A Very Pleasurable Universe

Internationally Acclaimed Mathematician Maxim Kontsevich Chooses Berkeley as His Academic Home

by Robert Sanders

Berkeley can be tumultuous, but to Maxim Kontsevich it is a peaceful haven compared to the turmoil today in Russia.

Kontsevich is one of many elite mathematicians to abandon Russia in the past several years, leaving behind the crime and unpredictability of Moscow.

Courted by both Princeton and Harvard, he is a young international star the mathematics department feels fortunate to have attracted. One eminent scholar praised him as being among the most talented mathematicians to come onto the stage in the last five years.

A mere two weeks after his arrival on campus, his Evans Hall office is a barren expanse of gray linoleum, but he is filled with mathematical fervor. Along with Alexandre Givental and Vera Serganova, two other Russians in the department, he is already sponsoring a weekly seminar on mirror symmetry, his obsession at the moment. And he is immersed in teaching an advanced graduate-level course on deformation theory.

The slight, dark-haired Kontsevich looks younger than his 30 years, and a quiet demeanor fails to hide his playfulness. Play may well be essential to success in mathematics, and he admits to his share.

After leaving Moscow State University in 1985--without a degree--he spent five years at the Institute for Problems of Information Transmission where he devoted half his time to Renaissance and Baroque music (he admits to being "not bad" on the lute and viola da gamba) and the rest to mathematics.

He also enrolled in an intensive French class, where he met his future wife, Katerina Rosanova.

Despite a "very free life" at the institute, he did manage to publish enough to interest the prestigious Max Planck Institute for Mathematics in Bonn, Germany, which invited him to visit for three months in 1990. The culture shock was so immense, he says now, that he had little time for productive mathematics.

Just before his planned return to Moscow, however, he attended a five-day international meeting--the well-known Arbeitstagung--that each year draws the world's leading mathematicians.

The very first talk was by Sir Michael Atiyah on the subject of quantum gravity, a field that emerged from physics as theoreticians tried to model elementary particles as pieces of string knotted in complex ways. Atiyah mentioned an important conjecture by Edward Witten that so intrigued Kontsevich that he forsook the evening party and sketched out a proof, which he presented to the group before the meeting broke up.

Impressed, the institute directors invited him to stay for three years. He finished the proof of the Witten conjecture within a year and worked on various topics in mathematical physics. He also completed a PhD in mathematics from Bonn University.

He was glad to get out of Moscow, which was exciting but stressful during the era of perestroika and the fall of communism. Like him, nearly all the best mathematicians have now fled to the West, primarily the United States, Kontsevich says.

Kontsevich now has more Russian friends in the Bay Area than he has in Russia. Among them is his brother Lenny, a computer vision specialist in San Francisco. Even his parents left Russia to live in Korea. His father, a specialist in Korean history and language, now teaches Russian, while his mother, a mechanical engineer, is retired.

Berkeley lured him for several reasons, not only because of his friends and the pleasant weather. The Mathematical Sciences Research Institute on the hill above campus is much like the very active Max Planck Institute, he said. The faculty here are friendly, with a great diversity of interests, he says. Berkeley's mathematics department ranks among the best in the world and was recently ranked at the top in this country along with Harvard, Princeton, and MIT.

In Kontsevich's eyes, though, nothing will ever match Moscow State University. In 1980, when he entered at the age of 16, it was the largest and best of the two universities for mathematics in the former Soviet Union, a nation known for its contributions to the field. Around 400 students were admitted each year in mathematics alone, while the 100-plus mathematics seminars per week were enough to satisfy any appetite.

"It was a fantastic place--I never met such a concentration of mathematicians," he says. One of his mentors was MacArthur "genius" Award-winner Israel Gelfand, who is now at Rutgers and at 81 going strong.

At the moment Kontsevich is trying to unify two areas of geometry--symplectic and algebraic--in a way that explains the mirror symmetry discovered recently in string theory. This is now one of the most exciting and active areas of research on the boundary between mathematics and physics.

It isn't clear whether this mirror symmetry is related at all to the physics of the real world, but it exhibits what he finds most attractive about mathematics, beauty.

"For me, mathematics is a kind of independent and very pleasurable universe," he says.


Copyright 1994, The Regents of the University of California.
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