Autobiography of Maxim Kontsevich
I was born in 1964 in a suburb of Moscow, close to a big forest. My father is a well-known specialist in Korean language and history, my mоther was an engineer (she is retired now), and my elder brother is a specialist in computer vision. The apartment where I grew up was very small and full of books – about half of them in Korean or Chinese.
I became interested in mathematics at age 10 – 11, mainly because of the influence of my brother. Several books at popular level were very inspiring. Also, my brother was subscribed to the famous monthly “Kvant” magazine containing many wonderful articles on mathematics and physics addressed to high-school kids, sometimes explaining even new results or unresolved problems. Also, I used to take part in Olympiads at various levels and was very successful.
In the Soviet Union, some schools had special classes for gifted children, with an additional four hours per week devoted to extra-curricular education (usually in mathematics or physics) taught by university students who had passed through the same system themselves. At age 13 – 15 I was attending such a school in Moscow, and from 1980 till 1985 was studying mathematics at Moscow State University. Because of my previous training in High School, I never attended regular courses, but instead went to several graduate and research-level seminars where I learned a huge amount of material. My tutor was Israel Gelfand, one of the greatest mathematicians of the 20th Century. His weekly seminar, on Mondays, was completely unpredictable, and covered the whole spectrum of mathematics. Outstanding mathematicians, both Soviet and visitors from abroad, gave lectures. In a sense, I grew up in these seminars, and also had the great luck to witness the birth of conformal field theory and string theory in the mid-80s. The interaction with theoretical physics remains vitally important for me even now. After graduating from university, I became a researcher at the Institute for Information Transmission Problems. Simultaneously, I began to learn to play the cello and for several years enjoyed the good company of my musician friends with whom I played some obscure pieces of baroque and renaissance music.
In 1988, I went abroad for the first time, to Poland and France. Also in 1988, I wrote a short article concerning two different approaches to string theory, and maybe because of this result, was invited to visit the Max Planck Institute for Mathematics in Bonn for three months in 1990. At the end of my stay there was an annual informal meeting of mostly European mathematicians, called Arbeitstatgung, where the latest hot results were presented. The opening lecture by Michael Atiyah was about a new surprising conjecture of Witten concerning matrix models and the topology of moduli spaces of algebraic curves. In two days I came up with an idea of how to relate moduli spaces but with a completely new type of matrix model, and explained it to Atiyah. People at MPIM were very impressed and invited me to come back the following year. During the next 3 – 4 years I was visiting mostly Bonn, and also IAS in Princeton and Harvard. My then future wife Ekaterina, whom I met in Moscow, accompanied me, and in 1993 we were married. In Bonn I finished several works which became very well-known: one on Vassiliev invariants, and another on quantum cohomology (with Yu Manin, whose seminar I had attended back in Moscow). Scientifically, a very important moment for me was Spring 1993 when I came to the idea of homological mirror symmetry, which was an opening of a grand new perspective. In 1994, I accepted an offer from Berkeley, but one year later I moved to IHES in France, where I continue to work. In 1999 my wife and I were granted French citizenship (keeping our Russian citizenship as well), and in 2001 our son was born.
For a few years I visited simultaneously Rutgers University, where my teacher Gelfand moved to after the perestroika, and IAS in Princeton. During the last six years I have regularly visited the University of Miami.
In my work I often change subjects, moving from Feynman graphs to abstract algebra, differential geometry, dynamical systems, finite fields. Still, mirror symmetry remains the major line. The interaction during the last two decades between mathematics and theoretical physics has been an amazing chain of breakthroughs. I am very happy to be a participant in this dialogue, not only absorbing mathematical ideas from string theory, but also giving something back, like a recent wall-crossing formula which I discovered with my long-term collaborator Yan Soibelman, and which became a very important tool in the hands of physicists, simultaneously answering questions concerning supersymmetric particles, and solving the classical problem about asymptotics for equations depending on small parameter.
17 September 2012