How many ways are there to cover a given figure on a square lattice with dominoes? This is a partial case of a global problem about the number of perfect matchings in graphs. Such a question has its roots in chemistry and statistical physics. The main goal of the course is to introduce the hafnian-pfaffian method. This method was developed by Dutch physicist P. Kasteleyn who counted domino tilings of a rectangle (1961) and further generalized the solution method to all planar graphs (FKT algorithm). We also consider another application of the method, namely, following G. Kuperberg we count plane partitions with different types of symmetry.

We expect listeners to know the basics of linear algebra. We will give some necessary extra topics which are not included in a standard course such as pfaffians, Kronecker products and sums.

Просьба к участникам обращаться к Андрею Леонидовичу Канунникову, andrew.kanunnikov@gmail.com, за данными для подключения к занятиям через Zoom.

First lecture of the 2021/2022 fall semester: September 14.

Financial support. The course is supported by the Simons Foundation and the Ministry of Science and Higher Education of the Russian Federation (the grant to the Steklov International Mathematical Center, Agreement no. 075-15-2019-1614).

Lecturer
Kanunnikov Andrey Leonidovich

Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Steklov International Mathematical Center