# Applied Non-commutative analysis and symmetry

## Official Course Description

## Description

The course ”Applied noncommutative analysis and symmetry” is about non-commutative analysis and modern analysis of symmetry based on symmetry transformations and their broad and important applications in physics, control theory and automatic control, chemistry, and several other natural science and engineering subjects where analysis of symmetries and symmetry transformations play important role. The course covers operator and matrix equations for non-commuting matrices and linear operators important in control theory and automatic control, quantum physics, quantum computers and quantum information; introduction to symmetry groups, crystallographic groups, lattice symmetries, and representation theory with emphasize on applications to solid state physics; spherical functions and oscillator algebra, commutation properties of difference and differential operators, Heisnberg-Weyl algebra as the foundation for differential calculus, integral calculus and quantum mechanics; shift and composition operators, non-commutative families of operators, and reordering commutation rules and their key role for the general operator method of solution of differential, difference and integral equations important physics and other natural science and engineering subjects. Other topics related to non-commutative analysis and symmetry research are included on the specific requests of the participants.