亚历山大 • 贝林森自传 (只提供英文版)
I was born in 1957 in Moscow. The city was much smaller then and still retained some rural character: small wooden houses with gardens, an occasional horse-driven cart. After the joy of early childhood, going to school was a setback. After 7th grade I went to mathematical school no. 2. It was a true change: lectures and seminars on advanced mathematical topics taught by professors and students from the University, the shining classes on literature and on history. I got to know A Parshin, and in 1972 he took me to I Gelfand’s seminar; this was the start of mathematical life. After school I entered Pedagogical Institute, and in 1977 moved to the University to be Y Manin’s student. Attendance was not enforced; skipping all classes of no interest (an officer informed me I was the champion of playing truant) gave much time for walking in the woods and for doing math. I graduated in 1980, and V Alexeev took me to his computer lab at the Cardiological Centre. Sadly, he died soon after. By the word of Gelfand, I became an engineer with no responsibilities at the biological division of the Centre and gained the same freedom as in my student years.
To those who wished to see things with one’s own eyes, and valued free time to think — not focusing on their career — the Moscow of my time was a very nice place to be. Since Khrushchev announced that his predecessor had been a criminal, much of the public relegated all things related to the powers that be to the domain of the ridiculous. People were connected by the flow of books; poetry was learned by heart. A unique art, light and free, came to life: to get a taste, one can watch Yu Norstein’s animated movies “Hedgehog in the Fog” and “Tale of Tales”, and read Yury Koval (it’s a pity the best of Koval’s books — the finest Russian prose of the time — are not translated into English). Mathematics was largely a part of that culture.
Doing math is akin to unfolding a melody; its first sounds are usually a gift from someone else. My first paper was written in the footsteps of the ADHM classification of instantons. I caught the idea of higher regulators while preparing a talk on S Bloch’s work; this led to conjectures on the values of L-functions (still widely open) and to speculations about mixed motives (largely realized by V Voevodsky and A Suslin). Conversations with R MacPherson and P Deligne brought forth our work with J Bernstein on the Kazhdan–Lusztig conjecture; we played happily with D-modules and perverse sheaves until Bernstein left Russia at the beginning of 1981. In the mid-80s, A Belavin taught me the basics of string theory and conformal field theory; his work with A Polyakov and A Zamolodchikov came to be a source of the idea of factorization geometry developed later together with V Drinfeld.
At the end of the 80s “perestroika” brought into Moscow streets immense crowds calling for changes. These arrived: the country was split and pillaged by the robber barons, the life losses on par with those in the Civil War 74 years earlier. In 1989 I went to the Landau Institute and, for two months in the Fall, I was at MIT. Around 1993 I began to work with Drinfeld on his approach to geometric Langlands theory via the quantization of Hitchin’s fibration, and on factorization geometry. In 1998 we moved to Chicago. Drinfeld joined us within a year. Since then, we have run “geometric Langlands” seminar at U of C, which resembles the Gelfand seminar of yore.
In America there are still some woods; the trees are magnificent, the animals full of grace and wisdom. Life is very kind to me. But one can’t help seeing everywhere the madman’s effort to build in his own image a fake world by destroying the real one, together with its live magic we are all part of. In his Dachau diaries E Kupfer-Koberwitz wrote that the worst of what humans do to themselves is a direct consequence of what they do to animals. Perhaps the death spiral cannot be stopped unless a phase transition in our attitude to ourselves and to Nature happens, and we realize that animal lives matter no less than human ones.
20 May 2021 Hong Kong