MATHEMATICAL PHYSICS AS A FIELD OF SCIENCE

It is difficult to offer a brief and comprehensive definition of mathematical physics research. In fact, the propensity of the field to rapidly change and evolve makes it entirely impossible. Advancements in physics – particularly theoretical physics towards the end of the 20th century – required the use of unconventional areas of mathematics such as algebraic geometry, symplectic geometry, topology, and even category theory (one of possibly the most abstract branches of mathematics). Moreover, theoretical physics not only “employed” the latest mathematical theories – it introduced “physical intuition” and methods used in theoretical physics into many areas of pure mathematics.

This mutually beneficial cooperation led to rapid progress both in physics itself and in pure mathematics. Therefore, with some reservations, we can say that modern mathematical physics is a science that has emerged where physics and mathematics meet.

This is where an interpenetrating and mutually fruitful synthesis of ideas occurs and new research methods of both physical and purely mathematical theories are developed.

Mathematical physics classes demand twice the knowledge and, what is perhaps even more difficult, fluency in two very different languages: those of mathematics and physics.

**OUR EDUCATIONAL PROGRAM **

It is well known that it is easier for children to pick up new languages and, most commonly, bilingual people are raised in families where parents speak different languages.

Ten years ago, the Institute for Advanced Study at Princeton led an attempt to “teach mathematicians physics”: they gathered a number of distinguished mathematicians who then attended lectures held by eminent physicists. They were then asked to solve problems. The greatest beneficiaries of this experiment were the graduate students and fresh new post-docs that also took part. Our Mathematical Physics master’s program is an attempt to create an environment where students simultaneously learn two languages from the very outset.

This type of program is offered by the Faculty of Mathematics of the Higher School of Economics (HSE). That said, the programs at Skoltech and HSE do not compete with each other. In fact, they complement each other. An agreement signed by Skoltech and the Higher School of Economics combines the programs and they are organized and run as a consolidated educational program.

**PROSPECTS **

A two-year master’s program is too short to fully master the breadth of knowledge necessary to pursue mathematical physics and conduct comprehensive research. Therefore, our master’s program forms the first stage of what would be understood as a PhD program in western universities, where the second stage involves postgraduate study.

Not all students will want and manage to see the course through to the end. Therefore, Skoltech, with its multidisciplinary approach, is the ideal choice: offering graduates knowledge with clear, real application. Successful graduates of our master’s program can be confident that they will obtain spots at our postgraduate school, but we also hope they will be sought after candidates at leading scientific centers abroad.

**THE DISTINCTIVE FEATURES OF OUR PROGRAM **

Our 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 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. We are planning for a number of leading foreign scientists to fully participate in the educational process by supervising our students as well as holding series of lectures.

The crux of our students’ scientific career involves compulsory scientific seminars and mandatory attendance at summer and winter scientific schools

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 thus career) growth. This has been proven by the extensive experience of our colleagues from the Institute for Theoretical and Experimental Physics, the Landau Institute for Theoretical Physics, the Independent University of Moscow, and the program’s main partner — the Faculty of Mathematics at the Higher School of Economics.

Our program produces students and graduate students with internationally recognized, top-level qualifications. The scientific world is their oyster: the doors of the world’s leading mathematical physics centers are open to them