planar graphs). As we
will see, Kasteleyn's theorem extends (this is due to Tesler), as well as
Cohn-Kenyon-Propp's double product formula (joint work with Adrien Kassel).
This allows us to evaluate the asymptotics of the dimer partition function on
Klein bottles, in the spirit of Kenyon, Sun, and Wilson's result on tori.