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Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces
September 7–December 28, 2021, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom, Moscow

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A connection between automorphism groups of K3 surfaces over the field of complex numbers $\mathbb C$ and groups generated by reflections in Lobachevsky spaces first appeard in a classical work of Piatetski-Shapiro and Shafarevich in which they established a global Torelli theorem for K3 surfaces. In particular, they showed that the automorphism group of a K3-surface over $\mathbb C$ is finite if and only if the automorphism groups of its Picard lattice is generated up to finite index by reflections in its elemets of square $(-2)$. The Picard lattice is hyperbolic over $\mathbb Z$ and determines a Lobachevsky space on which the group generated by reflections in elemets of square $(-2)$ acts discretely. Shortly before, Vinberg and Makarov obtained important results about arithmetic groups generated by reflections in Lobachevsky spaces. Both groups of authors attempted to use this connection in order to describe automorphism groups of K3 surfaces and arithmetic groups generated by reflections in Lobachevsky spaces. Important results in this direction were obtained by Nikulin around 1980, that is, 10 years later.

There has been a lot of progress in this area, which is the topic of the course.

Просьба к участникам обращаться к Вячеславу Валентиновичу Никулину, nikulin@mi-ras.ru, за данными для подключения к занятиям через Zoom.

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).

RSS: Forthcoming seminars

Lecturer
Nikulin Viacheslav Valentinovich

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


Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces, Moscow, September 7–December 28, 2021

October 26, 2021 (Tue)
1. Lecture 8. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces
V. V. Nikulin
October 26, 2021 18:00, Moscow, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom

October 19, 2021 (Tue)
2. Lecture 7. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces
V. V. Nikulin
October 19, 2021 18:00, Moscow, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom
  

October 12, 2021 (Tue)
3. Lecture 6. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces
V. V. Nikulin
October 12, 2021 18:00, Moscow, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom
  

October 5, 2021 (Tue)
4. Lecture 5. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces
V. V. Nikulin
October 5, 2021 18:00, Moscow, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom
V. V. Nikulin
  

September 28, 2021 (Tue)
5. Lecture 4. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces
V. V. Nikulin
September 28, 2021 18:00, Moscow, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom
V. V. Nikulin
  

September 21, 2021 (Tue)
6. Lecture 3. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces
V. V. Nikulin
September 21, 2021 18:00, Moscow, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom
V. V. Nikulin
  

September 14, 2021 (Tue)
7. Lecture 2. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces
V. V. Nikulin
September 14, 2021 18:00, Moscow, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom
V. V. Nikulin
  

September 7, 2021 (Tue)
8. Lecture 1. Automorphism groups of K3 surfaces and groups generated by reflections in Lobachevsky spaces
V. V. Nikulin
September 7, 2021 18:00, Moscow, Steklov Mathematical Institute, Room. 530 (8 Gubkina) + Zoom
V. V. Nikulin
  
 
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