Time: 2:15 – 4:30 pm (with a 15 minute break at 3:15)
Venue: LH-1, Mathematics Department
In the first half of the talk, I will define the dimer model on planar graphs and prove Kasteleyn’s groundbreaking result expressing the partition function (i.e. the generating function) of the model as a Pfaffian. I will then survey various results arising as a consequence, culminating in the beautiful limit shape theorems of Kenyon, Okounkov and coworkers.
In the second half, I will define a variant of the monomer-dimer model on
planar graphs and prove that the partition function of this model can be
expressed as a determinant. I will use this result to calculate various
quantities of interest to statistical physicists and end with some open