Study Plan

Structure of the program - 4 types of courses

1. Basic Mathematics

• Geometry;
• Lie Algebras and Representations;
• Functional Analysis;
• Supermathmatics;
• Conformal Geometry;
• PDE and Integrability;
• Homological Algebra.

2. Basic Physics

• Quantum Fields;
• General Relativity;
• String Theory. 

3. Interdisciplinary courses

• Mathematical Theory of Black Holes;
• Quantum Integrable Models;
• Topological Theories;
• Batalin-Vilkovisky Quantization;
• 2d Conformal Theories.

4. Advanced courses

• Higher Spin Theories;
• Holography;
• Superstring Sigma Models;
• Dynamical Systems;
• Seiberg-Witten Invariants.

Course outlines

Year 1

• Symmetries and Integrability of Differential Equations;
• Introduction to Supergeometry;
• Lie Groups and Lie Algebras;
• Differential Geometry and Topology;
• Conformal Geometry and Riemann Surfaces;
• Principles of QFT/Modern QFT;
• Functional Analysis and Theory of Operators;
• Introduction to CFT in Two-dimension;
• Symplectic Geometry and Quantization;
• Batalin-Vilkovisky Quantization.

Year 2 

• Introduction to String Theory;
• Conformal Field Theories and Holographic Dualities;
• Mathematical Theory of Black Holes;
• Topological QFT;
• Homological Algebra
• Seiberg-Witten Invariants;
• Higher Spin Theory and Holography;
• Selected Topics of General Relativity;
• Superstring Theory and Sigma Models;
• Theory of Dynamical Systems;
• Quantum Integrable Models;
• Topology of Integrable Systems;
• Geometrical Theory of Nonlinear Differential Equations.

Master's thesis

The program culminates in a Master’s thesis and an oral presentation of the work at a public colloquium. The students will have an opportunity to perform cutting-edge research and work on a Master’s thesis under the supervision of world-class experts in mathematics and physics. These include researchers from the Institute for Theoretical and Mathematical Physics (ITMP), faculty members from the Department of Mechanics and Mathematics, as well as researchers from the Russian Academy of Sciences (RAS) and other  reputable scientific research institutes (in or outside Russia) .