Course by A. L. Kanunnikov "Combinatorics of domino tilings" September 14–December 28, 2021, Steklov Mathematical Institute, Room. 303 (8 Gubkina) + Zoom
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 hafnianpfaffian 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. 0751520191614).
RSS: Forthcoming seminars
Lecturer
Kanunnikov Andrey Leonidovich
Institutions
Steklov Mathematical Institute of Russian Academy of Sciences, Moscow Steklov International Mathematical Center 

Course by A. L. Kanunnikov "Combinatorics of domino tilings", September 14–December 28, 2021 


October 19, 2021 (Tue) 

1. 
Lecture 6. Combinatorics of domino tilings A. L. Kanunnikov October 19, 2021 18:00, Steklov Mathematical Institute, Room. 303 (8 Gubkina) + Zoom






October 12, 2021 (Tue) 

2. 
Lecture 5. Combinatorics of domino tilings A. L. Kanunnikov October 12, 2021 18:00, Steklov Mathematical Institute, Room. 303 (8 Gubkina) + Zoom






October 5, 2021 (Tue) 

3. 
Lecture 4. Combinatorics of domino tilings A. L. Kanunnikov October 5, 2021 18:00, Steklov Mathematical Institute, Room. 303 (8 Gubkina) + Zoom






September 28, 2021 (Tue) 

4. 
Lecture 3. Combinatorics of domino tilings A. L. Kanunnikov September 28, 2021 18:00, Steklov Mathematical Institute, Room. 303 (8 Gubkina) + Zoom






September 21, 2021 (Tue) 

5. 
Lecture 2. Combinatorics of domino tilings A. L. Kanunnikov September 21, 2021 18:00, Steklov Mathematical Institute, Room. 303 (8 Gubkina) + Zoom






September 14, 2021 (Tue) 

6. 
Lecture 1. Combinatorics of domino tilings A. L. Kanunnikov September 14, 2021 18:00, Steklov Mathematical Institute, Room. 303 (8 Gubkina) + Zoom





