2025/2026
Supersymmetry for Mathematicians
Type:
Optional course (faculty)
Delivered by:
Faculty of Mathematics
Where:
Faculty of Mathematics
When:
3, 4 module
Open to:
students of all HSE University campuses
Instructors:
Filipp Uvarov
Language:
English
ECTS credits:
3
Contact hours:
36
Course Syllabus
Abstract
Supersymmetry is a concept in theoretical physics, in which there is a one-to-one correspondence between bosons and fermions. Mathematics that describes bosons in one way or another is related to symmetric algebra, while fermions are related to antisymmetric (external) algebra. The development of supersymmetry has led to the emergence of new and interesting mathematics that combines these constructions. For example, super Schur polynomials naturally arise, forming a basis for polynomials that are symmetric in some variables and antisymmetric in others. In this course, we will become familiar with the main objects of "supermathematics", starting with supergeometry and ending with Lie superalgebras and their representations.
Learning Objectives
- Super linear algebra, supergeometry, Lie supegroups and superalgebras and their representations
Expected Learning Outcomes
- Basic understanding of the introduced objects and their properties
- Basic understanding of introduced objects and their properties.
- Basic understanding of introduced objects and their properties
Bibliography
Recommended Core Bibliography
- Maldacena, J. (2014). The symmetry and simplicity of the laws of physics and the Higgs boson. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1410.6753
- Supersymmetry and equivariant de Rham theory, Guillemin, V. W., 1999
- Tapp K. Symmetry A Mathematical Exploration// Springer // https://www.springer.com/gp/book/9781461402985#otherversion=9781461402992
Recommended Additional Bibliography
- Symmetry : a mathematical exploration, Tapp, K., 2012