Arvind Ayyer (IISc., Bangalore)

The next talk in the Seminar on Special Functions and Number Theory is by Arvind Ayyer of IISC, Bangalore. The information appears below.

As announced in the last talk, Atul Dixit is now a co-organizer of this Seminar. The Zoom access for this talk has been kindly provided by Ashoka University. So this seminar series is now co-organized by Ashoka University, IIT, Gandhinagar and JNU. 

We are experimenting with various systems so that we can give options to speakers. Please get in touch with any of Atul, Krishnan or myself if you wish to try out zoom before the talk. It requires some installation. Zoom may be suitable for a webinar in case we organize a public lecture, which we plan to do at some point. 

Title: The Monopole-Dimer Model

Speaker: Arvind Ayyer, IISc. (Bangalore)

When: Thursday, June 18, 2020: 3:55-5:00 pm

Where: On Zoom: Link (available on request). Please send email to sfandnt@gmail.com

Tea or Coffee: Please bring your own. 

Here is a link to the talk.

Abstract:

The dimer model is a model which arose in statistical physics as a study
of adsorption. We will first define the model and state Kasteleyn's
groundbreaking result expressing the partition function of the model as
a Pfaffian for planar graphs. We develop a new model of monopoles and
dimers whose partition function is a determinant for any planar graph.
We then apply this to the rectangular grid and obtain a generalization
of Kasteleyn's miraculous product formula. Lastly, we study the
thermodynamic limit and obtain formulas for the free energy and entropy.
Some interesting special functions show up in this limit. Time
permitting, we will also show that in some special cases, the partition
function becomes a perfect square. This work is based on arXiv:1311.5965
(Mathematical Physics, Analysis and Geometry, 2015) and arXiv:1608.03151
(to appear in Annals of Combinatorics).

Graduate students are welcome. We plan to include a friendly introduction.