2020/2021
Research Seminar "Cluster Manifolds"
Category 'Best Course for Career Development'
Category 'Best Course for Broadening Horizons and Diversity of Knowledge and Skills'
Category 'Best Course for New Knowledge and Skills'
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
1, 2 module
Instructors:
Vasily Gorbounov
Language:
English
ECTS credits:
3
Contact hours:
30
Course Syllabus
Abstract
The theory of electrical networks developed in the work of Ohm and Kirkhoff has been a source of interesting mathematics for almost 200 years. Enumeration on graphs, discrete integrable systems, discrete complex analysis, symplectic geometry are among the areas the electrical networks are connected to. The purpose of the course is to discuss a relatively recent development. It turns out that electrical networks can be viewed as a deformation of another well studied structure, the cluster algebra structure on the classical Lie groups.In particular electrical networks give rise to a Lie group called the Electrical Lie group and it is a deformation of the Unipotant group. As a consequence one gets a non trivial deformation of the cluster algebra structue on the Uniportant group. The theory of total positivity in the Uniportant group also deforms to the Electrical Lie group in an interesting way. Describing these deformations is the main goal of the course. Рrerequisites: Standard courses on linear algebra, analysis and topology.
Learning Objectives
- Цель дисциплины познакомить студентов с основными идеями теории кластерных многообразий
