Urbana Campus Research Calendar (OVCRI)

View Full Calendar

Integrability & Representation Theory (IRT) Seminar

Event Type
Seminar/Symposium
Sponsor
NA
Location
Online. Email hvu@illinois.edu for the Zoom link
Date
Nov 7, 2024   12:00 pm  
Speaker
Trung Vu
Contact
Trung Vu
E-Mail
hvu@illinois.edu
Views
18
Originating Calendar
Integrability & Representation Theory (IRT) Seminar

The partition function is one of the key objects in statistical mechanics encoding the macroscopic behavior of the underlying models. In 1967, Kasteleyn, and independently by Fisher and Temperley, gave an explicit computation of the partition function for the dimer models on the square lattice as the determinant of the signed adjacency matrix. In this talk, I will introduce the notion of Kasteleyn matrix for the infinite, bipartite planar graphs with Z^2-periodic property, the height function of dimer covers and how the two objects related. Understanding these objects will be crucial for constructing invariant Gibbs measure and the phase diagram of the Gibbs measures for dimers on a particular graph, represented by the amoeba. This is the first talk in a series of 3 talks on the paper "Dimer and Amoeba" by Kenyon-Okounkov-Sheffield and (if time allowed) the correspondence between amoeba and the arctic curves from the T-system dimer model.

link for robots only