The HLF Portraits: Grigori Margulis
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The HLF Portraits15 / 66
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00:00
Internet forumMusical ensembleBitUniverse (mathematics)NumberGroup actionPhysical systemGame theoryMultiplication signCASE <Informatik>MereologyMathematicsMathematicianPoint (geometry)CircleDirection (geometry)Expected valueGradientCategory of beingFamilyLevel (video gaming)Computer chessRegular graphStandard deviationEnterprise architectureFile viewerRight angleDistanceData recoveryTerm (mathematics)FrequencyCorrespondence (mathematics)Decision theoryStudent's t-testMathematical analysisVideo gameInheritance (object-oriented programming)Neighbourhood (graph theory)Metropolitan area networkType theoryArithmetic progressionComputer animationMeeting/Interview
08:35
Faculty (division)Universe (mathematics)Observational studyMereologyMathematicsDifferent (Kate Ryan album)Axiom of choiceStudent's t-testNumberMechanism designPhysical systemExtension (kinesiology)Level (video gaming)Degree (graph theory)Process (computing)Fields MedalMusical ensembleCorrespondence (mathematics)Sound effectSurvival analysis2 (number)Boundary value problemHidden Markov modelGradientVideo gameFlow separationPhysicalismRight angleInheritance (object-oriented programming)MetreMetropolitan area networkSolid geometryState of matterCondition numberTraffic reportingTask (computing)HypothesisMeeting/Interview
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MathematicianRight angleErgodentheorie1 (number)Category of beingDiscrete groupProof theoryPoint (geometry)Dynamical systemDegree (graph theory)Direction (geometry)CircleMathematical physicsMathematicsObservational studyDecision theoryNumberException handlingStudent's t-testTerm (mathematics)Multiplication signPhysical systemOpen sourceFields MedalComa BerenicesElectric generatorWaveGroup actionMedical physicsLevel (video gaming)Metropolitan area networkMoment (mathematics)TowerBell and HowellCondition numberSineTheoryIndependence (probability theory)Power (physics)HypothesisProcess (computing)Personal digital assistantState of matterMeeting/Interview
25:39
BitPoint (geometry)Multiplication signFields MedalProcedural programmingRule of inferenceType theoryMereologyDifferent (Kate Ryan album)Computer fileImage resolutionPosition operatorGroup actionCentralizer and normalizerCASE <Informatik>Flow separationMultilaterationRight angleMathematicianWordGoodness of fitExtension (kinesiology)Execution unitQuicksortDigital electronicsDataflowMathematicsCausalityCodecDivisorSystem callSinc functionOpen sourceSubgroupMeeting/Interview
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Point (geometry)MathematicsType theoryInformation securityNeuroinformatikFrequencyFlow separationPosition operatorMultiplication signDegree (graph theory)Right angleStandard deviationSubgroupNumber theoryGradientCartesian coordinate systemOpen sourceGame controllerComputerInteractive televisionSubject indexingInformationStrategy gameDirection (geometry)CASE <Informatik>Range (statistics)NumberInternetworkingComputer scienceVideo gameDivisorDifferent (Kate Ryan album)Observational studyExpandierender Graph3 (number)Goodness of fitSpherical capRoutingDynamical systemRule of inferenceComputer fileDiscrete groupInformationstheoriePerfect groupMeeting/Interview
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Maxima and minimaCondition number2 (number)Term (mathematics)RootDirection (geometry)Natural numberStudent's t-testFields MedalPhysical systemDifferent (Kate Ryan album)Point (geometry)Hand fanAttribute grammarMathematicsMaizeMultiplication signGroup actionBookmark (World Wide Web)Level (video gaming)Touch typingVideo gameSpecial unitary groupSuite (music)InternetworkingSound effectMetropolitan area networkMeeting/Interview
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Process (computing)Goodness of fitFluid staticsResource allocationExpandierender GraphDecision theoryCartesian coordinate systemFields MedalPerformance appraisalDirection (geometry)MathematicsMathematicianLink (knot theory)NeuroinformatikMeeting/Interview
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Internet forumBit rateComputer animation
Transcript: English(auto-generated)
00:17
Professor, I'd like to begin with your earliest influences, your family.
00:22
Where are you as a child and what are your parents like? Yeah, I was born in Moscow in 1946, Moscow, Russia. And my parents, so my father was, he was a mathematician, but mostly he was in education.
00:48
And so he worked for, during his life in various institutes around Moscow. Secondary education? No, no, no, higher education.
01:02
Higher education. He was, okay, so called candidate of technological sciences, which is corresponds probably to PhD in education. When you were born was a rather terrible time.
01:21
In 46, but okay. I mean a terrible time in terms of economics and recovery from the war. Was the family situated comfortably or was it a very difficult way to live? No, no, probably I don't remember.
01:42
So it's the World War II finished ended in 1945. Exactly. In 46, but I probably don't remember anything. But even by the 50s, was it okay? Was it? No, you know, so it depends by what standard.
02:02
So it's, if it's you, you know, so it's my, yeah, so my mother actually was most of her life was, I was called her homemaker.
02:21
But later she worked for her son. Had she been educated? I mean at the university level? Your mother? My mother, maybe some kind of college probably, but yeah, I think so, but. How many children in the family?
02:41
Just me. Just you, only child. Are you aware, of course not at the first years, but maybe by 8, 10, of their expectations for you, hopes for you, direction of? Yeah, actually my father more or less
03:11
Would this be through games? No, no, no, no, probably sometime. You know, so I actually, I would say multiply two digit numbers at quite a little age.
03:28
And you know, somehow more or less it was kind of, it is probably clear to him and probably to me that somehow I will be a mathematician.
03:42
So your talent, because in some cases some of the extraordinary people I've spoken to have said their talent wasn't so obvious at an early age, their disposition, it developed later, but you would say as a child it was apparent that you had some mathematical talent? Yes, probably.
04:01
Did you have a tutor in this or was it? No, no, no, not in this. No, no, it's, you know, so also I was, I played chess in more or less some kind of, not professional, but yeah. So there was certain circles where some groups of children, okay, played chess.
04:27
There's actually chess in the Soviet universe kind of the government enterprise. Yes, and a discipline for the young. But it's kind of one of the prides.
04:43
Yeah, there's chess champions for quite a long period of time from the Soviet Union. And how good were you at chess? Yeah, now there's these numbers, but yeah, I had at the end what was called
05:03
period as their first category. So it's, I was not a chess master, but you know, it's relatively good. I don't know how it's translated into currently rated. But chess was an influence.
05:21
Yeah, but I played chess until I entered the universities because somehow it's, I tried to combine with how it didn't work. Tell me a little bit about your schooling before university.
05:40
What kind of school was it? What were the teachers like? It was more or less regular schools. And so it's, yeah, so at that time there was some transitions.
06:01
So it was 10 years then and at some point they wanted to do 11 years. But somehow during my time, somehow in my district there was only one school for 10 years and my father somehow arranged me to go there and somehow there are probably
06:25
some better schools. Yeah, there were probably some, you know, some students were from the neighborhood, but there are also some other students from the entire district.
06:41
So it was, is it fair to say, somewhat advanced? No, no, no, probably it was not advanced, but it was a regular school, but kind of. In that system, the Soviet system at the time, are you tested along the way to determine? No, but I think for my mathematical education or progress about what was maybe more important,
07:10
that there was Olympiads and there was mathematical circles. We just started it and started from the seventh grade and participated in the Olympiads.
07:22
I'm just guessing you did well? Yeah, I did well. Yeah, I was in the 10th grade. I got the first prize, but yeah, necessarily quite well. Is there a particular teacher again in your earlier years?
07:44
No, in school probably not. In school, probably not. So more likely outside activities? Yeah, probably in this system of mathematical circles, it was associated with the university, so we started this kind of solving problems, and this is how it was kind of
08:08
important part of the preparation to become. Right, exactly, and it's really preparation I'm thinking of. You're doing well in these. You're doing well in school, I can imagine.
08:23
So comes the time to decide university. How was that decision made? Was it inevitable that a clever young man? Yeah, somehow I was determined to become a tutor. So there was Moscow State University was somehow the system.
08:43
There is quite a different system here, so it's subdivided, it wasn't is subdivided into so-called faculties, which is like mathematics, faculty, it's maybe in German
09:05
there's something like that, mathematics and mechanics, physics, chemistry. So you begin in a faculty? Faculty, yeah. Yeah, faculty here means somewhat different. Yes, I understand, I understand, but they're in the line of study.
09:22
Yeah, somehow it was, yes, here somehow you end the university college, but then you choose your major. Right, but this is not it. The choice happens when you enter the university. Yes. And was it clear to everyone, particularly you, that mathematics would be aligned?
09:41
Yeah, yes, it was clear, yeah. And you would clearly... For example, about the size, so for example, each year's faculty and mathematics and mechanics was combined. I think number of students was something like 450, so it's 250. They would have come from all over the Soviet Union, not just...
10:05
I think, yeah, not so, I don't, I cannot, but I think maybe a significant part from Moscow, but also it's... Was it truly a national university?
10:21
Yeah, no, no, it wasn't a national university, yes. Yeah, yeah, for students who lived in Moscow, they lived with their parents and so, and who came from outside, they lived in dormitories, so there was... Yes.
10:41
Was there, again, a system, because I don't know it, of particular attention paid? I mean, I know you seem a modest man, but I still want to understand the extent to which you might have been noticed early, because in fact,
11:00
your undergraduate career is very successful, and I think you published three papers. So I'm just wondering, you've entered and the system of either noticing you or getting you involved in interesting problems? No, no, no, yeah, yeah, no, so I actually, again, so when entered this Moscow, okay, this mathematical biology faculty and mathematics mechanics,
11:24
so there, yeah, there was a huge number of seminars. Okay. And in various fields, so it's different parts of mathematics, and somehow I, maybe during first year, maybe second, I attended many of them somehow, even
11:45
not understanding what is, yeah, what is better, what is... Yes, your sampling. Yeah, the sampling, but yeah, but starting then second year, yeah, actually
12:05
the union, so altogether it was five years. So not for like here. Five years for the first degree? For, it depends what you go for. Okay, what degree would you get? Probably it's a bachelor, I don't know, it's, it's hard to compare, maybe
12:27
corresponds to maybe something in bachelor and master, but you get some what is called diploma, diploma, so it's... Right, but it's not a professor level degree. No, no, no, no, no, it's an undergraduate degree,
12:43
and then it's starting third year, so actually students were supposed to write some kind of, which is a kind of thesis, but it's kind of small.
13:01
Yeah, there's some quite a researcher, quite a research paper, and during the fifth year, there was diploma, in Germany, there was a diploma, maybe in other countries also, but,
13:22
and yeah. So again, the process of being allowed or encouraged to take on certain things, I think your first paper was after your second year? No, my first paper was published in 1966, which was during my
13:46
probably fourth year, but, but probably I, I wrote it maybe at the end of the third year. Oh, really, so you... Probably six, yeah, no, I ended in 62, so 63, 60, probably yeah, yeah, maybe at the end of
14:14
the third year, and then it was published in 66, which was the fourth year.
14:24
Was it unusual for an undergraduate in mathematics to be publishing so early? Actually not, you know, actually it's quite, yeah, I think so after undergraduate, you know, so it's, it was five years,
14:44
and actual subjects were mostly mathematics, but then also some physics, and also some kind of, not humanities, but social disciplines, history of the communist party. Kind of broadening humanities.
15:03
It's a political economy, Marxist philosophy. Right, of course. Yeah, so in this, that with this flavor. How did you focus on the subject that became this paper? How, and again, I'm not a mathematician, but... Yeah, no, so sorry, yeah, no, so I actually told you that I attended quite a few seminars,
15:25
and one of the seminars was directed by Professor Dinkin, who now is, who died. He was born in 1924, and then he was immigrated in 1977.
15:48
He was a professor at Cornell. Wow, so he left early. Yeah, so he actually... But what was, what was his... Yeah, yeah, but it was...
16:01
Okay, so seminar was at a, kind of, what's called, some kind of probability, marks and boundaries, and then he posed some question, and actually not to me, but, and then I was, yeah, I was able to solve this, and then
16:25
yeah, no, so I actually, yeah, no, so, and then, so after undergrad, some, some undergraduate students were recommended to graduate school, which was for three years. Three years, and that would lead to what we would think of as a doctorate,
16:44
but at least a credential to teach. No, it's, no, it leads to, to here, to go to PhD. Okay. So the, the dissertation, and actually to, kind of, to be recommended,
17:02
as at least in Moscow University, to be recommended for all this... Higher up degree. For this graduate school, yeah, I would not say it was a necessary condition, but it was quite desirable that people had published paper, submitted for publication.
17:25
Demonstrated some real ability. I know just from having read about you, that one of the significant professors, I think it was at this stage, was Yakov Sinay.
17:41
Yeah, who is now in Princeton. Yes, yes, amazingly. How did your relationship begin? Were you assigned? No, it wasn't, it's a, again, I saw somehow it's, yeah, so usually during this undergraduate years,
18:06
we're supposed for this, could survive for this year, you, you had to be, work with someone, and then,
18:24
yeah, but probably after, during the fourth year somehow, I started to interact with him. So it's actually, it's, I cannot point a moment, but actually... Right, but you were drawn together, because he also has to be...
18:42
Yeah, so also I attended one of the seminars, which I attended was his, and so it's... I know it's difficult to describe in layman's terms, but what was the direction of his work? What was... So his work? No, it was dynamical systems, ergodic theory.
19:09
Now he's also works in some aspects of mathematical physics. So he got the Albert Price in 2014 for...
19:20
But he didn't get it yet when he was your teacher, so... Yeah. At that point, what was he stressing, as a direction from... Yeah, I think it's... Then he started with, he was a student of Kolmogorov, and he is kind of one with first achievements was...
19:43
So there was a so-called Kolmogorov-Sinai entropy, so it's... And then he wrote quite a few, quite a number of papers on ergodic theory and dynamical systems. Did you ever do a paper with him?
20:02
No. Okay. Because we've had these colleagues along the way, but nevertheless... Again, I ask a very broad question, and that is... How one makes decisions about the direction of one's research?
20:23
I mean, I think by now you are already... Sure, you will be a theoretical mathematician. But there are many directions you... Yeah, so actually it was, you know, so related to Sinai, there was...
20:43
Did some work in dynamical systems, but then it's actually also interacted. So actually, one of my classmates was David Kashtan, who is...
21:01
Yeah, he emigrated in 1975, and he was a professor at Harvard, and he moved to Israel, and he was at Hebrew University, now he retired. He was a colleague or a professor for you? No, he was just the same generation, the same age, the same year,
21:30
maybe three months younger than me. And so I actually during, in 1967, there was in near Dushanbe, which is Tajikistan.
21:48
Tajikistan, yes. Yeah, there was nearby a so-called summer school, which is, okay, some kind of conference, but it took two or three weeks.
22:01
And then it's during that time, somehow we more or less started to finish shortly after that some paper, which is what's called proof circle conjecture, which was actually not in dynamical systems, but in league groups, discrete subgroups of league
22:22
groups, and actually maybe it's in the sense it was my first famous paper. Yeah, actually there was a talk by Armand Barrell, who was... He was an institute with one study, but at that time, and he gave a talk at Burbaki seminar,
22:44
which is actually, it's quite prestigious. And this inspired you? Yeah, and then it somehow started from that, somehow also under strong influence by Pityatsky Shapira, who is, who now, okay, he died, but eight years ago.
23:11
And so some direction about discrete subgroups of league groups, and then it's for quite a while I continued to work on that.
23:21
You published what I think is described as your first famous paper before you have gotten the, before you have finished your course in the graduate study or? Yeah, so actually this paper was actually written just after
23:42
my alma mater, maybe at the same time as undergraduate. So it's published during the first year of graduate. So I ask a question again from outside the profession, and that is that it seems, unlike my own profession, history or other fields, that it is not surprising
24:08
to see great talent begin to produce productively at a young age in mathematics. Is this? Yeah, it depends actually. It's about in this country, it's not true.
24:26
It's not true, but it seems very early for you to be? Yeah, those are some exceptions in this country, but mostly it's I think more or less first published paper is PhD thesis, which is about age 26, 27, 25.
24:51
But in the Soviet Union of your time? In the Soviet Union of my time, yeah, for example, this Kashdan actually, he had a very, very famous paper, and there was an international congress in Moscow in 1966, and
25:09
during this, he did some very famous paper, Property G, and he was 20 at that time.
25:22
Right. Was that remarked on, or was he such a young man? No, it was a very influential paper. Yeah. Okay, I ask another general question, and that is, particularly as I've read about you, you are celebrated as original in your approaches. I mean, anybody who produces something
25:46
has to do something original, but that you take on, and of course, we are not only talking about your graduate career, but on, you take on issues, questions, problems that other people
26:01
assume cannot be solved. Now, whether you agree broadly about that, I think, I think you seem to be very free in your accepting of problems that others feel are very hard to solve. Is this true? Yeah, yeah, this is, you know, actually the different types of mathematicians and
26:25
and somehow I, at least at the first stage of my career, I was more or less tried to kind of solve problems. That people thought were unsolvable.
26:42
No, at least they couldn't solve. That they couldn't solve. Yeah, and yeah, it's actually this paper with Kashdan who was also... Was such a paper. Yeah, it was for, and some people couldn't prove this, but then it's for some time,
27:07
I, you know, it's somehow, okay, I got a Fields Medal and probably mostly for work in this crystal group of league groups, and there was, maybe I'll use some medical terminology, but a group of arithmeticity of higher-end
27:26
classes, which was kind of a problem, which was posed by Selberg and Pachecki's appearance, and how it, there were several cases, and... And you...
27:40
Yeah, and it's okay, okay. Can we use the word solve the problem, or what is... So, okay, prove the conjecture, so solve the problem, maybe, okay, solve the problem. Okay, the field is awarded very rarely, I mean, what is it, every... No, it's awarded during conferences for every four years, and then when it started it was
28:07
for two people, and then it was raised to four, and then more or less it went to and for mostly four, but that...
28:21
You receive the award, I mean, we will talk a little bit about that, how you could literally receive it, but you were awarded this in 78. Eight. You were at that age of... 32.
28:40
I think also, is it right, I'm not sure, that the award is only awarded to people under 40. Yes. Yes. Yeah, I think the rule now is, should not be more than 40 during the year of the Congress.
29:02
Oh. So, basically it's... So, news comes of this award, which is a immense distinction. You are in Moscow at this point, and again, famously, you are not allowed to go and receive it.
29:22
Why, is this something that helps us understand Soviet academic culture, or was this something personal? Why were you not able to receive it? So, again, traveling abroad was not considered to be a right, but a great privilege.
29:49
For example, there was socialist camp, and then there was west. So, travel to Eastern European countries was...
30:02
Not hard. It was hard, but not bad. Very possible. No, but, yeah, now the procedure was, what to say, go to the west. So, your institution has to produce some file which consists of several parts.
30:30
One of this is so-called characteristic, which is kind between something between biography and recommendation, and it should be signed by director, and then
30:46
secretary of party committee, and secretary of the trade, professional trade union. Okay, then it should be approved by district party committee.
31:12
So, then it should be sent to... Unbelievable. Signs, okay, and then it should be...
31:21
Okay, then it goes through several many steps, and actually, in the case of the travel to western countries, it was approved by the center. It had to go very high. The central committee, but, okay, there was not to...
31:40
But close. Not to some minister. Why were you not suitable? No, but then there was something many steps in between. So, there were many, okay, there were many people who could stop,
32:01
and I think in my case, more or less, I'm quite sure it was a mathematical establishment. Yeah, it's not actually, in that case, it was kind of government. Right. So, it was, and why they didn't want? No, okay, so it's somehow they didn't, yeah, not somehow, so they didn't consider that
32:32
I didn't think that I had to be awarded this, and so it's... Was it remotely, and I can understand it was not, affected by the fact that your
32:45
your mentor, your great mentor, Sinai, had left the Soviet Union? No, he left much later. He left much later. Okay, so it wasn't because of your association? To a large extent, it was anti-Semitism, but also somehow,
33:11
in some sense, officially, I was not a mathematician, but I worked, I worked in actually quite good, in a quite good position in academic sciences,
33:20
but it was not a mathematical institute. You bring up anti-Semitism, we won't spend a lot of time with this, but it was a factor, I mean maybe not only in this. But it was possible to point some, you know, so there was so-called National Committee of Soviet Mathematicians, which at that time was General, was
33:43
Dinograd, who was the director of the mathematical institute, he was a great mathematician, but he was also Politically, oh, he was anti-Semitic. Anti-Semitic, yeah, but it's not just him, but somehow.
34:03
Was that, I mean, I can see perhaps it affected whether you could travel then, although we will reach a point where you can travel, but would it affect a career in something as pure as mathematics, where it's a matter of simply what you can do?
34:21
Could that affect, being Jewish, affect whether you could get a position? Or... Yeah, for example, in this mathematical institute, Stiklof Institute, for quite a long time, essentially, where almost no Jews and so on, yeah.
34:41
You were aware of this, as a factor. Yes. Okay, well, you do get permission in the anti-travel abroad, which is an acknowledgement, perhaps, of your growing reputation. Yeah, no, actually, I traveled abroad, but to countries like Hungary, which was...
35:06
Right, understood somewhat within the safe realm, but you are, in time, able to travel to the West as well. No, I traveled to maybe in 79, and more or less, in some sense, it was kind of compensation that they...
35:23
Oh. ...that I was not allowed to go to. What is the difference, just in your intellectual life, the point where you can travel to meet colleagues in a wider range?
35:43
Is there a kind of important liberation in this, or in fact, intellectually, can you visit together in publications in a way that it's not so significant? It was significant. Actually, also, there was kind of difficult to...
36:02
Okay, probably, okay, at that time, there was no internet, there was no... Right. So, to publish, and then also to communicate, to colleagues, that's how it was difficult. It was difficult. Yeah. Um, there's still some oversight over what you can have access to,
36:23
and not this kind of thing, or is it just the expense of getting the foreign publications? No, no, no, but it's... Yeah, but somehow, there was not many interactions that traveled to conferences. Right. Yeah, in some sense, there was great mathematical school in the Soviet Union,
36:46
in Moscow, they didn't grad, so it's... So even though you were restricted in international travel until you... Yeah, but... There was such a vibrant intellectual community... Yes. ...locally, that it didn't constrain your thinking?
37:03
Okay. No, but somehow, it's... Yeah, but somehow, this...
37:24
Yeah, this is how there were quite some obstacles for careers, so for that, because of this resistance of mathematical establishment and genesis. So the situation is not perfect.
37:42
Yeah, but in some sense, it was... Yeah, it was okay, so it was good. You got a position after you received what we think of as a PhD, but the degree of the graduate study, was the position also in Moscow?
38:02
Yeah, it was in Moscow. There was this... Since the Academy of Sciences at one of the institutes, but institutes actually by western standards were quite big, so for example, I worked in the relatively small institute,
38:22
but there was about 200 people. And some big institutes could be thousands. What did you... Were you thought of as occupying a particular mathematical strategy or position, or...? No, it was said, actually, it was not considered to be...
38:42
Okay, maybe some kind of computer science information theory, but... Oh. Yeah, I'm sorry, I had a couple of papers which is... Can be considered to be... Yeah, the index expanders, which is now quite popular subject in computer science.
39:05
What are the tools available? So we're now in the late 70s? What is the time period when you now were in the institute? No, I entered the institute... Earlier, yeah. Maybe in 69 or 70. Early 70s.
39:21
Um, and tools available to you at this point are... What do you mean by tools? Computers... Computers, no. No, actually, no, computers didn't exist in some sense.
39:41
Okay. Yeah, but for example, to type papers, so there was typewriters, but... So in any case, you're... Yeah, that's also to make a copy, it was also controlled.
40:04
Also controlled. For security reasons. Yeah, somehow there was, yeah, maybe you've heard about so-called samizdat, which is... Yes, the underground... Yeah, but somehow to produce copies, you had to type with several copies, and that's...
40:23
Called copy paper. Like a mimeograph. No, no, no, I had copy paper, there was four copies. Yeah, no, you put paper in between, put some, about kapirka, some black...
40:41
Yeah, no, you probably cannot type, can produce more than four copies. Right. And then it's... And then this would be distributed... Yeah, no, no, no, no, no, no, no. Now there are some copy machines, but somehow it was... Yeah, you had to get, okay... Not easy. Yeah, and also how you should get some permission, which is...
41:04
What is your next grade paper? It's not just a question of... But I mean, what is the work you are now doing? Where are you going mathematically at this point? Yeah, no, so it's, I get these papers about
41:22
these great subgroups of legumes, and probably this was kind of the main reason why I was awarded. It was, then I worked on what can be called homogeneous dynamics, which is applications to number theory.
41:43
So now it's probably, it's kind of my main interest. It has continued to be... Yeah, so probably starting about 1885, 1884. This direction. Yes.
42:00
Which as you say, you're still... Yeah, still, and then I left Soviet Union in 19... No, okay, 1991, 1991. So... Yeah, a year since 1991. You left, is it fair to say, the first opportunity, but it was possible to leave?
42:22
No, no, actually it was... No, it's... No, actually after, so when... So, okay, first my travel to the West was in 1979, to Germany, but then it was
42:42
in, next in 1987, which was to Norway, to the 17th birthday of Selberg, and then it's after that, it was all this... Yeah, again, there was some system, but in 88, there was four months in Germany, then it's...
43:04
Okay, and, but it was two weeks, three weeks, three months to France, to Paris in 89, 90. So in most of the Congresses... Yeah, but then in 1990, I went to...
43:25
I was one semester at Harvard, and then in the Institute for Advanced Study, and then already I got offers from several, from Harvard, Yale, Princeton.
43:40
So why did you, why did you accept Yale? What was going on here? Somehow there was some colleagues, for example, Professor Mostow, who recently died, and somehow I was very influential in my research, and then also some other considerations, which is
44:02
maybe harder to explain. Yeah, personal, but Yale was... Yeah, but it's quite, you know, so I... What are the conditions of your hiring? Are you expected to do some teaching? Are you allowed to do pure research?
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No, no, no, they're not here, so there's a teaching gap. It's more or less conditioned to undergraduate courses, semester, and one graduate, and then it's, okay, research advising of graduate students, and so on.
44:41
You had done teaching in Moscow. No. No, that was only research. Yeah, it was only... You had no teaching obligations. No, no. Okay, so how did you find this situation, where now we were teaching? Yeah, it was kind of challenging, because it's...
45:01
Not because of language, but because of... Yeah, it's different. Yeah, the teaching is kind of different. Who is it? I've spoken to some laureates who have actually said that their thinking was because of their
45:28
nature, somewhat dependent on their teaching, where they didn't have graduate students, particularly graduate students. They didn't think that their research was as good as it might be, I suppose, because of the challenge of their minds.
45:43
Did you find the effect on your research? No, actually, in the Soviet Union, essentially, I didn't have a graduate student. There was one, but actually, it was kind of occasional. So here, I already maybe had about 20.
46:06
And actually, it was quite rewarding, so it's to work with graduate students. Can you say that any of your significant ideas, without asking what they were,
46:20
were affected by work with particular graduate students? No, no, no. Actually, before I... So in the Soviet Union, more or less, my papers were made. I didn't have co-authors, but maybe in some cases, but probably after I
46:43
came here, most of my papers were with co-authors. Yeah, so that's a... Yeah, some of them are graduate students. Yes, so that's a change. Yeah, that's a change. Actually, somehow, if I stayed in the Soviet Union, probably, in Russia,
47:03
probably, I would not have graduate students, so maybe much less. And the direction of your work might have been... Direction of my work? ...would be different. The direction maybe would be similar, but the work itself maybe would be different.
47:26
Fair enough. I'm going to ask a very general question again. Were you in a culture shop, both in terms of the national community you find yourself in, but also in terms of the
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American educational system, as opposed to what you had known, or was it... No, no, no. I got the culture shop. No, it's a different life, so it's... And actually, maybe the difference between life in the United States and in Europe,
48:03
maybe more than the difference between Europe and the Soviet Union. Can you characterize some of the differences? I know, for example, essentially, there are almost no cities, and so it's... Januso, I live in Manhattan, of course. It's a city, but...
48:24
Yeah, but for example, this is one... Januso, it's... You know, okay, maybe it's a superficial difference, but it's an important difference.
48:42
It's an important difference to you. It's important. Do you know you've been here 16, 17 years? No, more. Even more? So it's... it's 26 years. 26 years, yes. That's different from 16 years.
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The present nature of your work, again, I understand, I won't understand the intricacies, but what is the direction of your work now? What is particularly interesting? Januso, more or less, I continue. In numbers? Januso, there's dynamics.
49:25
Januso, it's... yeah, I'm not so young, so it's mathematics. You know, some people claim that they work until very old age, but usually it's not true.
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The last question is really by way of advice. You may not feel it necessary, and I think in technology fields it's more expected that
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somebody would say, okay, the next great direction to think about because we're at the stage of discovering this is the following. In mathematics, which is, I think, more eternal, it's a conversation across time, but do you send your students
50:21
in particular directions in terms of the... No, no, no, no. Okay, more or less, I still, you know, so more or less, they work in fields close to me, but sometimes they find their own problems. Sometimes I give the problems, sometimes they were close with me, closely with me, but sometimes just independently.
50:49
Again, maybe a very superficial question. Are there fashions in mathematics? Yeah, probably there are fashions. You know, somehow it depends. Yeah, certainly.
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What, are you, are you pursuing something that is fashionable in mathematics now? No, no, but probably not, but yeah, but somehow it depends on personalities, so there's some charismatic people. Yeah, so it's, you know, certainly there are fashions.
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The last question would be, and again, it's difficult for a modest man to answer this, but again, the originality, but almost the stubbornness of your pursuit of certain questions at various points when others were not expecting solutions.
51:40
Have you found among, without mentioning name, among students and colleagues, people with that attribute who are pushing in directions that others expect will not lead anywhere? What do you mean? It's more about originality. Are you finding people who are
52:03
very original in the challenges that they are willing to take on? Is this good? Yeah, this is, yeah, yeah, so usually it's, you know, somehow to, you know, so
52:28
actually it's quite difficult to evaluate mathematical work, and for example, if, okay, if you solve some long-standing problems, it's easy to convince people that
52:43
you did a good job, but on the other hand, there are quite a few great mathematicians who just work completely differently. Again, at the end,
53:07
does the application of your work eventually, one day, it's certainly not the intention, I don't concern you, or is this... It's not too much. You know, as I said, there was this
53:21
about expanders, which somehow it's, yeah, there's expanders, actually there's one of the Navalny's, the prize winners, Dan Spearman, who works here in computer science, he's much younger, he did some good and expanded, but somehow it's quite popular subject.
53:47
But that's... But it's, but okay, it was kind of byproduct. Okay, but it's not a, it's not a major concern, you know, and you have what might even argue
54:01
in a field of luxury, just following... Yeah, so actually, I would call curiosity-driven research. Yes. Yeah, I think it's, I have this from the link with, you know,
54:21
right, so not exactly directed of applications, but... It can happen, but it's not important. Yeah, maybe it's important, but somehow it's not kind of the main concern.
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