He taught us to mathematics and joy of life

On April 10, 2013, after a serious illness, a famous mathematician, a student of Israel Moiseevich Gelfand, professor at the faculty of mathematics of the North-East University (Boston, USA) Andrei Zelevinsky passed away. He was born in 1953. In 1965 he entered the famous “second school”, in which such outstanding mathematicians as E.B. Pyunkin and I.M. Gelfand, and the teacher of history was a famous literary critic, publicist and human rights activist A.A. Jacobson. In 1969, he became a silver medalist of the International Mathematical Olympiad and in the same year entered the MHCAM of Moscow State University. He made an important contribution to several areas of mathematics, including the theory of representations, algebraic geometry, algebraic and polyhedrilic combinatorics. Together with Professor Sergey Fomin from the University of Michigan, he created the theory of cluster algebra, which was widely developed and has applications in different areas of mathematics. On January 30, he turned 60 years old. We publish several responses dedicated to his memory from his friends and colleagues, as well as fragments from blog entries.

Viktor Vasiliev , professor at the Faculty of Mathematics NIU-SHE, academician of the Russian Academy of Sciences

I worked a lot with Andrei Zelevinsky in 198588, when I.M. Gelfand called me to his hypergeometric project. Andrei was perhaps the main coordinator of this project besides I.M. His erudition and the ability to grasp new were needed in order to link the work of the project participants-and this is probably two or three dozen good mathematicians with their diverse knowledge, abilities and characters.

I vividly remember his ironic and approving word “devilry” when he was told something completely new and abstract. And yet, as he dreamed of learning from Gelfand to his art to find interesting tasks in (many hours) conversations with experts from different fields.

Although there is only 3 years between us, Andrei was much wiser and older. In the peculiar, but not always cheerful vicissitudes of our life, he always found an impeccable way of behavior, equally distant both from radicalism and indecent: it seems that this is an example of a person who never offended anyone. He had a wonderful reaction to unreasonable words and deeds - not condemnation, but a soft ironic commentary and surprised and even a joyful smile: well, it is necessary, what eccentricities are found in this funny world. Nevertheless, in this uninhabited way the position was fixed firmly and unambiguously. So Andrei remained in my memory: with a wise, joyful and grateful smile towards this funny and beautiful world, in which we all had a chance to be born, floundering and die.

Fedor Petrov , researcher at the St. Petersburg branch of the Mathematical Institute of the Russian Academy of Sciences

I just thought - it’s not the point for what reason - and which of the most significant mathematicians is active in the “Live Journal” and near (A. Zelevinsky led the blog http://avzel.blogspot.ru . - Ed .). Of course, he was the first to think about Andrei. That he had not written anything for a long time, for some reason did not think. The generalization of the Zelevinsky rule of Litlwood - Richardson had just passed with students. He just congratulated me on my birthday ...

To communicate with Andrei Zelevinsky, to go by invitation to Boston is a great joy and honor. We had dinner with Andrei and Galya, and the next day, Boston was repelled, and in the end I made a report only for Andrei and a graduate student who accidentally wandered him - but, I think, it happened for the best. He was weekly friendly, asked with interest about life in St. Petersburg, about my classes, actually not close to him (he was a pronounced mathematician of equalities and specific objects, and then I am more and more according to inequalities). Then he himself talked about cluster algebra. Undoubtedly, this is a deep phenomenon, to open which very little happiness falls out. Andrei, not without Self -irony, but without any coquetry, noted that Israel Moiseevich Gelfand would have had a long time to leave this matter, leaving others and moved on - but he did not let him go. ... And here is such absurdity, nonsense, not at all. I did not know that he was sick, I did not understand how it was and what.

Vladimir Retam , professor at the Faculty of Mathematics of the University of Ratger (USA)

I noticed Andrei Zelevinsky from the moment of his appearance at the seminar I.M. Gelfand. A visit to the seminar was capable of junior jackets or schoolchildren, but Andrei really burned with Andrei.

I was not very interested in his first works, there was clearly a combinatorial slope, and the combinatoric in those years in Moscow was not honored for various reasons. Andrei did not embarrass this, he never followed fashion, but rather, he created this fashion.

We made friends in Kratovo, where we shot summer cottages for the summer. My close friend Borya Feigin, a classmate Andrei, lived there, and we all the time discussed something. By this time, Andrei was already the closest employee I.M., the case went to the “hypergeometric project”, and Andrei was engaged in the formation of a new team around I.M. He suggested that I try his hand. As I was frankly explained by Andrei’s wife, Galya: “Andrei wants to work with decent people.” It should be noted that both she and Andrei always repeated: “Honesty is the best policy” and always followed this principle.

Then, in the country, we did our only joint work, which Andrei was very happy. He never hid joy from his own successes and was just as happy about the successes of others. With a special enthusiasm that I saw only at I.M., he showed me the A-System formulas that formed the basis of a hypergeometric project (at that time Andrei was still in bed after a long flu). Now the A-system is called the equations of Gelfand-Kapranov-Zelevinsky (it is more correct to include M.I. Graev in the number of authors).

In the fall of 1990, Andrei went to Kornelsk University to work, and I stayed in Moscow, and we met a year later at a conference in Japan. It was in August, because of the coup, the Japanese embassy detained me a visa, but after the noise raised by Andrei and his American colleague, the Japanese pressed on their embassy, ​​and I ended up in Kyoto. By this time, Andrei had already spent a week in Japan and took care of me as an old -timer.

In the fall of 1993, I arrived at the semester in Harvard. By this time, Andrei had already received a permanent place at the North-East University, and they settled in the whole family in Sheron, a small town 25 miles from Boston. I felt extremely uncertainly, and therefore I lived with Zelevinsky for a month until I rented an apartment. At this time, I.M., Andrey and Misha Kapranov finished work on the book on hyperoderminants. Andrei fully understood the importance of this work, although he constantly repeated that the style of the book was a mixture of French with Nizhny Novgorod and that with the help of the theory of D-modules, which Misha Kapranov masterly owned, any statement can be proved, not necessarily correct. Andrei worked in an incomprehensible way for me, sitting on the floor and overlaying papers, distracting to play in the th or something like that.

In general, the city of Sharon Zelevinsky, with their ability to constantly see in everything, was very fond of good. Somehow they drove a Russian colleague in the park. Andrei mentioned that they donated some amount to maintain the park. "Why?" The colleague asked. “Because this is our park,” Andrei answered. In the memorial park of Sheron Andrei and was buried. There are no tombstones, the graves are marked with small slabs in the ground.

In 2002, Andrei and Seryozha Fomin published the first work on cluster algebrams, founding a large, rapidly developing area. The ten -year results of this development will summarize the conference, convened in a few years in Boston. This conference was to celebrate the sixtieth anniversary of Andrei. Now we will celebrate his memory.

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Blog comments:

It seems to me that the main property of his mathematical activity was the desire to strive for some pristine simplicity, not forgetting about complex things, but politely leaving them to others (...). In other words, Andrei was always engaged in things that in the mathematical environment around me are considered “elementary” (in the sense of Low Tech as Opposed to High Tech)-he sometimes even flashed somewhat, but almost always these elementary things very quickly grew into some wild-elemental mathematical area.

Partly, apparently, this approach comes from his teachers-Gelfand and Bernstein, but Andrei’s personality made very important adjustments to this method (Andrei, perhaps, received aesthetic satisfaction from small details more than from some global picture). How, taking advantage of this “elementary” approach, he managed to find incredibly important and deep things many times, which then used thousands of people with a completely different mathematical background - we will never know this. (...)

I must say that when I was young and hot, such an elementary approach was not very impressed for me-1015 years ago it seemed to me all the time that Andrei was engaged in some kind of “non-war” things. The problem, of course, was (and is) in the fact that, unlike Andrei, I never knew how to see the tremendous perspective that opened behind these “elementary tasks” (at the same time, as I already wrote, I usually preferred to leave the study of this prospect for others) - I always needed everything at once. It’s not that he always saw where his activity could go-he simply had a very developed sense of beauty., 100%conviction that you can do only something very beautiful, and the deep faith that the truly beautiful things themselves do not appear ... As a result, he had a rather phenomenal ability to detect important things with the help of very simple and clear mathematics. (...)

For more details, see http://sasha-br.livejournal.com/94347.html

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I really do not know a single other person, the attitude to which from the part of absolutely everyone would be so unanimous: incredible pleasure from communication and boundless respect. About which this is why it is so, these days have been said: a truly unique combination of mind, rare intelligence, brilliant humor, compassion and tolerance, constant readiness to help with advice and deed, professionalism, amazingly friendly manner of communication and many other qualities, which are individually found not so often, but all together-almost never. And with all this, Andrei is unique in one more respect: he was a completely “normal” person in the best sense of the word - in the sense of absolute naturalness in any circumstances, the complete absence of “cockroaches”, shocking, poserity and other unnecessary tinsel. Again, I do not know other such examples.

We are used to cherishing and cherishing our cockroaches, considering them an important part of self-expression, and such words as “kindness”, “intelligence”, “tolerance”, and so on, seem to be even slightly shy: pathetic, they say, and it’s not too freshly. So, it was the communication with Andrei that personally returned my coordinate system to the right place: all this is nonsense, but in fact it is necessary like him, build his life, possess such kindness, intelligence, tolerance and other qualities, which can be listed endlessly, to treat your work and your family, and then no tinsel. We ruined the words with an inappropriate convert with them, and the concepts standing behind them-still the most important and valuable in life; Nevertheless, our cockroaches are only unconscious attempts to disguise their inconsistency with these concepts.

On the tenth of April, the world of everyone who was lucky to communicate with Andrei became tangibly angry, more hostile, more lifting. Subanimesome. We can only remember and try to become a little better for his memory - as we inevitably became better in the process of communicating with him.

http://ntsil.livejournal.com/240560.html

See also:

Personal page of A. Zelevinsky http://www.math.neu.edu/zelevinsky/andrei.html Nekrologist on the website of the Faculty of Mathematics Northeastern University www.math.neu.edu/news/andrei-zelevinsky-1953-2013/11_april_13

Words of memory of his daughter Katya (in English) http://veritykindle.livejournal.com/77694.html