Mathematics behind the northern polar circle

We continue to publish an interview with the conference “Integrated Systems and Automorphic Forms”, held in the new Mathematical Center “Sirius” in Sochi in the last week of winter (see reporting “Hunters for Special Centers, or“ Sirius “On the eve of the virus” [ 1 ]). Boris Kruglikov , professor of the University of Tromso, the Arctic University of Norway, which is located 350 km north of the polar circle, talks about his research and the specifics of studying the queen of all sciences in the homeland of Abel and Sofus Lee. Talked by Alexei Ognev .

- Boris Serafimovich, please tell us in which area you specialize in?

- Keywords are: symmetry, curvature, invariant structures in geometry, cardan geometry, parabolic and design associated with mathematical physics, and the geometry of differential equations.

- Is there a task that excites you now?

- Yes. This is integration through geometry. I work with the team in England: Evgeny Ferapontov, David Calderbank, Vladimir Novikov, the Danube match. There are colleagues in Russia: Maxim Pavlov, Leonid Bogdanov. Many years ago, Vladimir Zakharov published the book "What is integration?" 1 . By and large, there is still no answer, although there are a lot of examples and there are intermediate results. The idea is to formulate the answer, to bring it to the level of the algorithm. For ordinary equations, this is a very understandable thing, but for equations in private derivatives - no. But we are working on this.

There are tasks that I like, but do not cause an active response in other people. For example, deformation of pseudo -group structures. In the 1960s, it was very popular, but now there are few experts in this area. Denis Tae and other colleagues and I use this to study the phenomenon of destruction of nonlinear symmetry of various geometries.

- What other topics are mathematicians at your university now?

- Our graduate students work in the field of superheumetry. In the language of physics, this means that in addition to bosal particles, Fermionic ones are allowed. Classical mechanics are based on bosal particles. The inclusion of enzyme leads to new equations. From the point of view of mathematics, this means the existence of additional Nilpotents. Mathematics here is very interesting, but whether the super -symmetry exists in the world of elementary particles is an open question. By the way, this summer we hold a TRARO conference on super -symmetry and supergravity.

- How are things with mathematics in Norway?

- Unfortunately, in Norway, mathematics are not popular. There is practically no competition in undergraduate and magistracy. Young people are more likely to go to management, medicine, biology. They want to see the result of their work at once. At school, mathematics at a rather poor level. This crisis has been stretching since the 1970s. For example, in Finland the situation is much better: the country was on friendly relations with the Soviet Union and adopted a lot of good. Now they beat records in terms of secondary education in Europe.

At our university, the Department of Mathematics and Statistics is small: there are only 15 permanent employees plus researchers, postdrods and graduate students (temporary employees). One of my former graduate students remained at the university and has now become my boss - he is the head of our department. Two others left post -DOCS in the Czech Republic. Of course, in the Czech Republic, the salary is significantly lower than in Norway, but there were no other options, although they are quite established mathematicians. Now we have three graduate students: two from Catalonia and one of Tanzania. We did not manage to find a single Norwegian in our group (although all my previous graduate students are Norwegians).

As you know, the Norwegians established the Abel Prize, one of the most prestigious mathematical awards in the world, but it is quite difficult to get money on a state grant: about 6% of applications in the fundamental sciences. However, the recently famous billionaire Tonda Mon, the owner of the production of pumps for oil tankers, created a solid private grant “Pure Mathematics in Norway”. Rage Pina, a well -known specialist in algebraic geometry from Oslo, approached him at a banquet and convinced that to invest in mathematics is good. I work in the program committee of this grant, which significantly activated the mathematical life in Norway.

- What do you think about the development of mathematical schools in our country?

- Recently, I like to come to Russia. It seems to me that there are great scientific prospects. Now there is a lot of rivalry between the tower, Moscow State University, the glass and Skoltech for influence, state support and young scientists. This is very good. For example, in the north of California, about San Francisco, universities of Berkeley, Stanford, Davis and Santa Cruz, a lot of rivalry and cooperation were grouped. In Russia, too, of course, there should be more diversity.

PS additions during layout of the number.

- Please tell me, what is the situation with quarantine in Norway at the moment?

- Here quite quickly everything took control (in early March, as a percentage of the population, Norway, Norway, went immediately after Italy - this was facilitated by a large stream of tourists). But in a month of self -isolation, the situation has normalized, and now they will gradually open kindergartens, schools, etc. We will be pioneers, others will study by our mistakes.

Two factors played a role in improving the situation: (1) Nordic discipline of the population, (2) a large financial reserve that helps to solve the problems of the population. Both factors, alas, are not applicable to Russia, where the situation is more closer to Italy. However, in Russia, good medicine, no matter what. The “commandant hour” and other measures are necessary for the “positive shock” of the population (there was also one, but to a lesser extent) - otherwise the consciousness not to wake up even Herzen.

Boris Kruglikov
Talked by Alexei Ognev

1 Zakharov VE (ed.) What is integrability? Springer-Werlag, 1992.