Юноше, обдумывающему житьё

Tanya Khovanova posted a list of problems that Andrei had considered important for undergraduate students to think through and solve by themselves.

Problem 1. Let G be a finite group of order |G|. Let H be its subgroup, such that the index (G:H) is the smallest prime factor of |G|. Prove that H is a normal subgroup.

Problem 2. Consider a procedure: given a polygon in a plane, the next polygon is formed by the centers of its edges. Prove that if we start with a polygon and perform the procedure infinitely many times, the resulting polygon will converge to a point. In another variation, instead of using the centers of edges to construct the next polygon, use the centers of gravity of k consecutive vertices.

Problem 3. Find numbers a_n such that 1 + 1/2 + 1/3 + … + 1/k = ln k + γ + a₁/k + … + a_n/kⁿ + …

Problem 4. For x₁ not equal to zero, let x_k = sin x_k-1. Find the asymptotic behavior of x_k.

Problem 5. Calculate the integral from 0 to 1 of x^−x over x with the precision 0.001.

62

Andrei would have been 62 today.

___________________
Photo courtesy of Katya Z.

Память рокового дня

Andrei passed away one year ago today. He is missed dearly.

Update: thank you all for warm words and pictures!

http://vng28.livejournal.com
http://xaxam.livejournal.com/607262.html
http://vitum.livejournal.com/225432.html
http://jewgeniusz.livejournal.com/222682.html
http://xaxam.livejournal.com/614831.html
___________________
Photo courtesy of Katya Z.

Transformation Groups Obituary

Andrei's obituary was published in the March 2014 issue of Transformation Groups (vol. 19, no. 1, 2014, pp. 289-302.)  Subscription is required to get the full text :(  A sizable fragment is available for viewing, though (click on ">> Look Inside".)

Update: Thank you, Sergei Yakovenko, for making the full text available!

61

Andrei would have been 61 today.

___________________
Photo courtesy of Katya Z.

Calculus Lectures at People's University

Andrei Reznikov, one of the students at the Jewish People's University, posted the notes Andrei Zelevinsky had prepared for the calculus course he taught there in 1980-82.

The notes were xeroxed (a criminal offence according to the USSR legal standards) by Boris Kanevsky, who was later arrested and served a lengthy prison term on trumped-up charges.

Thank you, Andrei Reznikov, for saving the notes and making them available online!

Uni­ver­sity Dis­tin­guished Pro­fessor

On April 18th 2013, at the university’s Aca­d­emic Honors Con­vo­ca­tion, Andrei was posthumously awarded the highest honor Northeastern can bestow upon a faculty member.

The photo (courtesy of Brooks Canaday/Northeastern University) shows Galya and Katya as well as Andrei's colleagues Profs. Valerio Toledano Laredo and Jonathan Weitsman talking with the Northeastern Pres­i­dent Joseph E. Aoun.

ACRT Conference

The conference "Algebra, Combinatorics and Representation Theory": in memory of Andrei Zelevinsky (1953-2013) will be held on the campus of Northeastern University in Boston on April 24-28th.

The talks of speakers who agree will be streamed live here. Please spread the word about the talks' availability.

Update: The videos of the talks are now available for download.

Wikipedia

Our heartfelt thanks to everyone who took part in filling Andrei's Wikipedia page with actual content!

Thank you, B.Y. and L.K. for your help and advice!

Thank you, Sergey Fomin, for collecting and organizing the information about Andrei's mathematical career!

And - first and foremost - thank you, Sasha Givental, for doing such an amazing job creating a real Andrei's page!

Rabbi Hausman's Eulogy

ANDREI ZELEVINSKY

Avraham ben Zev

In the Book of Samuel, there is an interesting conversation between King David and a very wise woman. King David had exiled his son and the woman had been sent by Joab, the king's general, to plead with him to forgive his son. In the course of the wise woman's plea, she refers to the brevity of life, saying, "Ki mot namut u'kha-mayim hanigarim artza asher lo yai-asfu," "We must all die, we are like water spilled on the ground, which cannot be gathered up." (2 Sam 14:14)

"Life," the wise woman says, "passes quickly; it is like water spilled upon the thirsty ground. It sinks into the earth and soon is no more." This metaphor for life is troubling. For if life is like water absorbed by the parched earth, does this mean that all we are and all we have done and stood for, is gone forever, absorbed by the sands of time?

I do not believe so. For implied in the words of the wise woman of Teko is a consoling truth. Even if our lives are like water absorbed by the parched earth, it does not necessarily follow that our lives are therefore futile. Is water spilled upon the ground lost? Is it not true that it is precisely this submerged water that makes life possible? It is the rain and the dew that falls on the ground and ceases to be that makes for life. Without it, we would perish.

And this is the way it is with the life of the spirit. Our fathers and the many generations who preceded them, poured out the water of their lives, their dreams, their ideals and their hopes, and they have been absorbed by the hungry earth of life.

You and I are the harvest. They have given us not only our bodies; they have given us our minds, our appreciation of the good and the true, our will to live and to achieve. We have absorbed into our personality, the spilled waters of their lives, just as we, in turn, will be absorbed in the lives of our children and our children's children.

What is true of each of us in our individual lives is even truer of a teacher, whose life reaches out into many lives and helps shape the spirits of several generations. The fresh sweet waters of knowledge that flow from her lips helps awaken the seeds of idealism, of goodness, of devotion to God and Israel and country in the hearts of children and adults alike.

Now, Andrei Zelevinsky’s years have come to an end. His life is like water spilled on the ground that cannot be gathered again. But, what he has watered with his life has grown and developed and continues as a force in the lives of those whom he has touched. "Utzror bitzror hahayim et nishmato." "May his soul be bound up in the bonds of life eternal and may his memory always be treasured as a blessing."

It was just a few short months ago when we gathered for your mother’s funeral, Galina. We come together again…you, your in-laws Vladen and Natalya, your children Leo and Katya, with broken hearts…yet, thankful for the gifts and sheer brilliance that Andrei brought to this world, his profession and his family whom he taught just as zealously with even greater love, devotion and concern.

I have only heard stories regarding the difficulties endured by Jews in the Soviet Union regarding education and professional advancement. He excelled at the Moscow “Second School,” graduate Moscow State University and was even more concerned about those who followed who suffered blatant discrimination, he and mathematics colleagues organized the Jewish People's University for mostly Jewish students denied similar educational opportunities. What an act of courage and defiance not only against state-sponsored anti-Semitism but also against totalitarianism.

Andrei reveled in the success of others and his students with the pride of a distinguished educator. It is as if he understood the Rabbinic aphorism “I learned much from my teachers, but most from my students” underscoring his selflessness and dedication, how he touched the minds and hearts to many people the world over. It really does denote what an exceptional person he was to so many.

Galina, Andrei was your partner. Dmitry, he was a very loving brother. Leo and Katya, he gave from his heart. Vladlen and Natalya, he was a devoted son. He was a compassionate grandfather who wanted his family’s future here. For many years, his life involved teaching, and being a teacher. I know how it can become your entire life.

Andrei Zelevinsky lived well and made a mark on too many lives to count. Indeed, his life was like water covering a field, giving life to so many whose lives he touched. May he now rest in peace as his memory will be a blessing in time to come. Amen.

Andrei ז"ל

Andrei Zelevinsky was a Mathematics Professor at Northeastern University in Boston. Andrei was a truly distinguished mathematician.  Among many other things, he co-developed a new innovative concept (quite a rare event) that had a tremendous scientific effect and generated a lot of new research in many fields by a large group of followers.

Just recently, Andrei was named a Fellow of the American Mathematical Society. He was awarded the title of The University Distinguished Professor - one of the university’s highest honors - and the ceremony bestowing upon him this honor posthumously will take place on April 18, 2013. Later this month, a conference in honor of Andrei's 60th birthday will be held on the campus of his university.

In addition to his outstanding research, Andrei was a great teacher.  All his life he enjoyed teaching kids: his younger brother, then his children, and recently started teaching his grandchildren. It is a huge loss for them that they won't be able to get more of Andrei's lessons.  Not only a beloved professor at Northeastern, Andrei spent a lot of his free time giving lectures at the math circle for gifted high school kids.

Andrei was uniquely qualified to work with gifted students. To succeed in deeply anti-Semitic Russia of that time, a Jewish kid had to be exceptionally talented - and Andrei was all that and then some. His mathematical talent became apparent at an early age and Andrei's achievements speak for themselves. He was a top student at the famous Moscow "Second School" (the school for the brightest kids at the time), he became a participant and one of the winners of the International Math Olympiad (the toughest problem-solving contest among the school kids from all over the world), and then made it to the top ranks of his chosen profession.

Andrei was fortunate to be given much and he was always generous in giving back to people around him. When a group of courageous mathematicians decided to try to fight the state-sponsored anti-Semitism (Jewish kids were blatantly discriminated against and were (almost) never accepted at the top colleges, including Moscow University) and organize the "Jewish People's University" for (mostly) Jewish kids who were rejected by the official system, Andrei was among the first and most active lecturers. It must be pointed out that this activity was exceptionally dangerous: some of the people involved were arrested and served lengthy prison terms on trumped-up charges, and at least one person was believed to be killed by the KGB. Part 3 of this book contains several people's recollections of what it was like, including Andrei's.

Many of the students Andrei taught at this Independent University - and other places, including the high school attended by both his own children - became distinguished mathematicians in their own right, which is surely a mark of a great teacher.

Andrei was a great family man and a great friend to many people all over the world.  When people got the shocking news of his passing, many of the responses were virtually identical: "Andrei was one of the best persons I have ever met."

He will be (and already is) missed by very many. 

Links

Russian blogs

http://xaxam.livejournal.com/537641.html
http://ntsil.livejournal.com/240560.html
http://sasha-br.livejournal.com/94347.html
http://vitum.livejournal.com/183719.html
http://sasha-br.livejournal.com/95581.html
http://xaxam.livejournal.com/538350.html
http://xaxam.livejournal.com/541607.html
http://rus4.livejournal.com/78815.html
http://atlmrf.livejournal.com/9798.html
http://vitum.livejournal.com/183292.html
http://sasha-br.livejournal.com/93845.html
http://cheeha.livejournal.com/668526.html
http://roman-kr.livejournal.com/599853.html
http://udod.livejournal.com/243645.html
http://jurginas.livejournal.com/662656.html
http://92-lina.dreamwidth.org/298898.html
http://aron-turgenev.livejournal.com/494053.html
http://prof-yura.livejournal.com/609310.html
http://aron-turgenev.livejournal.com/493741.html
http://vitum.livejournal.com/183361.html
http://vitum.livejournal.com/182917.html
http://ninazino.livejournal.com/1057059.html
http://cema.livejournal.com/597243.html
http://marina-p.livejournal.com/234085.html
http://russhatter.livejournal.com/181863.html
http://tandem-bike.livejournal.com/693807.html
http://prof-yura.livejournal.com/608816.html
http://posic.livejournal.com/943665.html
http://avva.livejournal.com/2600944.html
http://sthinks.livejournal.com/317401.html
http://zveriata.livejournal.com/81217.html
http://amerik.livejournal.com/208479.html
http://roman-kr.livejournal.com/580033.html
http://aron-turgenev.livejournal.com/493349.html
http://vitum.livejournal.com/182610.html
http://tandem-bike.livejournal.com/693655.html
http://otkaznik.livejournal.com/448605.html
http://jewgeniusz.livejournal.com/219334.html
http://french-man.livejournal.com/639520.html
http://xgrbml.livejournal.com/249235.html


Other

Katya's eulogy
Vladimir Retakh (in Russian)
Andre Reznikov
Троицкий Вариант
Мемориальная Страница
Gil Kalai's "Combinatorics and more"
Doron Zeilberger's Opinions
Alexandre Borovik's "Mathematics under the Microscope"
Northeastern obituary (see comment below)

Please point us to things we have missed.
Пожалуйста, добавляйте пропущенные нами ссылки.

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.

Andrei Zelevinsky 1/30/1953 - 4/10/2013

Andrei Vladlenovich Zelevinsky died early this morning (April 10) after a hard-fought battle with liver disease. 

He loved to communicate with all of you via this blog and LiveJournal.

Words cannot express how much he will be missed.

Funeral services for Andrei will be held on Friday, April 12th at 11 AM EDT at the Stanetsky Memorial Chapel in Canton, MA. If you wish to attend the service, please plan on arriving by 10:30 AM.

After the service there will be a gathering of family and friends to celebrate Andrei's life. Please email andrei(at)neu(dot)edu for details.

-- Andrei's family

___________________

Photo (C) Robert V. Moody

Картинки из Юты

Ссылка на фото-альбом, составленный нашей Karen. Традиционное путешествие Кэрин со своим семейством, семьей ее сестры Барбары, ее родителями, и нашей Катей, в Snowbird, Utah, на неделю школьных каникул. 

Blizzard-2013

Ну что, насыпало, как и обещали, немало снега - фута так два с половиной.К счастью, обошлось (пока?) без аварий, потери электричества, и т.д. Если отвлечься от того, что чистить, наверное, придется не менее двух дней, красота невероятная.

Несколько фоток для иллюстрации (довольно бедной) количества выпавшего снега:

И до кучи, фотка, сделанная несколько дней назад на пруду в нашем парке:

Красота, правда?

60

Мда. Честно говоря, менее праздничного настроения трудно себе вообразить. Кажется, всё-таки некоторое улучшение самочувствия имеет место, но бесконечно медленное, и решительных изменений к лучшему пока не видно. Просто не знаю, что бы я делал, если бы не самоотверженная поддержка Г. и всего семейства. Вот сегодня вечером всё же соберемся в тесном семейном кругу у замечательных Володи и Heather - огромное им спасибо за эту инициативу. 

Вторая часть воспоминаний об И.М.Гельфанде

в AMS Notices доступна здесь. Напоминаю, что с первой можно ознакомиться здесь.

Достал спам

Блоггер завел злобную привычку прицеплять спам в качестве коммента к нескольким, по большей части, старым постам. Точнее, бОльшая часть этих спамных комментов отлавливается их спам фильтром, но я всё равно получаю по почте уведомление о них, и должен открывать эти старые посты и проверять, есть там этот спам или нет. Только что попробовал такую ответную меру - разрешать комменты только людям, имеющим Google accounts. Если в результате кто-то из моих друзей лишился возможности комментировать, дайте, мне, пожалуйста, знать. Буду рад предложениям, как с этим лучше бороться.

Прошу прощения за возможное неудобство.  

Karen's annual newsletter 2012

Karen has posted her traditional annual newsletter: enjoy!

Happy 2013!

Наконец-то кошмарный 2012 остался в прошлом. Конечно, были и радости, но в целом год оказался для нас очень тяжелым. А уж в таком отвратительном физическом состоянии как сейчас, я и не помню, был ли когда-нибудь.  В общем, итог года для меня - намного более отчетливое понимание хрупкости человеческой жизни и здоровья ...

Чтобы не всё о невеселом, вот ссылки на два альбома, выложенные нашей Кэрин:

1. Ханукальное с моими родителями.

2. Прошлая неделя на Арубе. Увы, без нас с Галей ...

Всем друзьям наилучшие пожелания в 2013! Не болейте и бережней относитесь друг к другу. 

Nightmarish ending of a difficult semester

The program at MSRI is finally over, and I am back home. Scientifically the program seems to have been quite successful, with a great group of participants, talented mathematicians of various ages from all around the world. Everybody looked like they were having a great time, with a lot of continuing and developing  interaction and collaboration on new projects.

The program was built around a concept discovered by my friend and collaborator Sergey Fomin and myself about 12 years ago. It doesn't happen very often that such a young subject will have a semester-long program devoted to it. I couldn't possibly miss such an exceptional occasion, and indeed was treated very well there, being given probably the best office in the whole building! It was actually a great fun taking to other participants or listening to their talks and conversations, freely using the concepts and terminology introduced by Serezha and myself only recently, so that they sounded like they've been around for a long time.

Unfortunately, the good stuff ends here. I've caught some nasty infection in mid-September, and never really recovered from it, feeling gradually worse and worse. Then G.'s father passed away in the beginning of October. After returning to Berkeley from the funeral, I continued to feel rather poorly but the real crisis developed in the last couple of weeks of my stay. I had to go to Bielefeld, Germany on December 8 - 15 to attend a conference and give three lectures there, which I did on sheer willpower - the two very long direct flights from San Francisco to Frankfurt with a long trip by train to Bielefeld made me feel even worse than before. And then on Thursday December 20 I finally made it home but in a really poor shape. After landing I've learned that when my flight to Boston was in the air, my mother-in-law has suddenly (and very quickly) passed away too, leaving G. without both parents in two months. The memorial service and funeral took place today but before that I had to be admitted to a hospital for two days where they gave me a not very pleasant procedure yesterday (I spare the reader not too appetizing medical details). Usually they keep a patient for 24 hours after this procedure but they kindly discharged me almost immediately so that I could attend today's service and funeral. Fortunately our great kids took care of everything, so G. did not have to worry about the food, etc.

Anyway it's all over now, except my health problems (rather serious, I am afraid) that I will have to take care of. By the way, if any of my readers can recommend a good specialist in liver diseases in the greater Boston area (especially in the South) , I will be very grateful.

Oh yes, and our traditional family trip to Caribbean (Aruba this time) for the last week of the year will  be obviously without G. and me this time. Too bad, we were really looking forward to it ...

I am extremely grateful to my colleagues and friends at MSRI and Berkeley for their friendly kindness and help under these difficult circumstances. And to my Walnut Creek relatives Alik and Lyalya, and to A.B. and Marina  for their wonderful hospitality (sorry if I forgot somebody). And to the LJ-user sthinks who has become a real friend. Sorry guys, I was probably not the most entertaining company this time ...

Epitomic cuteness

Unbeatable in the cuteness department.
Maybe one should use this as a unit of cuteness?

Первая часть воспоминаний об И.М.Гельфанде

вышла в  январском 2013 номере Notices of the AMS. Мой текст - в самом конце. 

Соловей мой, соловей ...

Дожились: Соловейчика переименовали в Соловья и произвели в президенты Йельского Университета. Нет ли в этом антисемитизма? :)

Boston Globe on ABC

Вполне грамотная  статья о  Mochizuki и ABC conjecture. Интересно, чем дело кончится. 

Ребенок сам с усам

Ну вот, стОило отлучиться на пару месяцев, и на тебе!

И еще от одной не могу удержаться, с Кэрин и Грегги. Looking good, guys! Missing you.

Грибочки

К сожалению, собранные не нами, но всё же не могу не предъявить. Чистые и необъятных размеров подосиновики лучше бы переименовать в подсеквойники. А грибной сезон, похоже, только начинается!

xkcd про волка, козу и капусту

xkcd, как всегда, проявляет безупречный здравый смысл.

Упорный котик

Кажется, постить котиков в своих журналах - это окончательно опорочить себя в глазах интеллектуальных блоггеров. Против такого соблазна я, разумеется, устоять не могу.

via greenbat:

Загадка (чур не гуглить!)

Никогда, кажется, еще не выступал в этом журнале с этим жанром. Хочу попробовать.

Купил в продмаге продукт под названием "Newton's Folly". Что это?