Sunday, April 14, 2013

Memorial Page

Please leave your tributes to Andrel Zelevinsky ז"ל in the comments below. Feel free to use whatever language you are most comfortable with.

We apologize in advance, but from now on comments will be moderated. We will do our best to shorten the time gap between the posting of a comment and its actual publishing.

8 comments:

bukvoyeditsa said...

Очень больно и горько. Из ЖЖ-френда Андрей превратился в настоящего доброго друга. Мне было тепло от мысли, что далеко в Америке есть у меня друг, и целая семья друзей.
И вот...

Мои соболезнования Гале, и родителям Андрея, и всем детям и внукам.

Наташа

vitum said...

Фотографии Андрея в 7-го классе (1965-1966) из архива Георгия Ефремова (Юры Збарского): http://jurginas.livejournal.com/662656.html

byoussin said...

I think I was one of Andrei's first students.
It was 1972/3, I was in the 8th grade (corresponds to the 9th grade in the US), and Andrei was in his 4th year of Mechmat's undergrad program.
We met weekly, found an unoccupied classroom in the Mechmat building, and Andrei taught us algebra: groups, rings, fields, linear algebra...
The proofs were split into small parts that were offered us as problems to solve.
That was great!
A few more of my classmates took part, including nieuwe_zijde .
It was free, volonteer and totally unaffiliated, and lasted for two years.
Thank you, Andrei!

Anyone can claim being taught by Andrei earlier?

nieuwe_zijde said...

byoussin, спасибо тебе за добрые слова. Но мы таки не были первыми учениками Андрея. Сколько я помню, он вёл занятия по "спецматематике" в классе на год старше нашего. А классной руководительницей там была Галина Борисовна, она, я уверен, помнит.

Boris Bukchin said...

Дорогая Галя

Чудовищная весть ошеломила всех нас, сотрудников
МИТПАНа, кто хорошо знал и любил Андрея.
За недолгое время работы в Институте он запомнился нам
как замечательный человек и творческая личность.
Глубоко скорбим и сочувствуем Вам.
Андрей оставил глубокий след в науке и в наших сердцах.

Искренне Ваши

Эрна Бессонова, Молчан Жора, Боря Букчин, Шнирман Миша,
Вилькович Женя, Женя Резников, Света Ганнушкина,
Владилен Писаренко, Саша Соловьев, Володя Кособоков,
Ира Ротвайн, Игорь Кузнецов, Саша Горшков,
Петя Шебалин, Люда Бутова, Андрей Хохлов.

Gil Kalai said...

Andrei Zelevinsky passed away a week ago on April 10, 2013, shortly after turning sixty. Andrei was a great mathematician and a great person. I first met him in a combinatorics conference in Stockholm 1989. This was the first major conference in combinatorics (and perhaps in all of mathematics) with massive participation of mathematicians from the Soviet Union, and it was a meeting point for east and west and for different areas of combinatorics. The conference was organized by Anders Björner who told me that Andrei played an essential role helping to get the Russians to come. One anecdote I remember from the conference was that Isreal Gelfand asked Anders to compare the quality of his English with that of Andrei. “Isreal”, told him Anders politely, “your English is very good, but I must say that Andrei’s English is a touch better.” Gelfand was left speechless for a minute and then asked again: “But then, how is my English compared with Vera’s?” In 1993, Andrei participated in a combinatorics conference that I organized in Jerusalem (see pictures below), and we met on various occasions since then. Andrei wrote a popular blog (mainly) in Russian Avzel’s journal. Beeing referred there once as an “esteemed colleague” (высокочтимым коллегой) and another time as ”Gilushka” demonstrates the width of our relationship.

Let me mention three things from Andrei’s mathematical work.

Andrei is famous for the Bernstein-Zelevinsky theory. Bernstein and Zelevinsky classified the irreducible complex representations of a general linear group over a local field in terms of cuspidal representations. The case of GL(2) was carried out in the famous book by Jacquet-Langlands, and the theory for GL(n) and all reductive groups was a major advance in representation theory.

The second thing I would like to mention is Andrei’s work with Gelfand and Kapranov on genaralized hypergeometric functions. To get some impression on the GKZ theory you may look at the BAMS’ book review of their book written by Fabrizio Catanese. This work is closely related to the study of toric varieties, and it introduced the secondary polytopes. The secondary polytopes is a polytope whose vertices correspond to (certain) triangulations of a polytope P. When P is a polygon then the secondary polytope is the associahedron (also known as the Stasheff polytope).

The third topic is the amazing cluster algebras. Andrei Zelevinsky and Sergey Fomin invented cluster algebras which turned out to be an extremely rich mathematical object with deep and important connections to many areas, a few are listed in Andrei’s short introduction (mentioned below): quiver representations, preprojective algebras, Calabi-Yau algebras and categories, Teichmüller theory, discrete integrable systems, Poisson geometry, and we can add also, Somos sequences, alternating sign matrices, and, yet again, to associahedra and related classes of polytopes. A good place to start learning about cluster algebras is Andrei’s article from the Notices of the AMS: “What is a cluster algebra.” The cluster algebra portal can also be useful to keep track. And here is a very nice paper with a wide perspective called “integrable combinatorics” by Phillippe Di Francesco. I should attempt a separate post for cluster algebras.

Andrei was a wonderful person and mathematician and I will miss him.

imarek said...

С трудом прихожу в себя: до сих пор очень трудно поверить, что Андрея больше нет с нами. Если подумать, я встречался с ним всего 3-4 раза (в Орхусе и в Кембридже), да и в этом блоге комментировал нечасто (хотя всегда с интересом читал). Но у меня чувство, что ушёл близкий человек.

Как многие уже написали, трудно представить себе человека более приятного в общении, чем Андрей. Очень сожалею, что мало говорил с ним о математике. То, чем я занимался раньше, вроде бы, было далеко от сферы его интересов. В последнее время всё чаще натыкаюсь на работы Андрея. Например, не так давно я прочитал его известную статью "A generalization of the Littlewood-Richardson rule and the Robinson-Schensted-Knuth correspondence" (Journal of Algebra, 1981). В этой короткой статье Андрей вместо традиционного (и малопонятного) правила Литтлвуда-Ричардсона вводит простую, красивую и "симметричную" формулировку, которая, к тому же, работает в более общем случае, чем изначальное правило. Мне кажется, эта формулировка ("Zelevinsky's pictures") должна войти в учебники по представлениям симметрических групп. Это только один маленький пример того, что сделал Андрей в математике. Многие другие его работы мне ещё, надеюсь, предстоит изучить. Жаль только, что поговорить с Андреем обо всём этом уже не получится.

Мои глубокие соболезнования всем родным Андрея.

Lindsey said...

So sorry to hear of Professor Zelevinsky's death. He taught me as a freshman in 2009 at Northeastern. I found that he was a wonderful teacher, and he was able to explain complex topics in language a non-mathematician could understand. He also had a wonderful sense of humor. He will be missed.