An educational track of the Summer school in mathematics and mechanics for pre-masters 2022
The track is aimed to aquaint attendees with basics of modern science branches — differential geometry, quantum mechanics and mathematical physics. The track is realized in cooperation with the ITMP MSU, and comes to anticipate master’s program "Geometry and Quantum fields".
Head of track
Andrei I. Shafarevich
Dean of Faculty of Mechanics and Mathematics, Lomonosov Moscow State University. Doctor of science in mathematics and physics, corresponding member of Russian Academy of Science.
Fields of research: — mathematical physics, — theory of PDE, — nonlinear PDE asymptotical solutions, — hydromechanics.
List of topics
Ideas of quantization.
Integrability and quantization.
Clifford algebras, spinors and Geometry.
Geometric structures in quantum mechanics.
Special tasks of calculus.
Special tasks of linear algebra.
Special tasks of ODE.
We expect listeners to have the listed skills
Basics of calculus
Integral and differential calculus, at least in one-dimensional case.
Basics of analytic geometry
Coordinate systems and transforms, curves and surfaces.
Ability to solve linear ODE
Standard methods of solving linear ODEs and fundamentals of the general theory
Basics of linear algebra
Coordinate transforms, systems of linear equations.
Basics of physics
We expect the listeners to understand lections in English.