Differential geometry

and mathematical physics

and mathematical physics

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".

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.

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

- 1
Ideas of quantization.

- 2
Integrability and quantization.

- 3
Clifford algebras, spinors and Geometry.

- 4
Geometric structures in quantum mechanics.

- 5Special tasks of calculus.
- 6Special tasks of linear algebra.
- 7Special tasks of ODE.

Required skills

We expect listeners to have the listed skills

- Basics of calculusIntegral and differential calculus, at least in one-dimensional case.
- Basics of analytic geometryCoordinate systems and transforms, curves and surfaces.
- Ability to solve linear ODEStandard methods of solving linear ODEs and fundamentals of the general theory
- Basics of linear algebraCoordinate transforms, systems of linear equations.
- Basics of physics
- EnglishWe expect the listeners to understand lections in English.

Contact us