The HLF Portraits: Caucher Birkar

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The HLF Portraits: Caucher Birkar
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Point (geometry) Complex (psychology) Group action Variety (linguistics) Direction (geometry) Multiplication sign Parameter (computer programming) Student's t-test Mereology Perspective (visual) Sign (mathematics) Mathematics Thermodynamisches System Strategy game Finite set Energy level Körper <Algebra> Condition number Dependent and independent variables Process (computing) Fields Medal Generating set of a group Moment (mathematics) Model theory Bound state Price index Category of being Radical (chemistry) Mathematical singularity Right angle Game theory Mathematician Family
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to begin at the beginning you were born in a difficult time in place can you tell me a little bit about the circumstances of your family when you were a child I was born and in the summer of 1978 that was just before the Revolution the Iranian Revolution so even before the Revolution the situation was not very peaceful it was not very stable a bit chaotic and so I was born in a village the village name is near just n E which is not very far away from the local town which is called a merry one at the time the town was actually pretty small but later got much bigger so where I lived in the village life was basically very traditional and the main means of people living was agriculture basically and that's what my power of my ancestors have been doing for a very long time the wrong land there our own land so we have different plants of learnt in different areas basically only close to the village and we used to go to work on this plot of land every day so we used to go to a different plants just depending on what we had to do and my grandfather he could read and write and my uncle adding menu of the first person who entered school it's more than a historic school in a more than sense I mean there are traditional school which are more like a touch with the religious institutions but I think my uncle was the first person in the family who entered modern style school after that so not long after I was born just a few a couple of years later than there are the iran-iraq war that lasted for eight years which makes it covered all my primary school education and even a certain point we had to leave that and immigrants with some other places so my hometown was right on the border of Iran and Iraq that meant that we were an easy target for especially aerial threats because of the mountains land invasion was very difficult from a military point of view but but aerial thrilled like airplanes or shelling and all kind of aerial bombs was really very easy for them because the town was so close to the border even you can walk to the border just like one hour we don't want kurdish people and you were one Kersh we assumed to be particularly loyal to one side or the other no a painful aspect of the war because it was really our war I mean it had absolutely nothing to do it with a Kurdish issue with the Kurdish issue has a long history especially in the last 100 yes it's a very complicated thing in the region but that iran-iraq war didn't have anything to do with with the Kurdish issue so we were just being killed basically for your reasons yes but not active participants no I mean the thing is that parallel to that also there are some more or less another war which was between the Kurdish forces outlawed forces and Iranian government and without that of the border also between the Kurdish forces and the Iraqi government so it had the quite complicated thing and that's one had to do more with the Kurdish issue in your family just to place you how many children are you which order where do you come in the family the children how many the first are you the first child are you the third child we are six children six children I have four brothers and one sister and I'm the third litter I am third brother so and I haven't one older brother I have an older sister so I'm the second and then you what are the conditions of the possibility of an education in a time of war there are schools so all the time I think maybe just accept that the time when we had to just leave the village and go away other right there always was school but the thing is that in that kind of situation you just can't get a proper education is just very hard so I remember so many times that we were sitting in the classroom and then suddenly the airplane would come and just we had to run out run to the mountain basically and the schools where there weren't much in the school really just was a building and then the blackboards and teachers and the student that's basically it even didn't have adequate heating I mean the equipment there are almost nothing really there are so little and the teachers I should say that I'm grateful to all the teachers in my whole life who did their best to eat eat especially in such a difficult situation but at the end of the day that's really that compared to what you get a reasonable education in the West what I got was really inadequate you know who the child as he's growing up let's put you in eight shows a talent and something shows curiosity shows an inclination in some way or the other are they seeing that they have a clever young fellow in the family how how is your mind beginning to develop and your curiosity so in my case really had to have more to do with family especially my older brother than with the school itself as I said the school wasn't really the school whole system was under such difficult circumstances wasn't really just good enough to induce that kind of idea in in children especially I should also mention that for example beating was very common at the time so until I was 14 I have been beaten I don't know maybe the time that's completely illegal to bid the teachers could beat children physically I mean with the stick for behavior for getting an answer wrong for both both are both yes and then of course it's difficult to motivate people and another thing is that before inter school I like almost everyone else we had absolutely no preparation there was no even no nursery so I never attended that nursery and then once I enter school I had to study in a different language it's of course person is related to Kurdish sounds like Italian it's related to French so the schools in Farsi school in Farsi but that was our problem at least it was the problem it was wrong we had no idea in my time before I enter school I think I didn't know maybe one single word in fact except a common so it's difficult for children in that kind of circumstances to just start education so I'm not seeing a future Cambridge done yet what did your brother do to stimulate your mind in the face of this difficult political situation difficult schooling framework where did you mind
begin to take off yeah so my brother in a way he was a really very unique and I'm extremely lucky to have a person like that around me he he was just so different from everyone else he was extremely creative he would do things at that time of war and chaos that no one else was even thinking about she just loved building things making things designing new things and he just had this passion for doing inventing things that was just somehow the place so for example I remember once he he built a projector this old-style projected that you seen about a long time ago he build a projector himself he even did animation and then he gathered us a bunch of children in a basement and he showed us this movie the deceive me I mean you don't have to be a genius to do with that nowhere else to think of doing it yes that was the key I think he did a lot of the sort of thing and not surprising the later on he became an engineer ah so I think that was in a way as far as my education is concerned that's the genesis that the guy who pushed me toward was it math in particular that was beginning to emerge as an interest or he was educating you at home and almost everything I mean it wasn't like a formal education he taught more he was doing something and I was curious them and right I was interested in the things that he was doing it wasn't so much about mathematics at least in the beginning in the beginning but later on after primary school then it became more mathematical and physical so I remember he used to try to teach me when I was maybe seven girls I calculus some primitive easy kind of elementary physics so that was more a little bit forward but still I mean there was no pressure or push I mean he didn't I tell me you have to sit down and do the event and that he just tried to make it interesting to tell me that it is something actually interested interesting and I when you responded I responded and we will call him your first teacher your first real teacher who is your second is there a time as school progresses where you find the beginning of a mentor or somebody else who then takes you to the next level at secondary school perhaps no unfortunately we have to wait another until I started to do PhD in really tweed I've got I've met a lot of interesting people nice teacher the thorn but in the sense of influence I think the Robin released much especially in high school I was you could say completely isolated from the rest of the world hmm but you don't get to a PhD without stages before there has to be some point where preparation my high school University and I entered high school but I already had developed a passion for but when I try to the only thing really I have to rely on was the book so we there are the local library not even the school library for some reason for some strange reason there were really really many nice books about mathematics and not surprisingly I for many other miles may be the only or the first person who actually picked them up from the library especially the rather book about the lives of maintenant mathematicians this is also actually quite famous in the West it's called men of mathematics it's a big book about the lives of all the generations of mathematicians like 16 17 up to first half of 20th century mathematicians and I read the biography of these people and I just got so much more interested in mathematics thought that these people spending time discovering things creating things it just so interesting in a way is just more interesting than and completely ordinary life and were you optimistic about the possibility that you might join them I mean from your circumstance where you were the life you were living you were you were not pessimistic about the future you know I was young in fact in high school I already decided to become a professional mathematicians that was when I was maybe around 16 years old and now the thing is that I told you High School is maybe the most important stage in my education is that not only reading mathematics so I read a lot of books but I also got this idea that just reading is not enough for me it's a dozen satisfy me I have to create also new mathematics it's not just learning it's being a participant in exactly I think maybe didn't have to do also with my personality I don't like so much to be a spectator I like to also participate yes when I go to a music concert after a few minutes I have the feeling I want to go on the stage from the guy and say another gate let me play I don't know how to play but you get yeah yeah I think I had the same exact idea for mathematics just to learn just to watch what they do is not enough for me I want to do my own mathematics and I try to do in fact but I didn't do anything significant but the idea yes it was really important now there are economics involved in education I mean the economics of paying for school going on to university I know you do go on to university you go to town and university but how is that possible what is the economic basis for doing so well in Iran education was free at least at the time it was first though you didn't have to pay to enter university okay otherwise I would just have not really that economic Minister go to university as I said my parents were farmers in fact in that period of I don't know maybe when I was 10 until I lived I left the country I in fact spent a huge amount of time doing farming yes so in that high school yes especially when I live I was trying to read books and and so and so quite after when we had the exam tomorrow the day before I actually had to go at work or on the farm we produce almost everything that we needed but it didn't generate money
we didn't have cash but also the the opportunity to go to university even though it was free represented you're leaving the family's place leaving your labor taking your labor and going somewhere else so this is a serious decision for the family for you to leave to go to Tehran no not really by the time already there are a huge number of people entering University so it was highly encouraged to god it was encouraged yeah your family was from the beginning my parents were very much trying to get an education so there are no resistance at all so they were encouraging okay you go to the University I know you passed the exams and I I know you were welcome there because you demonstrated talent how do you make the intellectual decisions within university maybe you're already a committed mathematician and you you take the mathematics course or you begin with physics how do you so I entered pure mathematics pure I only beginning from the inside any right when you take the example for university you can choose many different subjects so in my case I only picked pure mathematics and nothing else and I'm going to ask you to define pure mathematics in terms of the options that were there I mean applied mathematics would be for engineers something like that and so I could teach applied with math experiment amantes engineering of all kinds I could see all the other sciences physics chemistry so there were so many options and people would choose maybe many different subjects especially if they were unsure or what to do but in mind is because I was completely sure what I want to do so I picked I had like 100 choices to make I did pick that he like six seven pure mathematics in different universities maybe I'm wrong to say this but for somebody from a poor family it's a rather bold decision rather than to go into one of the fields that would lead to a kind of dependable income and so forth this was yes in fact the only thing maybe that was under discussion when I before I entered so my family tried to say well if you do people mathematics you maybe end up with no job why not go to do engineering and there are some perfect yeah but maybe I was experiences Darwin but and then my father also said ok no one is allowed to put the amount of privilege just let him do whatever you like you were lucky in your family very lucky your brother or your father your mother probably supporting you in this almost unimaginable career choice so there you are in Tehran at the University you've chosen pure mathematics are you finding an exciting mentor there somebody who's begins to direct you in your career well there are a lot more interesting courses compared to high school there were more advanced there were more advanced teachers also professional mathematicians for the first time in my life that I actually met and so professional mathematicians so in a way it was more interesting I wasn't as isolated as before in high school I was completely isolated but not other University but the truth is that that experience in high school just to read on my own and also try to do research I just continued that into undergraduate also so I just picked up books I mean beyond the lectures just for example the first year I enter the university I just picked up booking and remarque topology and I try to read the subject minute yeah I could have attended that course maybe a few years later but I didn't want to wait for courses and so on I just followed my interests ultra-right topology then mathematical logic then commutative algebra then later on algebraic geometry so I talked to to the professor's time to time but I think I was really very independent especially the first year and fourth year I attended very little lectures I just read my my own to the exams and it was just considered a problem from the traditional academic perspective or were you encouraged allowed even celebrated for your independent mind thing it wasn't allowed normally and nothing encouraged but in my case I think that the professor's were more relaxed so I remember that once one of the professor's say that okay if this guy even doesn't attend the exam I'm going to just give him the marks at the end in fact I did not and he gave me not for months but but he gave me enough to pass to the rest now the next thing that comes to mind because I've talked to a number of mathematicians in this series some of them were Jews in the Soviet Union and I bring this up only because they literally found bear years to their intellectual progression simply by being Jewish in that system at that time was there an ethnic problem of being Kurdish at the University even a very intelligent young mathematician or was that absolutely not a factor in how you were going to progress well just to enter university and get a degree no no that was not a factor in fact in a way the system especially the entrance examination was in a way which was very much in favor of people like me because it was probably computerized so that me that there was no essentially no person directly involved how many paths but the thing is that indirectly of course there is discrimination when you don't get a proper education in primary school or high school or so on but of course you you don't have a good chance compared to others to enter University and continue to be to be good so there is indirect discrimination where there is economic problem where there is political problem right and it goes much much deeper in the sense it's psychological when went further up in school there was very very little about Kurdish history yes so the naturally we would just think that we don't have anything in our history and in fact only after I left Iran and came to UK I got more books to read and I realized how rich the Kurdish histories but when people don't tell you that then you just feel kind of you are maybe less than others but that still is I'm not minimizing it it's tragic still is indirect discrimination but there was never a sense that has occurred you could not progress in the academic system if you stayed in Iran after you get a job and you continue I don't know because I didn't I didn't but just to study if you don't talk about politics if you just keep quiet there is no problem to enter university and get a degree you know there is no so instead you decide to again just broadly to leave you you've got your degree from Tehran University yes and you completed the program yes may I ask before we take you away from the University what the direction of your thesis was where did you not have a thesis it we didn't have to you did not like that okay so UK is going to be the next stop
you make this decision on your own to go or how do you how do you wind up there just a an academic aspiration you know after that I had the feeling that maybe there isn't much future if I stay in the country I mean if even if I got a degree if even if I did PhD then I mean in a way you could say that the education was good up to maybe math but starting from PhD then it's much less behind compared with Western country right so it was natural for a mathematician who wanted to participate in the wider world yeah educated education that's why most most would do it but but there are other reasons for ending option which yeah those so in terms of the history of your mind where do you wind up going for your next stage of your education so I came into the UK the first year in the UK I was a refugee so basically I didn't even I could not even choose where to live you couldn't choose no I said I happen to live in Nottingham the city of Nottingham just because the government sent me nothing what happens is that they send you to a place wait for a decision of the government I say to whether to give you refugee status or not so in my case we know unfortunately that took only one year but in fact I know a lot of people who have been waiting for 10 years or more at the end even yet no okay end of 10 do you know in their life are almost completely wasted so we count this lucky that it was just the year for you I think it was kind of lucky but see it was a difficult year that's true and completely and underestimated I can imagine you can barely imagine actually um now this is the right point to stop before we develop your career your remarkable career if I've got this right the name you use now is the translation of migrant mathematician is that true yes basically so after I got the refugee status in the UK then I decided to change my my name that's something that really reflect me my personality of the person and culture means both it means a migrant but also can means like explorers don't stop in one place they go from one place to another place and because just means mathematician so in a way you could say it means a migrant mathematician or an explorer meaning to me it's a remarkable decision to change your name absolutely it was your family surprise first but I just thought that I should call myself something that is reflected to me were yes not just name someone picked for me okay with the new name and the new status you go to university I'm you go to the next stage of university you already have a bachelor's are you admitted then into the graduate program so during that one year that I waited for the refugee center I talked to the mathematicians mathematics department in Nottingham just informally okay even yeah attended maybe some lectures so that there are communication with them and then they already knew my level how much I know my interest and so on but during that year they couldn't give me a scholarship just for formal reasons but after I got the refugee stated then they did it immediately they already knew about me and so I just started immediately appears in Nottingham did they respect the education you had gotten I mean sometimes there's snobbery sometimes there's a sense go back to square one and build within our system but it was not a problem for you know I think I mean they they didn't rely just on the fact that I had a bachelor degree but they just relied on the conversation that we had on for example they gave me a book to read I read it and then the wreath came back to them we talked and so they they had a sense of how much I'm interested in mathematics and how much I know about mathematics so they they appreciated that is there a direction to the mathematics department and Nottingham something that they favored as a community of mathematicians that may have influenced you one way or the other so they had a relatively large group of an athletic geometers which is okay let me close to algebraic geometry that are the most natural for me to Colossus because I already was interested in algebraic geometry from undergraduate taste I had decided to go out to write a drama tree so it was not wrong for me to go to these people so it was a good fit really you know where you're not exactly because my interests were a little bit different okay actually number theories but I was more like trying to be a pure of jabrai job but they they are they knew some algebra geometry especially even Fesenko became my PhD advisor he's a number theories but he in fact knows a lot about algebraic geometry so it was not difficult for him to at least give me some other direction but in fact I spend a lot of time outside nothing I'm doing my PhD so I stayed in war you can Cambridge for six months in the first year I stayed five months in John Hopkins in us in the third year I spent a couple of months in Moscow so all over the treasure of my great mathematician in the literal sense you're choosing places to go presumably because of their competence in algebraic geometry I mean they are I mean how are you picking those times in Cambridge or why are you going to Johns Hopkins what what are you seeking what community of mathematicians are you in search of so in the first year even am I as why that he knew what I wanted it to be to be able to write geometry then he suggested that I go to a workshop in Warwick which was formally introducing young people PhD students to some part of algebraic geometry which happened to be by rational geometry my field now I see and then there was a follow up a much longer program in Cambridge at the news and Institute and even again suggested that I come there and in fact I didn't even accept me to participate in the program but finally he put a lot of pressure and accepted me and I just came here rented a room and so I have no fees or anything but I just found this program and at the end I met shocker of my second PhD advisor so much of this program in Cambridge I then attended was about a paper that he has written recently and it's other very long and complicated paper people were trying to understand what she was trying to do and that paper also reads and I tried just to make sense of it as much as I could and then it was very natural for me to follow shocker which I did at the end so I'm also very interested in the process of of picking the problem if you will that would define your your thesis your dissertation so is that happening
through his suggestions are you just exploring and do you come up with the problem that will be at the core of the dissertation how did that work for you so the first and second year I did it nicely together in my own I picked the problem then I tried hard to solve them and I couldn't maybe not very surprisingly because the same problems are still open until now but in the third year then I went to Hopkins I talk to show curve and then I think I felt the by job doing have been half time because just one year left and then I asked him for a problem he suggested a problem to me and then I wrote my teeth looking back so the University can you explain to a layman the the elements of the problem and what attracted you to it so the problem where I mean the core problem was about fun a variety in fact is in the conjecture that I thought just a couple of years ago which was in a way one of the main reason for the film a doctor so he told me to look at this problem that's round myself was already known in dimension two and he tried to do it in a completely different way reprove it he just asked me to reprove that statement which was had been proved by Alexia in a different language because you know different techniques using his theory of compliments and the thing I really liked about the problem was that it was related to many other problems not just one isolated thing I think me knowing that became probably one of the things that defines my work in a way it's not just about one problem is it's about web of problems and just to understand how these problems are related how they are connected is also in a way part of the whole process so for the following years for many of is on and off worked on these problems not only dimension too but also in higher dimension you know that the notion which is central to the PhD see the balloon is about funnel varieties the farmer I did our algebraic variety there algebraic geometric space is defined by polynomial equations which have positive curvature so for example a sphere is an example of a final variety but when you go to a higher dimension they become much more complicated and then the problem is just to understand these varieties in higher dimension and fast anything like that is related in understanding is related to so many other problems like termination of leaks is related to singularity is related to void and of flips and and so many central notions is it fair to say you're still working and some of the problems that were framed by your dissertation or have you since gone into another direction there were so many other problem but there are all somehow related just to understand how they are connected you know it's part of them to the problem I want to advance your career now you've gotten your dissertation have you published before that or is do you publish that dissertation I publish on the archive but I actually never published it in Journal which was I think I had the feeling I wanted to do more because to publish a paper even after writing it actually takes a lot of time yes polish it and then submit a journal you often get rejected submitted again it takes time I risk somehow I didn't do that instead I try to do news to prove you a resource but you need an academic berth you need recognition you need a place that will accept you after your dissertation how does that happen so when I was a PhD before I finished I applied for postdoctoral research fellowship by EPSRC so this is similar to NSF in the US I got one of the fellowships for three years so that means that or for another three years and then after that I was worried about a chop okay you know I thought I kind of risky think that I just didn't maybe pay so much attention to the distant future so you have three years before you have to worry about the distant future what kind of inquiry happens in those in those free three years so to speak when you can really just explore what you want to how do you I'm always interested in the choice of the problems the direction of the mind in this case the problem somehow natural for me because as I said there is a web a problem and then it's just a matter of which one to pick to work so after I've even before I finish the PhD denies again working on this termination of flips conjecture and then the meaning on modal conjecture so much of the post like years I spent on this kind of thing but also again on singularities when final varieties and so on so it's not it wasn't really hard to pick a problem is was just whether one can solve it or not I'm very interested for the sake of those who are watching this to ask and maybe it's not answerable your process how do you think it's not just the direction you're going in terms of your interest but are you are you a brooder are you always thinking are you isolating yourself what's the process of research for you so in practice when I pick a problem let's say focus on a problem usually not just one problem but some related problem and maybe at each given time might pick focus on one of them and just learn about it as much as I can although unfortunately I kill the problems I were working actually there wasn't so much to read in the literature doesn't mean we have to come up with new things yes so that means much of the tailspin I spent on thinking about just maybe getting a new idea somehow do something new that mean there was a huge amount of time just to say but when you focus on some problem for weeks and months and then somehow you get into a state where then you feel maybe there is some ideas coming out a kind of recognition that you're going in the right direction well you have to decide it for not always sometimes you have sided a six month and then you realize that this is just not working and you have to maybe go back to the beginning and take a different strategy apply different ideas again it may be
romantic of me to ask but is there a moment let's say in the in the perspective that led to your field where you feel that yes you know it can be called a Eureka moment it can be called anything but is there a moment or is it just the constant process and the feeling that you're in the right direction I think there are the kind of moments but not one or two the trust happens many times not so because that's the kind of guidance and I suppose since you're not a student at this point you're a full practicing mathematician those moments are once you have to determine that's your instinct that tells you that you're going in the right direction or not homes so again I can only marvel with that from outside but I'm sure there's a guidance that your your mind and God gives you as you proceed but what was the basic insight and maybe complex web of insights that led to the field level would you only just received yeah the film mother was for two separate works okay so they were done of different times one of them was back in 2006 a jointly with our Cassini Christopher Hagen and James McKenna that was about me or models finite generation flips and many things and the other worker was about fan of erotic which was more related to my PhD see this that was done much later in 2016 like they were separated like ten years basically it's true that I'm either there is given me some intuition to progress and you know if you have a feeling that maybe you are going in the right direction and then of course you have to prove that you are going in the right direction so you spend months but if you don't get anywhere then maybe this is a sign that you are not going into that the right direction maybe you have to go back or at some point in the process you have to change your direction maybe you know it's a part of the whole game and it's not actually so easy just to decide where to give up I'm not remotely suspecting that it is easy I'm assuming quite the opposite that is very good this part of the learning you need to learn these part of the profession right well when you should say that is enough you have to go back and take a different strategy you said that the field there was a response to to if you will two pockets of insights so 2006 was the first you're saying it and the second a 2016 to does so two years ago two years ago yet probably does time before another but yeah I mean 2016 and what was that again spoken to a language what was that insight so these are the most fun or you know I understand the whole thing was fun a variety and the main problem was about showing that if you put some conditions on these varieties which worried about their singularity then you can prove that they form a bounded family and that's basically me that you can somehow parameterize them you can index them just by using finitely many parameters you know sometimes if you have a group of varieties and they are bounded that means that they share many properties there many of their environment a numerical data attached with them somehow are in a finite set so it can tell you a lot about the whole family but it did also relate to many other things so for example related to understanding singularities related to the so-called termination conjecture and the mineral model conjecture related to stability or from a variety of them I think that's what I like about the problem that the tie work they're just somehow religious into so many different things that I don't feel like I'm working in just one isolated problem right I'm gonna end with again an outsider's look at this question which I've asked others about the assumptions about youth and mathematical creativity I'm very struck I don't know of any other award there may be many that restricts that has an age restriction I mean the Fields Medal may even be said to be the highest honor in mathematics and the cutoff point is 40 I think yes what do you think about this assumption particularly as I don't know what age you are now just just snuck in so that being said I mean do you look forward and I say this really very lightheartedly because I know it's not true to a life of decline kalenna vation what is this assumption that the young are particularly prone to mathematical insight yeah well of course I cannot say from my own experience but I know many other mathematicians in the 1562 grating so programmable shock wore off I think he did his best work after 40 so this is a superstition in a way younger people are more energetic it's not only mathematics it's pores in us and everything so they trust more energetic and maybe also when they don't have family they have more time to do whatever they they like for example I have my son he was born in 2013 and I just can see how more difficult it is to work after yes that you know I invited my kid ironically I was much more productive after he was born for whatever reason understandable then I have to spend a lot of time playing with him on his development and when you are 20 maybe you don't worry about this kind of thing these days people even if the SIL 30 they don't have children right so there are many practical reasons but also just age you when your age you get less maybe energetic so there is nothing it's not about particularly about mathematics it's more about just the human life experience life experience I think I like ending with your son so thank you very much thank you very much