Master of Science in Mathematical and Theoretical Physics

The program is aimed at giving researchers a grounding in mathematics and deep knowledge of mathematical physics, as well as giving the chance to pursue in-depth study of the fundamental models of modern theoretical physics. We put emphasis on students' independent scientific study that encourages their rapid fundamental scientific (and thus career) growth.

Solid knowledge of theoretical physics and the ability to apply it in order to perform reliable calculations of real physical effects are crucially important for the valuable interpretation of new experimental findings as well as for the development of successful ideas towards new technological applications.

The key features of the Mathematical and Theoretical Physics program are:

• Cutting edge research in fundamental concepts of theoretical physics;
• Covers the lack of joint education in physics and mathematics;
• Special emphasis on the research activity of students themselves;
• Provides a unique educational environment in the fields of theoretical and mathematical physics;
• Renowned faculty with international experience and collaborations;
• Incorporates a variety of disciplines covering major topics in mathematical methods;
• Diverse and strong collaboration with international and Russian partners and publications in top journals.

The MSc program is 2 years long: the first year is to strengthen your theoretical background, and the second year is to focus on research. Students have the freedom to choose courses and extracurricular activities to shape their individual trajectory, acquire soft skills, and gain entrepreneurial skills to prepare for job placement.

Aim and objectives

The program is aimed first and foremost at giving researchers a grounding in mathematics and deep knowledge of mathematical physics. It also offers students the chance to pursue an in-depth study of the fundamental models of modern theoretical physics. Students are expected to take part in research projects alongside eminent specialists, teachers, and foreign colleagues specially invited to participate. The crux of our students’ scientific careers involves compulsory scientific seminars and mandatory attendance at summer and winter scientific schools.

This program has no analogs abroad and can be compared only with the Master’s program in mathematical physics at the Department of Mathematics of the Higher School of Economics (HSE). That said, the programs at Skoltech and the HSE do not compete with each other. In fact, they complement each other. An agreement signed by Skoltech and the HSE combines the programs and they are organized and run as a consolidated educational program.

The main scope of the Theoretical Physics program is to provide top-level education and professional training for specialists in the field of contemporary theoretical physics, with emphasis placed on condensed matter theory. Solid knowledge of theoretical physics and the ability to apply it in order to perform reliable calculations of real physical effects are crucially important for the valuable interpretation of new experimental findings as well as for the development of successful ideas towards new technological applications. Graduates of the program should have the skills of a modern researcher in this field and meet the highest professional requirements of leading Russian and international research and educational centers. They must have a broad professional vision, know the relevant methodological approaches, and have sufficient skills to participate in research projects.

The program is realized in a network form with academic partners: the Moscow Institute of Physics and Technology and the Landau Institute for Theoretical Physics.

This program gives you the ability to:

• choose your own educational path and study tailored, individual courses depending on the specific area of your scientific study
• gain the skills of a modern researcher and meet the highest professional requirements of leading Russian and international research and educational centers
• continue education and research within the Ph.D. program at Skoltech and leading scientific centers in Russia and abroad
• participate in research projects independently and alongside eminent specialists, teachers, and foreign colleagues
• apply the culture of scientific discussion and ability to carry scientific research to function in the scientific research community or multidisciplinary team

Track A:

A successful graduate of the program will know and be able to:

• Apply mathematics and modern methods of theoretical physics to the most advanced problems of present fundamental science;
• Use a high level of mathematical education (in algebraic geometry, topology, representation theory) and theoretical physics (quantum field theory, integrable systems, statistical mechanics and complex systems, etc.) to continue a successful career in the most popular directions in science and technology;
• Apply the culture of scientific discussion and ability to carry scientific research to function in the scientific research community or multidisciplinary team;
• Continue education and research within the Ph.D. program at Skoltech and leading scientific centers in Russia and abroad.

Track B:

A successful graduate of the program will know and will be able to use:

• Mathematical methods of contemporary theoretical physics, including complex analysis, topology, functional integrals, multi-dimensional asymptotic methods;
• Analytical methods and approaches to the broad range of physical problems: phase transitions (classical and quantum), thermodynamics and kinetics of mesoscopic systems and nanostructures, quantum field theory, hydrodynamics, quantum transport of charge, spin and heat, quantum-coherent effects in macroscopic systems, including qubit’s theory and engineering.

Content

The key tenets of our Mathematical and Theoretical Physics educational program are compulsory scientific seminars (including student seminars) and a strong scientific community. Students study tailored, individual courses approved by their supervisors, who determine the range of selected courses depending on the specific area of the student’s scientific study. We put emphasis on students’ independent scientific study that encourages their rapid fundamental scientific (and career) growth.

Program structure

The 2-year program comprises compulsory and recommended elective courses on the most important topics, a wide set of elective courses (depending on the research and professional needs of the student), components of entrepreneurship and innovation, research activity, and 8 weeks of industry immersion.

Research

Main research directions:

• Topology;
• Algebraic geometry;
• Representation theory;
• Symplectic geometry;
• Category theory;
• Integrable systems;
• Super-symmetric gauge theories and conformal theories.

Career paths

• Ph.D. positions in academic & research institutions;
• Specialist positions in various economic sectors including Skolkovo resident companies and startups.

Entry requirements

Relevant Bachelor’s degree, or its equivalent in mathematics, applied mathematics, and physics.

It is expected that applicants to Track A of the program should be able to demonstrate knowledge of the following topics:

• Basics of combinatorics, elements of group theory, linear algebra, topology, limits of sequences and functions, derivatives and differentials, geometry: affine and projective spaces, maps, second-order curves (conics), complex analysis, ordinary differential equations, classical mechanics, classical electrodynamics.

Applicants to Track B must demonstrate excellent knowledge of:

• Quantum mechanics (in the scope of the Landau-Lifshitz course)
• Mathematics (calculus, linear algebra, basic complex analysis, differential equations)

The entrance exam in quantum mechanics is equivalent in complexity to the Landau theoretical minimum.

English language requirements:

If your education was not conducted in the English language, you will be expected to demonstrate evidence of an adequate level of English proficiency.

Application requirements

The online application​ makes the process easier for potential students. We advise you carefully read the application instructions, requirements, and deadlines for the chosen academic program.

The application includes the following documents: a CV, two letters of recommendation, a TOEFL/IELTS score report, and a motivation letter. Applicants who do not have proof of English proficiency may take the TOEFL ITP during a Selection Weekend at Skoltech.

Selection process

1. Prepare your portfolio
   Prepare your competitive selection application materials.
2. Submit your application
   Upload your materials into the application system and submit your application.
3. Online testing
   Every candidate must take an online profile test. You will be notified by email about the specific date and time of your test.
4. In-person interviews (online)
   The final selection stage takes place in Moscow. You have to pass the TOEFL ITP exam on-site, or present a valid TOEFL certificate and pass an in-person interview. Extra written examinations may be required for certain programs during this time (you will be notified in advance).

©The Skolkovo Institute of Science and Technology (Skoltech)

What our students say

Anastasia Sharipova
BSc, Moscow Institute of Physics and Technology → MSc, Skoltech → Ph.D., Pennsylvania State University

"For two years I studied Mathematical Physics in one of the best places in the world! I say it about Skoltech. The scientific atmosphere and the level of professors are definitely higher than in many top universities. All lectures and seminars were super complicated and incredibly interesting, we had conferences with great mathematicians and different schools each semester. Now I am doing my Ph.D. in the USA and really miss Skoltech."