Translated material
Mathematical constellation
In early May 2020, the names of ten new laureates of the European Mathematical Society Prize became known. They became:
Karim Adiprasito (Karim Adiprasito, Jewish University in Jerusalem / Copenhagen University)
Ana Caraiani (Ana Caraiani, Imperial College London)
Alexander Efimov (Mian, Moscow)
Semyon Philip (Simion Filip, Chicago University)
Alexander Logunov (Princeton University)
Kaisa Matyaki (Kaisa Matomäki, University Turku)
Fan Tan (Phan Thành Nam, Munich University named after Ludwig and Maximilian)
Joachim Serra (Joaquim Serra, Swiss Higher Technical School of Zurich)
Jack Thorne , University of Cambridge)
Marina Vyazovskaya (Maryna Viazovska, Federal Polytechnic School of Lausanne)
In this issue, we will talk about several laureates from around the world - about Semyon Filip , Marina Vyazovskaya , about Alexander Logunov and Alexander Efimov . Perhaps one of them will become a laureate of the Fields Prize, the presentation of which will take place in two years at the International Mathematical Congress-2022, which will be held in St. Petersburg.
The editors expresses gratitude to Andrei Okunkov for help in preparing this collection.
Viktor Vasiliev , Academician of the Russian Academy of Sciences, professor of the Faculty of Mathematics of the Higher School, President of the Moscow Mathematical Society:
The EMS award is a pretty good youth award, many of its laureates reach great heights in mathematics. Among the laureates of past years, ten years later became Fields medalists, including Maxim Kontsevich, Grigory Perelman, Andrey Okunkov and Stanislav Smirnov; Of the mathematicians working now in Moscow, this award was received by Alexander Kuznetsov and Stefan Nemirovsky. Both laureates of this year of Russian origin received the Prize of the Moscow Mathematical Society: Alexander Efimov in 2016, and Alexander Logunov in 2017. I already shared delights about the work of another laureate, Marina Vyazovskaya (see TRV-Science.ru/2016/12/20/Viktor-vasilev-Mathwalks/ ).
At the junction of two mathematical civilizations
Anton Zorich , employee of the Center for Promising Studies of Skoltha, professor at the University of Paris VII:
Semen Filip 33 years old. He was born in Chisinau. In addition to his native language, English, Russian and French, he also knows Turkish: the school in which he studied was unusual. The teaching of subjects such as physics and chemistry was conducted in English in high school, and as a foreign language, Turkish was taught. Semyon talks about his teachers with great warmth. Successful participation in the International Olympiads allowed him to study at Princeton University. During his studies, Semyon came to the semester in Moscow at an independent university under the Math in Moscow program. His diploma work in Princeton was led by Mariam Mirzakhani. After graduating from the university, Philip spent a year in Cambridge, after which he went to graduate school at the University of Chicago to Sasha Eskin (Alex Eskin) - to the co -author of Mariam.
Mirzahani and Eskin worked together for many years on a very difficult task and solved it just in those years when Semyon Philip studied in graduate school with Eskin. For the work cycle, including the solution of this problem, Mariam Mirzahani received a Fields medal in 2014 (and Sasha Eskin received Breakthrough Prize in 2019); Semyon Philip also participated in this project. In a short speech at the presentation ceremony, Mariam Mirzahani Field medal Kurt McMullen (Curt McMullen, the laureate of the 1998 Field Prize) identified three fundamental results in this cycle of work: classification of invariant measures received by Mirzakhani and Eskin; Topological classification received by Mirzahani, Mohammadi and Eskin; and the algebraic structure found by Semyon Philip.
The fact that Semyon managed to get very deep results already in graduate school is not an accident. Semyon Philip - station wagon. There are almost no specialists who are as deep as it are versed in the theory of dynamic systems and algebraic geometry in the world. Semyon works at the junction of these two areas. He studies the dynamic systems in the spaces of the modules of complex curves (that is, the way the surface of the surfaces under the influence of a special class of deformations) and on the spaces of the modules of the surfaces of Kalabi-Yau (such dynamics are responsible for many, many displays of special four-dimensional sympleic diversity).
For a series of brilliant results in this very actively developing area of modern mathematics, Philip received one of ten awards of the 2020 European mathematical society. These bonuses are awarded once every four years to young mathematicians; They are dedicated to the European Mathematical Congress.
After defending the dissertation in 2016, the prestigious glue scholarship allowed Semyon to spend three years in Harvard, where he had a special Junior Flow -Flow status. Since the fall of 2019, Semyon Philip has been working at the University of Chicago. His wonderful charming wife, Talia, writes a dissertation about the interaction of art, science and technology in the second half of the 20th century.
Semyon does not fit into the image of a "crazy genius not from this world." He is a station wagon in ordinary life. I won’t know when and how he manages to read a lot of books, watch a sea of films, spend time with his nephews in Bucharest and friends in Chisinau. I have known him for ten years and never once saw in him signs of stress, sports excitement of rivalry or nervous fever from the sensation of proximity of the solution. But with all the external softness and relaxation, when he begins to talk about mathematics, you wonder how accurately and clear its formulations are, how much he knows and how much different techniques are fluent.
I must explain what, in fact, is amazing the versatility of Semyon. The fact is that until recently, the theory of dynamic systems and algebraic geometry seemed infinitely remote from each other - both by what objects they study, and according to the research technique, and even according to aesthetic criteria. When studying dynamic systems, you study only asymptotic behavior of a complex system: relatively speaking, you are interested in what will happen in a hundred, a thousand or million years, and not the details of the current moment; In addition, almost always you soon or later with fatal inevitability come across objects of bizarre fractal nature. To study dynamic systems, numerical methods and modeling on a computer are often used.
Algebraic geometry is the direct opposite of this. It is characterized by the sophistication of the form and crystal honeness of the algebraic structure. A beautiful theorem in algebraic geometry as a good poem in which no word can be replaced. Until recently, most algebraic geometers belonged to the very idea of a computer experiment in mathematics as something shameful: proof should be obtained by the strength of the mind, and not a humiliating computer enforcement.
When the “dynamists” manage to strictly prove that the dimension of the object with which it or it work is not 1 (like the line) and not 2 (like the surface), but a certain unknown number, clamped in the interval between 1.6 and 1.8, they are happy: it seems to them unusual beauty. For most algebraic geometers, such an object looks at least repulsive, if not disgusting. Dynamics specialists, in turn, many results of algebraic geometry from the side seem too abstract. Most of the “speakers” believe that they are exploring existing phenomena from “real life”, while many algebraic geometers are sure that they are sole creators of their universe.
Ten years ago, many professional algebraic geometers of a high -class never in life have never heard of an ergodic theorem (which any student who is interested in dynamics knows), and many high -class dynamics have an unknown concept of the degree of stratification (which any student who is interested in algebraic geometry). Simplifying, we can say that until recently, the theory of dynamic systems and algebraic geometry coexisted as two civilizations that did not suspect each other. You can imagine how many new and beautiful results (including the results of Mirzahani, Mohammadi, Philip and Eskin mentioned above) it was possible to get when these two developed and powerful civilizations began to interact!
"I am studying dynamic systems"
Semyon Philip , a researcher at the Faculty of Mathematics of Chicago University, answered several questions of our newspaper.
- How did you decide to come to mathematics? Were there any doubts about the choice?
- When I studied in the second grade, our teacher recorded everyone on a mathematical competition for junior students, called Kangaroo. This lesson to me - to think about mathematical puzzles - really liked it, and besides, I spoke more decent than expected. At school, participation in mathematical olympiads allowed me to get acquainted with the subject better, and so I understood that I am interested in mathematics. It was much more important that I was surrounded by friends who were also interested in mathematics, informatics or physics; We were also led by an excellent teacher - Marciel Viktorovich Teleuke.
At the university, I quickly realized that mathematics is extensive and vast and very different from my school ideas. Nevertheless, I was interested in learning further, and again I was lucky with good leaders. I went to the courses and seminars organized by Yakov Grigoryevich Sinai, and in the last year, under the leadership of Maryam Mirzahani, I got acquainted with research work. Then I decided to go to graduate school. I learned a lot from my supervisor Alex Eskin - both mathematics and how to approach research.
Were there any doubts? Certainly. For example, in my school years, computer science was very interesting to me, and for some time at the university I considered it as a possible direction of work. It seems to me that at different stages the presence of an active group of people who were interested in mathematics and with whom I was interested in spending time played an important role in the fact that I continued to engage in mathematics. Of course, one has to work for a very long time, but then I always want to share thoughts with someone, and it's nice when someone else is also interested.
- How would you describe the area of your mathematical interests?
- I study dynamic systems. The general goal of work in this area is to understand how the systems behave, which, following a certain law, change over time. The systems and laws themselves can come from from any way, for example, from physics, biology or economics. The range of questions that can be studied by strict mathematical methods is very limited. For example, we cannot make the weather forecast 20 days ahead and, probably, we can never, regardless of progress in computers.
I note that the very understanding of why such predictions are impossible is the result of mathematical studies, which, in turn, indicated more meaningful issues and methods of studying dynamic systems. It turned out that many dynamic systems are unexpectedly associated with other sections of mathematics, such as algebraic geometry and numbers theory. An example of a dynamic system that models elementary physical phenomena and is very interesting to mathematicians is the movement of a billiard ball on a table of an unusual shape - such as a pentagon or polygon in the form of a Latin letter L.
Some of my works are related to the study of such systems or, more precisely, the space of all systems of this type.
-Could you not in the popular science format (we are read not only by physicists, but also philologists) to describe the result that was awarded the Prize of the European Mathematical Society?
- Risking to upset mathematicians and confuse all the other readers, I will try. Remember the circles on the plane that took place at school. The points on the circle can be described through the angle, or you can - designing the circle to a straight line. These are fundamentally different descriptions of the same object. The generalization of these two methods for more complex figures and in higher dimensions gave rise to two different approaches to geometry, which are called algebraic and analytical geometry. Some tasks are easier to solve with the help of one approach, some with the help of another, and sometimes there is an interesting connection between these approaches. For example, if you divide the circumference into 17 equal pieces, like a cake, it is easy to describe with corners, but, it turns out, it is very interesting to describe it through a projection to a straight line. (Why 17? I hope that your readers will find the answer to this question on the Internet.)
As I said above, my work is associated with dynamic systems on the surfaces. The geometry of the surface, as well as the geometry of the space of all surfaces of a given type, can be described in very different ways, similar to how I described the circumference above. The essence of my work was in evidence of the connection between the two methods of describing the surface, as well as in the study of how this description affects dynamic systems on this surface.
For more details, see math.uchicago.edu/~sfilip/