1 00:00:12,460 --> 00:00:16,570 Hello. I'm Martin Brighton and I'm here today to interview Nigel Hitchen. 2 00:00:16,960 --> 00:00:22,570 After a long and illustrious career here at Oxford is just retiring as the civilian professor of geometry. 3 00:00:22,840 --> 00:00:30,590 So, Nigel, shall we begin with John to tell us a bit about your early life and how you decided to study mathematics? 4 00:00:30,590 --> 00:00:34,030 So at what point did you decide you might want to study mathematics? 5 00:00:34,390 --> 00:00:40,570 Okay. So well, I grew up in a small village called Duffield near Derby. 6 00:00:41,980 --> 00:00:56,770 As a matter of fact, it's the same same village where one of our colleagues, Hilary Ockendon, from her father, was a family doctor and in 1957. 7 00:00:57,160 --> 00:01:04,530 And so that was when I was 11. So there was actually a brand new grammar school built in Duffield and I. 8 00:01:04,780 --> 00:01:09,380 I started there along with about 73 other students. 9 00:01:10,690 --> 00:01:14,530 So students, they call students nowadays pupils. 10 00:01:15,580 --> 00:01:23,380 So this was like two classes. And of course, obviously with a small number like that, the school didn't have a full complement of teachers. 11 00:01:25,150 --> 00:01:31,320 So the mathematics actually was initially taught by a variety of teachers. 12 00:01:31,330 --> 00:01:38,530 It was a French teacher. It wasn't very good, really, but even worse was the PE teacher. 13 00:01:38,900 --> 00:01:46,470 You know, he kind of got as calculating the the stagger, the staggered distance for a fool for her. 14 00:01:47,650 --> 00:01:54,459 But eventually, as the school grew, after a couple of years, they hired more teachers, more specialist teachers. 15 00:01:54,460 --> 00:02:02,050 And there was one teacher who actually took an interest, a serious interest in mathematics. 16 00:02:02,050 --> 00:02:10,060 And in particular, you know, when when pupils responded positively to what he was telling us, he took an interest in them, too. 17 00:02:10,810 --> 00:02:18,400 So he probably was was an influence on me, although, you know, there are lots of things which I quite liked at school, 18 00:02:18,670 --> 00:02:30,340 some things I didn't my but but the reasonably well in chemistry for that I never liked chemistry was too much too much to learn and so can you. 19 00:02:30,670 --> 00:02:35,140 What age do you think mathematics might be? What? I'll study at university, for example. 20 00:02:35,500 --> 00:02:38,980 Was that clear to you when you're 15 or 16? Not really. 21 00:02:39,280 --> 00:02:44,780 I mean I mean, I suppose in my younger years, I was I was quite influenced by my older brother. 22 00:02:44,800 --> 00:02:52,810 I used to do all the things that I want to do or things that he so he was he was always building things with meccano. 23 00:02:52,810 --> 00:02:58,750 He built a kind of an automatic transmission or something. 24 00:02:58,960 --> 00:03:04,360 I could never do that, but I know he was always kind of following on what he was he was doing. 25 00:03:04,360 --> 00:03:09,300 And for a long time I thought that I wanted to be an engineer, engineer. 26 00:03:09,700 --> 00:03:15,760 And of course, the mixture of subjects which I chose to do it at school reflected that. 27 00:03:16,630 --> 00:03:25,230 But gradually in the sixth form, I guess I realised that actually I really probably wouldn't be a very good engineer and somehow the, 28 00:03:25,550 --> 00:03:29,660 the mathematics came or moved to the fore and was a geometry. 29 00:03:29,660 --> 00:03:33,020 You did you sort of fall in love with geometry at some point. 30 00:03:33,170 --> 00:03:37,150 Do you remember all those Greek proofs that we used to do in school? 31 00:03:37,430 --> 00:03:45,030 Well, I remember them, but I don't think it was. That wasn't my favourite part of mathematics. 32 00:03:45,040 --> 00:03:57,670 No, no. I think I was quite, had quite a broad appreciation of mathematics and pure and applied mathematics and ah actually the headmaster was, 33 00:03:58,750 --> 00:04:00,729 he was a mathematician as well, 34 00:04:00,730 --> 00:04:10,720 but he taught us applied mathematics, but it was quite an old fashioned, you know, he was going back to Cambridge trifles questions 1906 Okay. 35 00:04:13,270 --> 00:04:22,599 But yeah, finally, actually what also happened was that I was quite ill for a month or so and I dropped 36 00:04:22,600 --> 00:04:27,070 one of the A-level subjects that I was going to take really focussed on mathematics. 37 00:04:27,520 --> 00:04:33,010 So at that point I really thought that mathematics was going to be my, my what I would do at university. 38 00:04:33,440 --> 00:04:37,420 Right. And so how did how did you end up at Jesus College? 39 00:04:37,630 --> 00:04:44,590 So why Oxford? My Jesus. Yeah. Okay. So then we have to talk about the headmaster, Mr. Redfearn. 40 00:04:44,590 --> 00:04:52,370 This day was so he had so he he tried to create this this school. 41 00:04:52,390 --> 00:04:53,950 It is it was a new school, 42 00:04:54,250 --> 00:05:02,080 and he wanted to create it in this kind of I would imagine there are a lot of things which he did which were a little bit controversial. 43 00:05:02,140 --> 00:05:08,770 I mean, he was kind of modelled on public schools and so on because so we weren't allowed to play football, we had to play rugby. 44 00:05:09,280 --> 00:05:14,750 On the other hand, this was good for the surrounding schools because. They didn't have reputations, but they created them in a hard place. 45 00:05:15,380 --> 00:05:22,280 But one in particular, he in the 1930s, he'd actually been offered a place to study mathematics at Jesus College, 46 00:05:23,270 --> 00:05:33,190 but had not been able to afford to take that. And so somehow vicariously I was I was appointed an ambition actress. 47 00:05:33,890 --> 00:05:39,890 He didn't have any particular links with the college, but it was just that that he wanted, you know, a mathematician to go. 48 00:05:40,580 --> 00:05:50,149 I wasn't actually the first mathematician from the school to come to Oxford because I stayed 49 00:05:50,150 --> 00:05:55,480 on for the extra time to take the entrance examination on the scholarship examinations, 50 00:05:55,670 --> 00:06:02,630 all those things. Whereas one of my peers, she went directly, in fact, to Somerville. 51 00:06:03,220 --> 00:06:09,660 Okay, that. So do you have clear memories of your interview from. 52 00:06:10,080 --> 00:06:19,620 Yeah, well, I had two interviews because, I mean, they actually offered me a place in after the interview in October. 53 00:06:19,690 --> 00:06:23,090 Uh huh. But then they encouraged me to take the information. 54 00:06:23,260 --> 00:06:31,110 Mm hmm. Um. Yeah, so. Well, this was more or less like the interviews we do nowadays. 55 00:06:31,110 --> 00:06:36,450 We, you know, pick up maybe on the topic in the entrance exam, which are not particularly interesting to me. 56 00:06:36,540 --> 00:06:39,000 Mm hmm. I remember the problem was. 57 00:06:39,840 --> 00:06:50,600 Was about estimating the the size of a ball of why I think you take a length and why you screw it up and you say, what is what is it? 58 00:06:50,610 --> 00:06:57,749 What a good estimate of the the radius. It's extraordinary the way that these moments of life stay with you at the detail of that interview 59 00:06:57,750 --> 00:07:05,730 is that's what I say you you make a crude one and then then you kind of have these approximations. 60 00:07:07,050 --> 00:07:11,940 So when you arrived at Oxford, was it what you anticipated to do? 61 00:07:12,270 --> 00:07:15,090 Did you find it immediately stimulating or a bit off putting? 62 00:07:15,630 --> 00:07:25,530 Uh, you know, whenever you come into a new environment, you know, that, okay, maybe you were one of the best at your school in mathematics. 63 00:07:25,530 --> 00:07:31,859 Of course, all the others feel the same way. You know, it's always the question of, you know, measuring yourself against the others. 64 00:07:31,860 --> 00:07:35,870 And so I was a bit nervous at first about that and. 65 00:07:37,050 --> 00:07:43,620 But so the teachings of Jesus at the time, whether it was Edward Thompson and Christopher Bradley, 66 00:07:44,490 --> 00:07:48,210 and they had very different ways of approaching things, I think. 67 00:07:49,470 --> 00:07:58,290 The Bradley was, I think, quite influential in that they encouraged us to well, to read up on something which, 68 00:07:59,580 --> 00:08:05,879 you know, we could choose and give a talk a half hour and talk about it to the other students. 69 00:08:05,880 --> 00:08:14,550 And so and that was that was good because, you know, we'd go to the library and look through the books and find what actually, 70 00:08:14,550 --> 00:08:18,930 I think I gave a talk on a chapter in the home and Violence classical groups. 71 00:08:19,120 --> 00:08:24,389 Oh, right. Kind of sheltered what it's about and the identities, I don't know. 72 00:08:24,390 --> 00:08:31,050 Now, after all these years where I learned about lead groups and so forth, I still don't know what the company idea has. 73 00:08:31,260 --> 00:08:34,260 But in those days I think I thought that I did. 74 00:08:35,360 --> 00:08:41,100 So you weren't obliged to stick too closely to the syllabus during these college tutorials? 75 00:08:41,130 --> 00:08:45,150 Oh, really? I mean, Edward Thompson, you would I mean, 76 00:08:45,150 --> 00:08:50,850 you would go there in this cloud of pipe smoke and you'd sit down and and he would 77 00:08:50,850 --> 00:08:55,650 sit there waiting for you to come up with problems which discuss had discussed. 78 00:08:55,840 --> 00:09:00,090 Like, uh, Christopher Bradley was different. 79 00:09:00,090 --> 00:09:06,360 So he, he actually would, you know, deal with applied mathematical problems. 80 00:09:06,360 --> 00:09:13,830 But he always had a very clean approach, even though, you know, he taught us about Cartesian tendencies and using matrix methods. 81 00:09:14,790 --> 00:09:20,999 It was a kind of a modern approach to, I would say, clean approach to doing applied mathematics, 82 00:09:21,000 --> 00:09:24,260 which I think actually was influential and subsequent. 83 00:09:24,480 --> 00:09:29,010 Right. And so who your contemporaries, did any of this go on to be? 84 00:09:29,010 --> 00:09:36,330 Mathematicians. Yes. So so Lynn Thomas, who unfortunately died earlier this year. 85 00:09:36,810 --> 00:09:45,330 So he was he became well, he moved from mathematics, operational research and business school, 86 00:09:45,330 --> 00:09:49,890 but he became professor and in Edinburgh and in Southampton, 87 00:09:50,580 --> 00:10:00,320 as Gareth Jones, who was a group theorist, and he was professor at Southampton and the others. 88 00:10:01,470 --> 00:10:05,010 And I see. Well those two in particular. Yeah. 89 00:10:05,250 --> 00:10:10,620 And with their proclivities for the directions they followed, did these emerge early on? 90 00:10:10,620 --> 00:10:14,250 Were you obviously the John Ritter, for example, as there? 91 00:10:14,850 --> 00:10:18,780 Yeah, I think I was, actually. I mean, we didn't get. 92 00:10:18,810 --> 00:10:26,160 There wasn't much geometry in the course. And I that and I used to go down to the college library in the books. 93 00:10:26,910 --> 00:10:33,280 And there was there was one book I remember in particular this was by Flanders. 94 00:10:33,600 --> 00:10:37,799 Flanders, it was called The Differential Forms in the Physical Sciences. 95 00:10:37,800 --> 00:10:41,850 And that was I was always attracted to that even though it was, 96 00:10:41,850 --> 00:10:45,749 it was a non rigorous book, so it didn't actually tell you what the differential form was. 97 00:10:45,750 --> 00:10:55,890 And that worried me a little bit as I was, you know, I went to the when you come to university, you I know that you starting from scratch, right? 98 00:10:56,460 --> 00:11:00,660 Things have to be built up logically. Mm hmm. And he introduced these objects. 99 00:11:01,440 --> 00:11:09,530 I mean, nowadays, you know, I'm more flexible if you have to be more research, more flexible in your interpretation. 100 00:11:10,290 --> 00:11:13,140 But that was that was a book which I was thinking of going down on looking. 101 00:11:13,410 --> 00:11:21,360 But also as a researcher, you sort of have you have a better grasp somehow of the reality of the objects you're wrestling with. 102 00:11:21,360 --> 00:11:24,810 I think when you're an undergraduate, as you say, you like these clear definitions. 103 00:11:24,900 --> 00:11:30,810 Yes, that's right. Yeah. I mean, I remember, you know, getting asked somebody, you know, what is the vector space? 104 00:11:32,670 --> 00:11:37,440 Yeah. You know, you jump over these hurdles and everything becomes more natural. 105 00:11:37,650 --> 00:11:41,910 And so so who were the dominant figures in Oxford Mathematics at that time? 106 00:11:42,000 --> 00:11:55,620 And so was t influence already very strong. Yeah, well, the first year, my months year, they decided to put the top brass to give the month lectures. 107 00:11:55,630 --> 00:12:03,180 So yeah. So Michael Taylor was giving the algebra course, Charles Coulson was giving the applied mathematics course. 108 00:12:03,990 --> 00:12:12,780 And then they had Hammersley giving the analysis which cause some problems because his, his problem sheets were very, very difficult. 109 00:12:13,050 --> 00:12:19,320 So tutors were really engaged with each other up asking, How do you do this? 110 00:12:19,680 --> 00:12:28,259 Okay, now some start questions, but even the ones that I had never heard and as you might expect, McAteer went very quickly. 111 00:12:28,260 --> 00:12:36,420 It was very good, very quick. So we started we sat there and by the end of the term, he was talking about Galois groups that I think. 112 00:12:36,710 --> 00:12:41,300 They dropped that system, but it was clearly influenced. 113 00:12:41,300 --> 00:12:44,850 I mean, I enjoyed it, but it caused it cause problems. 114 00:12:45,170 --> 00:12:49,500 Yeah. But then as as your undergraduate career developed and did, 115 00:12:49,580 --> 00:12:55,280 was it the lecture courses that that had a particular influence on you or you or your 116 00:12:55,280 --> 00:12:59,840 peers or and how did you sort of settle on the direction for the next part of your career? 117 00:13:00,600 --> 00:13:08,770 Yeah. Um, I think there were things which I, I did like and things which I didn't like. 118 00:13:08,800 --> 00:13:12,260 I mean, probability and statistics I didn't like at all. 119 00:13:12,260 --> 00:13:18,829 So I avoided that. I things like fluid dynamics, like playing around a bit. 120 00:13:18,830 --> 00:13:27,920 But then I gave up. Eventually I focussed on more geometrical subjects and biology and there was, 121 00:13:28,160 --> 00:13:36,980 there was a course on algebraic geometry with a very foundation course as well, commutative algebra, some function analysis. 122 00:13:37,550 --> 00:13:43,400 They were kind of, you know, tutors gave you advice. 123 00:13:43,700 --> 00:13:49,280 In my final year, Brian Steer used to give me tutorials in topology and differential geometry. 124 00:13:49,310 --> 00:13:55,970 Mm hmm. Mm hmm. And so gradually I settled on these things I had always been interested in. 125 00:13:56,230 --> 00:14:01,430 In popular reading about topology, sheet geometry. 126 00:14:01,430 --> 00:14:05,660 I was right, you know, before I came to university, I was quite keen on that. 127 00:14:06,290 --> 00:14:09,530 And then when you got points at Topology, it was a bit of a let down, right? 128 00:14:09,590 --> 00:14:16,580 Yeah, right. On the other hand then when it came to doing algebraic topology, 129 00:14:17,930 --> 00:14:23,360 so it was Graeme SIEGEL who gave that across there that when they started talking about, 130 00:14:24,920 --> 00:14:28,399 you know, syntheses and so on, I thought, Oh, this is kind of combinatorial. 131 00:14:28,400 --> 00:14:36,410 This is not a problem to that. But then when he started talking about the nerve of recovering the managing and things that I knew right. 132 00:14:36,530 --> 00:14:42,140 And together much better. So it's actually the way in which these things are presented, I think. 133 00:14:42,920 --> 00:14:46,680 Is this Frenchman guiding you through this? 134 00:14:46,820 --> 00:14:53,510 And so later in your career, I think of your influence on physics, but also physics, 135 00:14:53,720 --> 00:14:58,580 influence on the sort of geometry and the physics influence the sort of mathematics you've done. 136 00:14:58,970 --> 00:15:04,020 Was that always true? Is it true? Then, for example, you sort of you found that motivating? 137 00:15:04,040 --> 00:15:11,480 Oh, really? I never I never took any physics course any well, I didn't take any quantum theory courses or relativity courses. 138 00:15:11,540 --> 00:15:21,440 I guess I was interested in cosmology in general relativity, but largely because of it was using the same formalism as the differential geometry. 139 00:15:21,560 --> 00:15:26,990 Uh huh. But I didn't. I never got the hang of, you know, like curves and things. 140 00:15:27,440 --> 00:15:30,580 I mean, it was remaining in geometry that was that. 141 00:15:30,600 --> 00:15:33,020 I had a, I had a feel for that. Aha. 142 00:15:33,570 --> 00:15:44,030 So, so although I had a passing interest in relativity and I used to buy one or two textbooks on it and, and I didn't take any courses on it. 143 00:15:44,030 --> 00:15:49,490 So in fact, um, I basically avoided the physics related courses. 144 00:15:49,500 --> 00:16:01,280 Okay. Oh, that's interesting. And what I so what you're up to versus so I 65 to 60, 68 was when I took my file. 145 00:16:01,310 --> 00:16:05,840 Okay. So that's what so was the index then was what, 63. 146 00:16:05,840 --> 00:16:09,140 So was that very much in the air. Did you have an appreciation of that? 147 00:16:09,410 --> 00:16:14,510 Yeah. Okay. So that was when I began as a research student then. 148 00:16:14,690 --> 00:16:18,730 Yeah. So I. Index then was definitely in the air. 149 00:16:19,150 --> 00:16:23,170 And so brain stem is my supervisor. 150 00:16:23,320 --> 00:16:30,360 Mm hmm. And in my first year, he is trying to push it towards various topics. 151 00:16:30,400 --> 00:16:38,800 Well, first of all, he tried to get me interested in dynamical systems, because this was the time of the snail and all this stuff, right? 152 00:16:39,010 --> 00:16:50,169 Mm hmm. And I think there was a kind of preference in giving and giving research grants to, uh, in this area in SLC. 153 00:16:50,170 --> 00:16:55,780 I think it was a good thing it was doing something like that. I read a few books on that, but I didn't. 154 00:16:56,140 --> 00:16:59,440 You weren't drawn to it, I think, by the flavour of the subject. 155 00:17:00,310 --> 00:17:03,390 But I learned a bit about smell, horse shoes and things. 156 00:17:04,180 --> 00:17:11,790 So then he pointed me. Then I said, No, this wasn't pointed in another direction, which was to do with k theory of the groups. 157 00:17:11,800 --> 00:17:15,160 And that was that. I didn't really get very far with that. 158 00:17:15,400 --> 00:17:21,400 Mm hmm. But still, I was learning k theory, and then I got in touch with the index there, and. 159 00:17:22,030 --> 00:17:31,849 And finally I started working on the Dirac operator where course there was this important application of the index there. 160 00:17:31,850 --> 00:17:34,930 But the. I had just spent months. Mm hmm. 161 00:17:35,020 --> 00:17:43,450 And it was at that point that that yes, I started to read read the papers on index panels, papers, etc. 162 00:17:44,110 --> 00:17:52,629 And so so as you as you said, you you started with Brian Steer, but with the intention always that you would talk to Mike later as well. 163 00:17:52,630 --> 00:18:00,760 Or is that as a result of this evolution of interests? No, it was because Michael had actually left for Princeton. 164 00:18:00,760 --> 00:18:07,030 So he was a permanent member of the institute in Princeton. So maybe after the first year I can't remember which year it was, 165 00:18:07,810 --> 00:18:13,690 but he always used to come back in the summer for the summer term because in Princeton, the finished paper, I guess. 166 00:18:13,720 --> 00:18:24,490 Mm hmm. Um, so, I mean, obviously, I always felt that it would be nice to, you know, to actually work under my out there. 167 00:18:25,450 --> 00:18:30,280 But then the opportunity came when Brian went on sabbatical for one term. 168 00:18:30,610 --> 00:18:37,340 Mm hmm. And so. And so Michael took me on as a student for that. 169 00:18:37,850 --> 00:18:44,220 That period of that summer term. Mm hmm. And then he pointed me in lots of different directions, gave me ideas and so forth. 170 00:18:44,230 --> 00:18:47,230 It was really. Yeah. Which in my research. Mm hmm. 171 00:18:47,320 --> 00:18:54,160 Yeah. That kind of gets to go back to when you were doing these things that did didn't resonate so much with you. 172 00:18:54,550 --> 00:18:59,470 Was there a point at which you got disheartened at all and you thought, maybe maths isn't for me or so? 173 00:18:59,830 --> 00:19:08,650 Sure. Um. In fact, before I came to Oxford as an undergraduate because I'd take the entrance exam and, 174 00:19:08,890 --> 00:19:12,850 you know, I was admitted in, you know, I was accepted in December. 175 00:19:13,540 --> 00:19:21,730 I got a job for the next nine, eight months with Rolls-Royce and Derby in that computer engineering computer department. 176 00:19:22,230 --> 00:19:31,030 Mm hmm. And that was that was interesting while I was earning money 7000 shillings a week. 177 00:19:34,180 --> 00:19:40,930 But there were some interesting problems there. But I went there kind of not knowing much, and I didn't even know what matrices were. 178 00:19:40,930 --> 00:19:47,409 And so they were always talking about stiffness, matrices and engine design and so forth. 179 00:19:47,410 --> 00:19:55,809 And so actually I picked up some mathematics there and and I worked there maybe two vacations. 180 00:19:55,810 --> 00:20:02,890 And so they don't have always said that if, you know, if I wanted to there have always been a job for me. 181 00:20:03,310 --> 00:20:11,320 And so, you know, it's true that halfway through my first year when I felt that I wasn't getting anywhere, I thought, well, should I go back? 182 00:20:11,320 --> 00:20:18,610 And it was really only when I had the task of writing the what we now call the transfer dissertation 183 00:20:19,780 --> 00:20:26,170 that I really got engaged with something which I really don't and encouraged me to stay. 184 00:20:26,770 --> 00:20:31,540 Mm hmm. So jumping ahead. So. So when you've written your thesis. 185 00:20:31,810 --> 00:20:35,290 So what next? What were your thoughts at that stage? 186 00:20:36,050 --> 00:20:42,990 Um, okay, so I actually, I haven't quite finished my thesis by the end of the three, three years. 187 00:20:43,000 --> 00:20:45,700 I mean, I hadn't written it up. I got various results. 188 00:20:46,540 --> 00:20:57,700 But then, then Michael invited me to be his assistant in the institute, so he was back permanently by that stage. 189 00:20:57,910 --> 00:21:03,340 Well, he was still he was still permanent. Professor at Princeton, I mean, permanent member of the. 190 00:21:03,400 --> 00:21:07,450 Aha. Mm hmm. So that was great for me. 191 00:21:07,450 --> 00:21:11,560 I was wonderful that, you know, I had something to go to. 192 00:21:12,040 --> 00:21:16,420 You know, I haven't fully finished like this, right? Mm hmm. So, actually, it was in my first year in. 193 00:21:16,470 --> 00:21:20,520 Princeton that I finished the thesis and that, okay, that was very good. 194 00:21:20,700 --> 00:21:27,749 And well, the institute just being in the States was a wonderful experience, you know, because well, 195 00:21:27,750 --> 00:21:32,110 you're surrounded on the one hand by postdocs are in a similar situation to you, 196 00:21:32,110 --> 00:21:37,290 but then there are visitors that have the time to answer your questions as well. 197 00:21:37,650 --> 00:21:43,380 And it doesn't matter if they're fairly naive questions, and then there are the big shots as well. 198 00:21:43,410 --> 00:21:51,290 And then also, you know, I will get some invitations to give talks in various universities. 199 00:21:51,300 --> 00:21:54,480 I found that people were interested in whatever I was doing. 200 00:21:55,290 --> 00:21:59,730 So actually, yeah, I actually finished off the thesis in. Okay. 201 00:21:59,820 --> 00:22:02,850 Yeah. And how long did you spend in Princeton at that time? 202 00:22:03,390 --> 00:22:12,060 So that was two years. So that I the my stay there as a teacher's assistant went on for another year. 203 00:22:12,100 --> 00:22:18,580 Mm hmm. And did you change direction at that time, or is it more just a flowering of things you were already interested in? 204 00:22:19,410 --> 00:22:23,370 So, no, I think I was still working on that. 205 00:22:23,970 --> 00:22:29,040 Well, okay, I. It expanded my horizons in various ways, so. 206 00:22:29,140 --> 00:22:31,370 So, yeah. Was there one of those? Yeah. Okay. 207 00:22:31,380 --> 00:22:39,060 And so we used to talk a lot about, for example, the Columbia conjecture was okay and the implications it had. 208 00:22:39,060 --> 00:22:46,400 And so I was I got interested in, in particular in K3 surfaces and they had Einstein metrics. 209 00:22:46,830 --> 00:22:55,130 Yeah. I suppose it was then that, that although there were still problems, issues related to the Drake equation, 210 00:22:55,140 --> 00:23:06,070 then more general differential geometric problems relating to Einstein matching scalar curvature came into play and we said that. 211 00:23:06,600 --> 00:23:10,820 So your first brush with algebraic geometry as well would you already know? 212 00:23:10,830 --> 00:23:19,139 So, so. Right. So my thesis I started out by looking at Raymond Surfaces which so my introduction to how to break geometry 213 00:23:19,140 --> 00:23:26,490 was really through studying Raymond Surfaces and then by so by having Michael materials supervisor, 214 00:23:26,490 --> 00:23:29,880 he was encouraged me to look at algebraic surfaces moving up. 215 00:23:30,630 --> 00:23:37,800 So but it was, you know, I, I learned stuff about algebraic geometry well, in different ways, actually. 216 00:23:37,800 --> 00:23:47,670 One was by having a particular problem, namely how to interpret harmonic spinners on a came a manifold but also actually 217 00:23:47,790 --> 00:23:52,709 there was a yeah and in Warwick there was a special year in algebraic geometry. 218 00:23:52,710 --> 00:24:03,500 David Manfred was in Warwick and so they used to have days of seminars in Warwick and then a bunch of us graduate students used to, 219 00:24:03,600 --> 00:24:13,230 we used to drive up there and back to actually not just to Brian stage used to come sometimes and we would spend the day and learn. 220 00:24:14,130 --> 00:24:21,780 I learned a bit of those visits as well and so obviously being there, talking to other visitors program. 221 00:24:22,900 --> 00:24:29,400 So I think so. So early on you had this this famous paper with a tier and singer. 222 00:24:29,760 --> 00:24:33,480 How did that come about or what stage did that work take place? 223 00:24:34,210 --> 00:24:39,150 Yes. So that was in 19, I guess, 1977. 224 00:24:39,150 --> 00:24:50,580 Yeah. So I came back from the States, so and I had a year in NYU and then I came back to the States as a postdoc working with well, 225 00:24:50,730 --> 00:24:52,379 in principle working with Michael. 226 00:24:52,380 --> 00:25:01,920 But at that time I was really following my own interests occasionally and doing something with the Eastern Band which related to his interest. 227 00:25:01,920 --> 00:25:12,900 So at the time, the Aether Invent the heat equation approach to the index theorem was, was and in the work at Bertone it was very a current. 228 00:25:14,010 --> 00:25:19,319 Um, and so I was playing around with one thing another little bit with solid times, 229 00:25:19,320 --> 00:25:28,500 trying to understand the geometry behind some equations and not doing it to be honest, not doing very much nowadays. 230 00:25:28,500 --> 00:25:33,149 I mean, I know I should. I should have been producing papers. Well, yeah, that's one view. 231 00:25:33,150 --> 00:25:36,690 Anyway, I didn't see this impression that I have right know. 232 00:25:37,080 --> 00:25:42,060 Looking back on it, I realised that, you know, I should have actually written more. 233 00:25:42,810 --> 00:25:48,890 But then. Then Singer came across from M.I.T. 234 00:25:49,920 --> 00:25:57,960 And he came with this problem about instant funds, which is completely new to us here. 235 00:25:57,990 --> 00:26:04,580 I mean, on the one hand, it was about things that we knew about, about money, principal bundles and connections on. 236 00:26:05,040 --> 00:26:13,250 And it was on the false fear, you know. On the other hand, the questions that were being asked are very different, right? 237 00:26:13,590 --> 00:26:17,400 Gates Transformations Equivalence Classes Under Gates Transformation. 238 00:26:17,800 --> 00:26:19,290 So this was really new at the time. 239 00:26:20,280 --> 00:26:31,560 For me, it was the objects I knew about and I knew about what notion of an ice amorphous office was, but somehow studying solutions to equations. 240 00:26:32,010 --> 00:26:36,030 But, you know, this notion of equivalence is a kind of new idea. 241 00:26:36,180 --> 00:26:41,250 Mm hmm. Um, and anyway, that came along with this particular problem. 242 00:26:42,300 --> 00:26:48,930 So the physicists constructed some solutions with a very natural differential geometric question. 243 00:26:49,800 --> 00:26:56,400 And it's I mean, for me personally, of course, they linked up with Penrose's work as well. 244 00:26:56,600 --> 00:27:02,490 I think with algebraic geometry, the twisted theory. There are a lot of ideas hovering around the time. 245 00:27:02,910 --> 00:27:06,720 And then they kind of got directed on to this one particular problem. 246 00:27:06,840 --> 00:27:19,950 Mm hmm. Uh, for me, I got involved in it initially because of some of the things that I was working on, actually starting in NYU, 247 00:27:19,950 --> 00:27:27,630 which I never wrote out, which was about elliptic complexes, which were conformal invariants and non-standard elliptic complexes. 248 00:27:29,210 --> 00:27:36,150 And one of these kind of came up, at least a twisted version of it in studying the deformations of these instance. 249 00:27:36,300 --> 00:27:40,640 So I already had a background that studied these elliptic complexes. 250 00:27:40,650 --> 00:27:45,200 I knew what the index theory gave us. I now understand the problem. 251 00:27:45,210 --> 00:27:55,410 And so the first the first thing that I kind of contributed to this was the calculation of the infinitesimal deformation space of the base. 252 00:27:55,530 --> 00:28:00,809 Mm hmm. Then the singer came along and said, Well, look, these modernise base are very similar to what you're doing now. 253 00:28:00,810 --> 00:28:07,320 Spread geometry with modernised current issues, such as when you at what point you start saying moduli spaces. 254 00:28:07,320 --> 00:28:11,220 Was this at the point in your life where you start thinking about moduli spaces? 255 00:28:11,460 --> 00:28:15,840 That's right, yeah. I didn't know much about the algebraic geometry long before that. 256 00:28:16,600 --> 00:28:22,140 And that's right. Mm hmm. So then. Then, of course. And with the rapid development, using all these techniques. 257 00:28:23,070 --> 00:28:32,720 So. Okay, so eventually we we had this construction with the ADA construction, but the one with the lead singer was. 258 00:28:32,730 --> 00:28:36,900 Was more the differential geometric background to the equation. 259 00:28:37,170 --> 00:28:40,860 Mm hmm. And then how did the ADA. How did that develop? 260 00:28:41,160 --> 00:28:44,430 Were you a team of four working in a concerted way? 261 00:28:45,060 --> 00:28:46,500 So, no. 262 00:28:46,530 --> 00:28:55,860 So the Russians, I mean, there were there's an exchange of letters, had letters in those days to a long time to get from Moscow to, uh, to the West. 263 00:28:56,760 --> 00:29:01,630 And so, I mean, Michael was, was in contact with them. 264 00:29:01,650 --> 00:29:08,730 And so but and I guess through other conversations with other mathematicians. 265 00:29:08,880 --> 00:29:21,390 Mm hmm. But we were kind of working on it for my I mean, it was all using twisted theory and the result and some stable bundles and things like that. 266 00:29:22,500 --> 00:29:27,840 But it it is true that I mean, Michael's described this in his memoirs as well, 267 00:29:27,840 --> 00:29:34,680 that that we we eventually put together the vanishing theorem, which came from the differential geometry. 268 00:29:34,680 --> 00:29:40,740 That was the movie with the algebraic geometry that the monads that Michael was familiar with. 269 00:29:41,160 --> 00:29:53,049 We put these this thing together and then went off to lunch at St Catherine's College and then and well, actually, I was in Jensen Katz in those days. 270 00:29:53,050 --> 00:29:57,270 So East Greenwich, which was I went to Wolfson College and Katz. 271 00:29:57,300 --> 00:30:03,540 Uh huh. And I came back. I saw him waving a piece of paper at the end of the car. 272 00:30:03,540 --> 00:30:09,960 And I just got this letter from Greenfeld and money went out there that they'd done it as well. 273 00:30:10,230 --> 00:30:13,469 Okay. So it actually was, you know, we learned about it on the same day, 274 00:30:13,470 --> 00:30:18,720 although obviously if you actually look at the timeline, then they probably had a little bit earlier. 275 00:30:19,320 --> 00:30:24,960 Mm hmm. So we sort of skipped the bit of. So you went to the States and then you decided to come back. 276 00:30:25,080 --> 00:30:28,710 Was that an obvious thing, or were you tempted at that point to stay in the States? 277 00:30:28,740 --> 00:30:33,060 Or if you've been tempted at other times your life to to base yourself there? 278 00:30:33,420 --> 00:30:36,760 Yeah. At that point. Yeah. 279 00:30:36,760 --> 00:30:40,210 I could have stayed I could have stayed longer as a post-doc at NYU. 280 00:30:42,360 --> 00:30:45,780 I think so, Mike, my husband. So those things. 281 00:30:45,780 --> 00:30:53,490 But Michael was encouraging me to come back to Oxford and I've been away for three years. 282 00:30:54,150 --> 00:31:03,640 I've always liked being in Oxford. And I got married, and, yeah, we decided to come back. 283 00:31:03,960 --> 00:31:05,470 Mm hmm. And. 284 00:31:07,400 --> 00:31:17,240 Did you look ahead and anticipate that Oxford would be sort of the centre of your life or was a de facto assumption about do you think I just gave up? 285 00:31:17,800 --> 00:31:26,810 Uh, I know. I guess I never really looked ahead so much as I wanted to get on with the things that I was doing. 286 00:31:26,840 --> 00:31:30,760 Mm hmm. Mm hmm. And I suppose I. 287 00:31:30,880 --> 00:31:38,450 I kind of dragged my feet a little bit when it came to, um, to getting a more permanent job. 288 00:31:38,900 --> 00:31:48,620 And so I after the postdoc position, I got an advanced fellowship as I saw C or maybe as SIRC. 289 00:31:49,370 --> 00:31:53,270 Mm hmm. Um, so that gave you the time and freedom to think? 290 00:31:53,300 --> 00:32:02,280 Yeah, that's right. So. Mm hmm. And I guess in the back of my mind, I thought, well, you know, eventually I've got to give it up and teaching, but. 291 00:32:02,300 --> 00:32:06,320 And then I started applying for jobs in college, you know. 292 00:32:06,410 --> 00:32:13,430 CV Uh huh. Jobs in Oxford. I wasn't successful initially, but I think I don't think I was very convincing. 293 00:32:13,430 --> 00:32:20,200 And I still want I didn't give her a convincing argument that I actually wanted to engage myself in college life. 294 00:32:20,220 --> 00:32:26,990 But eventually I, you know, I realised that I ought to have my ideas out there. 295 00:32:27,650 --> 00:32:32,780 So yes. So I got the, the, the two, the shepherd and Katherine's going. 296 00:32:32,780 --> 00:32:38,330 But later on you've enjoyed tutorial teaching, right? I know you kept some going even when you were a civilian professor, right? 297 00:32:38,520 --> 00:32:48,860 Yes, that's right. I mean, you know, in retrospect, I realised that after becoming a tutor, I realised that. 298 00:32:51,190 --> 00:33:00,370 You know, mixed dieting is good for you, that if you're always doing research, you can be banging your head against the wall all the time. 299 00:33:01,720 --> 00:33:12,820 And that when you see students, when you give lectures to do tutorials, then it frees up part of your mind and has the cogs working again and. 300 00:33:13,700 --> 00:33:22,910 And it centres is healthy healthy to mix together all these things in it apart from your own the legacy your own work in mathematics, 301 00:33:23,570 --> 00:33:26,660 you've had many good students be good, good PhD students. 302 00:33:26,870 --> 00:33:32,100 So how did that start as we. Yeah. 303 00:33:32,110 --> 00:33:42,150 So I guess the first official assignment, Solomon was my first official student and I can't remember which year it was. 304 00:33:43,020 --> 00:33:46,530 I'd. Yeah. 305 00:33:46,560 --> 00:33:51,360 So he's okay? He turned 60 a couple of years ago, maybe Placer, huh? 306 00:33:51,630 --> 00:33:54,270 Mm hmm. Mm hmm. Yeah. 307 00:33:54,280 --> 00:34:06,390 So then I guess at the time, coming out of the work in Sometimes and South Duality, there were all sorts of questions about neonatology. 308 00:34:06,690 --> 00:34:15,330 There are a lot of questions that have potential topics which which, you know, I thought should be worked on and. 309 00:34:17,000 --> 00:34:20,180 And then I got students who were able to do that. 310 00:34:21,470 --> 00:34:27,560 How did it work out? I mean, I think I think probably. 311 00:34:28,820 --> 00:34:36,350 So I guess John James was civil in professor at that time and he was in charge of the geometry and mission. 312 00:34:37,100 --> 00:34:45,860 And he he would feed me. And did you sort of have a program at that time where you would like students to work on this and 313 00:34:45,860 --> 00:34:52,310 that idea of you to take in the student and then and then think about what you want them to do? 314 00:34:53,120 --> 00:34:54,970 It was the latter. Really? Yeah. 315 00:34:55,280 --> 00:35:05,870 I take the student explained to them what I was working on and explained things which were related to it and gradually seeing what they were happy, 316 00:35:05,930 --> 00:35:14,780 happy doing. And I can't remember chronologically the but yes, but sometimes student had to just show up. 317 00:35:14,800 --> 00:35:18,050 I mean, check these for example, is been very successful. Mm hmm. 318 00:35:18,350 --> 00:35:21,530 He was kind of washed up on the shores of Oxford as a Rhodes scholar. 319 00:35:22,130 --> 00:35:25,760 Didn't know, you know, nobody was a culminating and. 320 00:35:26,030 --> 00:35:29,450 And then he became my student. Very happy to have him. 321 00:35:29,570 --> 00:35:34,240 And but others were kind of trying towards me that I could change direction. 322 00:35:34,250 --> 00:35:37,870 But if I sort of dragged you off the linear path. 323 00:35:37,880 --> 00:35:45,440 But I remember you telling me once that you had a sort of a eureka moment about your famous paper on on Raymond Surfaces and Higgs Bundles. 324 00:35:45,480 --> 00:35:48,830 Do you want to talk about that eureka moment? 325 00:35:50,020 --> 00:35:55,590 Oh, yeah. And have they punctuated your life or do you think? 326 00:35:55,640 --> 00:36:01,730 Yeah. Yeah. I mean, of course, the eureka moment is always built on lots of work underneath. 327 00:36:01,730 --> 00:36:07,730 Yeah. I don't know whether it was the Higgs boson, but certainly in the monopoles. 328 00:36:07,730 --> 00:36:10,160 Well, neither you. I remember a eureka moment. 329 00:36:11,570 --> 00:36:20,180 This was when I was studying the construction of monopoles by looking at scattering along straight lines through three space. 330 00:36:21,290 --> 00:36:31,630 And yeah, I mean, I was walking home across South Park and then I remember passing these bushes. 331 00:36:32,020 --> 00:36:35,860 You know, stupid thing. But I remember thinking, Oh, a straight line has to end, you know? 332 00:36:35,860 --> 00:36:41,439 So and that was and then in the in the 10 minutes that it took me to get home from there, 333 00:36:41,440 --> 00:36:46,300 I kind of figured out how everything together in terms of algebraic geometry. 334 00:36:46,630 --> 00:36:52,180 Previously, I've been looking at solutions to this equation along a straight line which decayed at one end. 335 00:36:52,540 --> 00:36:58,700 And that gave me an entry point. Mm hmm. But then I've kind of forgotten about the other end. 336 00:36:58,720 --> 00:37:04,450 I mean, I guess I thought that it was pure symmetry changing, complex conjugation, which gave me what was happening. 337 00:37:04,470 --> 00:37:08,530 And then I realised that there was a whole morphing aspect to it, which. 338 00:37:09,040 --> 00:37:14,140 So. So that was, I remember was a particular bush in South Park that let that happen. 339 00:37:14,800 --> 00:37:18,459 And by the time I got home, I just wanted to write everything that was. 340 00:37:18,460 --> 00:37:24,160 That was still there. Mm hmm. 341 00:37:24,690 --> 00:37:30,640 So. So. So we've been taught by a very rich time in Oxford geometry and that. 342 00:37:30,960 --> 00:37:37,180 So how did things develop? Did you think of that as a sort of a great time in Oxford? 343 00:37:37,180 --> 00:37:41,079 And yes. You conscious? It was a special moment. Yes, it was. 344 00:37:41,080 --> 00:37:44,450 Because there was there were all these I mean, there was the twist, the group, 345 00:37:44,450 --> 00:37:50,080 the a lot of ideas coming from them because we'd seen that the twisted the theory was so valuable. 346 00:37:50,740 --> 00:37:53,139 And then in the instance, um, picture. 347 00:37:53,140 --> 00:38:04,450 But I'd also actually even earlier I'd seen that um, constructing solutions to Einstein equations and then known compact situation. 348 00:38:04,840 --> 00:38:12,219 But the sort of thing that was bothering me even back in Princeton could be done through them, through Gibbon's and Hawking's work. 349 00:38:12,220 --> 00:38:16,860 I mean, that showed me that you could use Twisted Theory to make these constructions. 350 00:38:17,470 --> 00:38:20,490 So I think there was the the twisted theory, the algebraic geometry, 351 00:38:20,490 --> 00:38:28,610 and then there was the gauge theory that was making it is, you know, telling us all the new things that were happening. 352 00:38:28,630 --> 00:38:35,170 You would always in a seminar, you know, give us an account or something. 353 00:38:35,680 --> 00:38:40,870 And I was in Harvard or whatever, and it was it was very exciting. 354 00:38:41,530 --> 00:38:44,859 And then did Dan Quillin arrive at this time with that? 355 00:38:44,860 --> 00:38:56,709 A little bit, I guess. Yeah, that was a bit later. Yes. So I remember giving let's say I gave a kind of graduate course on vector bundles on real 356 00:38:56,710 --> 00:39:01,520 surfaces where towards the end I was just beginning to introduce the Higgs bundle package. 357 00:39:01,570 --> 00:39:05,229 And I remember he was actually sitting in on this on this course. 358 00:39:05,230 --> 00:39:10,150 I guess it must have been around then. Yeah. Mm hmm. But I didn't really interact so much with them. 359 00:39:10,390 --> 00:39:15,700 Mm hmm. Mm hmm. So. So then at some point, you. 360 00:39:15,700 --> 00:39:20,440 You decided to leave Oxford. And was that a difficult decision? 361 00:39:21,460 --> 00:39:27,180 It seemed natural at the time. I think it's. Yeah. 362 00:39:27,190 --> 00:39:33,250 So, um. So I left Oxford in 1990 to go to worry. 363 00:39:33,990 --> 00:39:45,340 And so what had happened was that, uh, actually in the few years before that, so and so in like the mid-eighties, early eighties. 364 00:39:45,370 --> 00:39:54,670 Mm hmm. I'd been offered a position at Stony Point where there had a very strong geometry group. 365 00:39:55,150 --> 00:40:01,660 Mm hmm. And I went there for about two semesters to try it out. 366 00:40:02,230 --> 00:40:06,610 So, um, I suppose my. 367 00:40:07,570 --> 00:40:13,719 It wasn't so much a complaint about Oxford, but but, but, you know, c u f lectureship was a lot of teaching. 368 00:40:13,720 --> 00:40:21,660 A lot of college teaching. Yeah. Mm hmm. And I really wanted to have more time for my research, so it would be 12 hours college, just that time. 369 00:40:21,670 --> 00:40:26,460 Plus, I was actually pretty good. But it was to be a maybe 10 hours like that. 370 00:40:26,680 --> 00:40:33,370 Mm hmm. And it wasn't so much the actual teaching. It was the way it impacted on the daily life that, you know, 371 00:40:33,370 --> 00:40:39,670 if there was a seminar somewhere in Warwick or London or something I wanted to go to, there's no time to do it. 372 00:40:40,060 --> 00:40:41,280 Mm hmm. Um. 373 00:40:42,610 --> 00:40:52,960 So I was fortunate that because at the time teaching buyouts were really quite rare, but I was fortunate that in fact in my absence in Stony Brook, 374 00:40:53,860 --> 00:41:00,670 certain things were put together and it was there was an arrangement that said I could have a buyout of teachers and kids. 375 00:41:01,790 --> 00:41:08,840 Um, but then, uh, and that was largely on my committee know Grant. 376 00:41:09,110 --> 00:41:13,370 Uh huh. So I was still working with him on various topics. 377 00:41:13,430 --> 00:41:18,490 Mm hmm. So then, I guess towards the end of the 1980s. 378 00:41:18,500 --> 00:41:23,620 Well, on the one hand, it was a question of, uh. Yeah, you sit back and say, am I going to do this right? 379 00:41:23,810 --> 00:41:28,580 The rest. Right. Yeah. Um, and also, things were changing. 380 00:41:28,580 --> 00:41:37,480 So Sir Michael went to Cambridge all my time to be a master of Trinity. 381 00:41:38,090 --> 00:41:45,010 Graham SIEGEL went at the same time. And it was a time to, you know, I thought it was the time to change, right? 382 00:41:45,020 --> 00:41:48,910 Because I didn't want to revert to full time advice. 383 00:41:49,250 --> 00:41:52,410 Mm hmm. So then there was a chair assignment. 384 00:41:52,700 --> 00:42:01,760 Christopher Zeeman and. And Warwick had moved and retired, I guess, but then subsequently became head of the college here. 385 00:42:02,840 --> 00:42:09,910 And so there was a vacancy in Warwick and I decided to apply for that and. 386 00:42:10,200 --> 00:42:13,400 And I. And I got in. Mm hmm. 387 00:42:13,710 --> 00:42:17,810 Um, so that was. And that was change. 388 00:42:18,200 --> 00:42:25,010 I enjoyed the change. I enjoyed the change of environment as a very different department is run in a different way. 389 00:42:25,760 --> 00:42:28,870 It brought me face to face with departmental issues. 390 00:42:29,110 --> 00:42:34,940 I college issues. Mm hmm. I had kind of. I hadn't taken. 391 00:42:36,970 --> 00:42:42,010 Much part in mathematical institute business, actually. 392 00:42:42,550 --> 00:42:45,610 Before that. Mm hmm. Um, so. Yeah. 393 00:42:45,640 --> 00:42:49,210 So then I was. So. So work, actually. You know, when you. 394 00:42:49,990 --> 00:42:55,280 When you change environment, sometimes your mathematical ideas change as well. 395 00:42:55,300 --> 00:42:59,930 Yeah. That's go ask you about that. And it did. It did it to give you new interests. 396 00:43:00,000 --> 00:43:07,480 Uh, so, um, yeah, it's difficult to say that the, the environment that I have because there was a natural progression. 397 00:43:07,690 --> 00:43:14,890 Yeah. I mean, it's, it's true that there was a, there were visitors there, I guess, uh. 398 00:43:16,020 --> 00:43:21,630 Yeah. Yeah. Different visitors pushed me in different directions on different subjects. 399 00:43:24,580 --> 00:43:28,600 Actually were. It was where I first learned to use a computer. 400 00:43:31,480 --> 00:43:35,260 In fact, when I got there, they said so. 401 00:43:36,360 --> 00:43:40,050 Do you want a monitor or whatever it is? I have those things. 402 00:43:41,030 --> 00:43:45,810 I said yes and so I said, fine. So that was on my desk and I didn't do that. 403 00:43:46,410 --> 00:43:52,200 So I learned, I learnt to write papers intact and it brought me up to speed. 404 00:43:52,980 --> 00:44:00,300 Have you ever used the computer as a research tool or as I use it, to search the literature? 405 00:44:01,560 --> 00:44:06,330 And I've used that to do with mathematics. 406 00:44:06,330 --> 00:44:09,890 Done calculations. That algebraic calculations. Yes. 407 00:44:10,140 --> 00:44:16,020 Mm hmm. Though, to be honest, not in a very serious way. 408 00:44:16,020 --> 00:44:25,770 I mean, you know, we always like to have if we have a closed form solution, we always like to have it eliminates the need to form as possible. 409 00:44:25,920 --> 00:44:29,640 Mm hmm. And I've used, you know, algebraic manipulation. 410 00:44:29,670 --> 00:44:36,030 Oh, okay. Uh huh. Mm hmm. On the other hand, I, I there was an occasion, 411 00:44:36,030 --> 00:44:44,540 so when I was working on pan of equations and I got some algebraic solutions and they came out very nicely, 412 00:44:44,550 --> 00:44:48,420 I thought, well, these are really nice formulas. And, and I thought, well, they must be right. 413 00:44:48,540 --> 00:44:55,019 Uh huh, uh huh. But I never substituted them back in the equation using the computer. 414 00:44:55,020 --> 00:45:03,719 And in fact, subsequently they became of use to Wolfgang Zeller and his collaborators in studying 415 00:45:03,720 --> 00:45:08,940 metrics of positive curvature and an imbalance and to show that this formula is correct. 416 00:45:10,350 --> 00:45:14,970 And then I had to go back to my paper and I realised that there were some medical errors. 417 00:45:15,000 --> 00:45:25,220 Uh huh. So he actually put it in the computer and I said, Well, it's a nice for it can't be wrong that you're not totally happy. 418 00:45:25,230 --> 00:45:27,350 And I don't, I don't have to. 419 00:45:27,840 --> 00:45:34,920 I just skipped over the period when, when Simon Donaldson was your student, which, which was presumably an exciting time in all sorts of ways. 420 00:45:35,040 --> 00:45:41,069 Oh, what was going on? And obviously, that that was a two way street, as it were. 421 00:45:41,070 --> 00:45:45,120 But did that influence your subsequent research much, you think? 422 00:45:46,050 --> 00:45:49,260 Uh, yeah, I guess so. So, yeah, so. 423 00:45:49,260 --> 00:45:55,300 SIMON So this was another occasion when you and James told me, look, 424 00:45:55,320 --> 00:46:03,890 we've got this applicant and Ray Liquorice is the best student for ten years or something like that. 425 00:46:04,090 --> 00:46:12,960 And so I said, maybe we should make him only offer. And so he came and, and, and that was very rewarding time because. 426 00:46:14,010 --> 00:46:21,300 You know, I would set a problem and then, you know, he would come back in a few weeks time and saying, okay, what should I do now? 427 00:46:21,460 --> 00:46:26,130 Right. And gradually so but at that time, 428 00:46:26,310 --> 00:46:37,889 it was interesting because I changed he kind of changed my view and I kind of put it I was after I'd done this work on instant 429 00:46:37,890 --> 00:46:45,270 tons and I thought that this whole self duality kind of package was a kind of Kryptonian version of Raymond Surfaces, 430 00:46:45,300 --> 00:46:51,860 and he was like kind of self-contained, a piece of geometry which replaced the complex then as by the quotidian. 431 00:46:52,530 --> 00:46:56,759 But then there are these little bits of information coming from other areas. 432 00:46:56,760 --> 00:47:02,690 So Talibs that showed that actually you could find self to your solutions on these non self your manifolds. 433 00:47:02,700 --> 00:47:13,050 And then there's this link with stable bundles and, and so so there was clearly a kind of bigger picture emerging. 434 00:47:15,510 --> 00:47:22,730 And that's kind of shook me out of my complacency about this, about where this whole area was sitting. 435 00:47:22,900 --> 00:47:28,590 So so I began to give assignment problems related to this. 436 00:47:29,160 --> 00:47:37,170 And he he was avidly reading the work back to the towns that I guess came here for a while as well. 437 00:47:38,070 --> 00:47:46,889 And so so gradually he began working on these these broad general uses of some of the equations. 438 00:47:46,890 --> 00:47:52,469 And but but he, of course, he passed on to the work with my idea. 439 00:47:52,470 --> 00:47:55,980 And that was the the stage when, when he saw the. 440 00:47:55,990 --> 00:48:04,170 So there was a conjecture there about the relationship between stable bundles and the existence of these emission Einstein connections. 441 00:48:04,950 --> 00:48:13,770 And it was a clear conjecture. And he he noticed that actually you could reformulated in an infinite dimensional moment in that picture, 442 00:48:13,920 --> 00:48:25,049 which was the kind of flavour of the month at the time there was lots and there was all the work that I tend done on convexity and moment maps. 443 00:48:25,050 --> 00:48:29,160 And then the idea about picture for young males on Raymond Surfaces. 444 00:48:30,160 --> 00:48:33,840 So moment maps, if you could phrase something in the language of a moment, 445 00:48:34,140 --> 00:48:38,250 then you you kind of use the time somehow you'll be able to see the equations. 446 00:48:38,430 --> 00:48:45,540 Mm hmm. And so that was, you know, at that time, that was when I thought, well, you know, Simon has identified this particular problem in those terms. 447 00:48:46,000 --> 00:48:49,950 I benefited greatly by being there. 448 00:48:50,370 --> 00:48:55,230 And so Michael and I had obviously a very personal. 449 00:48:55,740 --> 00:48:59,050 Mm hmm. So can I skip it? 450 00:48:59,070 --> 00:49:02,730 Skip ahead to your time in Cambridge. 451 00:49:02,760 --> 00:49:08,820 So it was that was that a happy time? Was that a a new direction again or. 452 00:49:08,940 --> 00:49:12,030 Yeah. So. So. Right. So. 453 00:49:15,630 --> 00:49:29,730 You know, so I was approached I was approached for this chair in Cambridge, and it was clear that, you know, okay, I kind of knew that. 454 00:49:31,100 --> 00:49:41,210 As I put it in some respects, I know that it would have been nice to come back to Oxford and, you know, in the chair. 455 00:49:41,250 --> 00:49:44,720 Yeah, but that wasn't I wasn't available. 456 00:49:44,900 --> 00:49:56,420 Available to her and so. But, you know, to be to be a, you know, office, they have a chair in Cambridge is a terrific thing. 457 00:49:57,320 --> 00:50:02,540 And so I was very happy to go there. And I thought, this is going to be one of, you know, the rest of my life. 458 00:50:02,840 --> 00:50:07,160 Uh huh. Mm hmm. Chair And one of the best departments in the UK. 459 00:50:08,300 --> 00:50:19,100 And that was. And, of course, that meant kind of, hey, was the change, you know, going back to bwari to an environment which was more life. 460 00:50:19,520 --> 00:50:28,070 Right. So it's familiar in some respects. Mm hmm. And I had a college attachment there, a in college, which is very nice. 461 00:50:28,880 --> 00:50:34,420 I had other responsibilities there. And it was it was good. 462 00:50:34,430 --> 00:50:42,559 In fact, there I had more contact with a physicist, actually know people like Gary Gibbons. 463 00:50:42,560 --> 00:50:50,600 And we used to hold the geology seminar in the endowment so that Stephen Hawking could can. 464 00:50:51,920 --> 00:50:57,110 Graham SIEGEL was there. We yeah, I, I used to. 465 00:50:58,080 --> 00:51:02,600 Yeah. I followed different courses of. 466 00:51:04,570 --> 00:51:08,800 Well, I follow different pieces of mathematics and research projects. 467 00:51:09,900 --> 00:51:21,500 So I was I was happy that we had a nice house. But then then I got this phone call that because I'm in the civilian chair, it was held briefly. 468 00:51:21,500 --> 00:51:30,170 And then I came back and again and then I got this, this phone call from Oxford suggesting I, I applied for that. 469 00:51:32,210 --> 00:51:38,750 And that was you know, that was something I you know, I somehow had always liked Oxford better than. 470 00:51:39,350 --> 00:51:42,740 I think it all goes back to where they whenever you know. I agree that. 471 00:51:42,890 --> 00:51:50,810 Yeah. It was your heart. Yes. Then you got to know every street corner and every street corner means something to you. 472 00:51:51,770 --> 00:52:02,690 And Cambridge is a wonderful place. But but still somehow also I mean, our children had grown up in Oxford and we we made we have many friends. 473 00:52:02,720 --> 00:52:10,280 And so so it was coming back with something which I was happy to do and no reflection on. 474 00:52:10,880 --> 00:52:18,560 So yeah. Yeah. So, so you mentioned you had some of the physicists in Cambridge, but so throughout your career, 475 00:52:18,560 --> 00:52:24,610 I guess the sort of stimulus of physics asking questions of mathematics and the mathematics that's produces it, 476 00:52:24,890 --> 00:52:27,799 but was that that particular time when that came more into focus, 477 00:52:27,800 --> 00:52:34,640 or was it really something that was always that is I think the first time it happened was, 478 00:52:34,670 --> 00:52:41,480 uh, in the seventies when, when I learned about this, this work of. 479 00:52:42,680 --> 00:52:46,070 Hawking and his collaborators on Euclidean gravity. 480 00:52:46,250 --> 00:52:57,190 So this was where. So I'm trying to do quantum gravity where they shifted from the Laurentian signature to positive definite signature. 481 00:52:58,750 --> 00:53:08,829 Um, so this meant that, that they had these constructions and the rents in case which they adapted to the Romanian case, 482 00:53:08,830 --> 00:53:16,030 and suddenly they were producing examples of these solutions to Einstein's equations. 483 00:53:16,390 --> 00:53:21,910 Ritchie Flat manifolds, which we mathematicians though when I was in Princeton, 484 00:53:22,170 --> 00:53:27,400 there were mathematicians there trying to even look at local solutions and getting any lower. 485 00:53:27,880 --> 00:53:33,790 And yet here with the physicists, with their intuition and their methods actually producing examples of these, 486 00:53:33,790 --> 00:53:35,680 I think that was the first time that I realised that, 487 00:53:35,940 --> 00:53:45,850 that, that, that, that their intuition, when it was focussed on something which was relevant to the real mathematics, 488 00:53:46,630 --> 00:53:57,070 that was really something valuable to hold onto. And I guess then and also the work of Penrose and his and his collaborators. 489 00:53:57,070 --> 00:54:04,450 So the twist, the theory that again departed from the Lorenz signature because they were usually working over the complex numbers. 490 00:54:04,540 --> 00:54:12,189 So for Penrose, he would say that the complex numbers are fundamental for quantum theory. 491 00:54:12,190 --> 00:54:16,750 If we're going to have a quantum theory of gravity, which should building the complex numbers right at the beginning. 492 00:54:16,930 --> 00:54:24,100 Mm hmm. So, again, what was Lorenz and became complex and complex and what was you know, 493 00:54:24,100 --> 00:54:29,800 if you complexity by something which is positive definite then it's it's you know, it's the same with the same setting. 494 00:54:30,610 --> 00:54:37,629 So those two pieces of that kind of change of point of view even meant that the 495 00:54:37,630 --> 00:54:43,060 intuition in the background of the physicist could actually be relevant to positive, 496 00:54:43,060 --> 00:54:48,720 definite signatures, changes that remain in geometry. So, so that was that. 497 00:54:48,850 --> 00:54:56,770 Those are the first two instances where I really thought, okay, I can take physicists intuition seriously. 498 00:54:56,920 --> 00:55:05,580 And then along came the instantaneous stuff, which is where the physicists had a problem, which was perfectly accessible and resilient. 499 00:55:06,910 --> 00:55:09,760 Suddenly the flow of information was perhaps the other way there, 500 00:55:09,760 --> 00:55:18,750 that that their intuition enabled us to make certain constructions, but we had no general point of view to to go back. 501 00:55:19,480 --> 00:55:23,830 But I think it all started in the seventies with the whole given as well. 502 00:55:23,870 --> 00:55:29,410 Mm hmm. And then the whole sort of symmetry story, is that influenced you a lot more recently? 503 00:55:29,500 --> 00:55:34,659 Uh, so, yes, definitely. Uh, I've tried to. 504 00:55:34,660 --> 00:55:40,870 Okay. So that was one of the things that I guess I started trying to learn about when I was in Cambridge, 505 00:55:41,890 --> 00:55:50,560 because at that time there was this strange Ja Zaslow interpretation of symmetry, which was very geometrical. 506 00:55:52,060 --> 00:56:01,990 And it was so trying to put that into effect made me try and look at what special advantages and enhance and fast the 507 00:56:01,990 --> 00:56:10,979 various things that and subsequently they the Higgs bundle bunch of nice base which fitted into this s y z scheme very, 508 00:56:10,980 --> 00:56:21,760 very nicely. I've been, you know, following up the implications of mirror symmetry and now largely by listening to physicists, people like Gourcuff, 509 00:56:21,940 --> 00:56:27,100 Witten and Capus and others who tell me that, okay, you know, according to us, 510 00:56:27,490 --> 00:56:32,770 something should happen, this correspondence between this and that, then checking with it. 511 00:56:32,890 --> 00:56:37,570 And generally speaking, you can see you see how it happens in a particular instance. 512 00:56:38,110 --> 00:56:43,809 That's, you know, that's that's been valuable in recent years. I pick up on that. 513 00:56:43,810 --> 00:56:49,930 So and there's lots of interesting mathematical objects that bear your name, the hitchin component, the hitchin vibration and so on. 514 00:56:50,230 --> 00:56:57,800 But then people take these up and run with them and you try to keep track of how people are using your name, as it were. 515 00:56:59,180 --> 00:57:05,079 So, I mean, the mathematics that flows from it, do you feel a particular attachment to it as well? 516 00:57:05,080 --> 00:57:13,959 That you know that it's true? There are conferences on the hitchin this and I know that maybe it's gone far beyond. 517 00:57:13,960 --> 00:57:25,480 I have you know, I'm just in the work of go you know right over again is far removed from her that I work on. 518 00:57:27,040 --> 00:57:38,290 And equally, these hitchin components, I mean, I'm very interested in the the work of people like Guichard and me not gnabry on these components, 519 00:57:38,290 --> 00:57:42,849 but I know that that techniques are very far removed from the ones that I use. 520 00:57:42,850 --> 00:57:47,950 And so following them means, yeah, understanding what they're saying about it. 521 00:57:48,700 --> 00:57:51,820 But then in the back of my mind, I'm thinking, you know, 522 00:57:52,270 --> 00:57:58,020 is it possible that I can actually use the techniques I'm familiar with to do some of these rights? 523 00:57:58,920 --> 00:58:02,370 Um. But it's. But it's. 524 00:58:02,380 --> 00:58:06,950 Yeah, it's. It's true that. That these things can be. 525 00:58:07,140 --> 00:58:13,950 And have you been drawn. Specific. Have you been drawn into geometric langlands through in this sort of way? 526 00:58:15,250 --> 00:58:26,910 But for the game, I restrict my so I rest restrict myself to to seeing in what way langlands duality reflects their symmetry. 527 00:58:27,720 --> 00:58:30,780 So actually, you know, 528 00:58:31,740 --> 00:58:41,340 formulations of the geometric langlands correspondence in terms of their I have categories that equivalence of different categories 529 00:58:41,340 --> 00:58:50,520 is is something which I know I would never be able to formulate that is in the language which I only partially understand, 530 00:58:51,960 --> 00:58:59,790 but it's the specifics which which intrigued me. The prediction usually I think of them as predictions from the physicists, 531 00:59:00,180 --> 00:59:06,950 but of course the seeing them realise in algebraic terms is very, very satisfying. 532 00:59:07,110 --> 00:59:11,040 Mm hmm. I think so. And talking satisfying. 533 00:59:11,040 --> 00:59:17,010 So. So. So you just won the show prize this year and was that very satisfying? 534 00:59:17,580 --> 00:59:23,760 Obviously is very nice in many ways. But and and it's not that you were short of international recognition before. 535 00:59:23,760 --> 00:59:32,040 And and but it's did it bring a sense of as a warm glow of appreciation or is it. 536 00:59:32,160 --> 00:59:38,730 Yeah, I think it's um and it is. I mean, I did appreciate it as international recognition and I mean, I know, okay, 537 00:59:38,850 --> 00:59:43,739 maybe this recognition because I get asked to give me lectures around, you know, old and so forth. 538 00:59:43,740 --> 00:59:51,760 But this, this was you a tangible. A tangible appreciation. 539 00:59:51,760 --> 01:00:04,209 I was very honoured to get it. Obviously it was a great surprise and but but I've been fortunate to win various prizes from the society, 540 01:00:04,210 --> 01:00:08,770 but this was an international profile of the prize. 541 01:00:08,800 --> 01:00:14,620 I mean, was what really appreciated both. If you had to. 542 01:00:15,550 --> 01:00:22,960 So as we've discussed, your work has wide influence and you and you have great students who perpetuate your influence in many ways. 543 01:00:23,650 --> 01:00:27,610 But what are you most proud of yourself? 544 01:00:28,630 --> 01:00:32,650 Which part of your work I am most proud of or most fond of? 545 01:00:35,200 --> 01:00:37,800 I guess a tough question, I guess. 546 01:00:38,860 --> 01:00:50,050 You know, the I think the citation for the show prize talked about corners of geometry, which I lay dormant or something like that. 547 01:00:50,860 --> 01:01:01,100 I mean, I always like it when there's something that I've been working on which has some historical, you know, the quaternions, for example. 548 01:01:01,120 --> 01:01:10,989 Yeah, that's, uh, uh. Um, and even, you know, these 19th century mathematicians knew what they were doing, 549 01:01:10,990 --> 01:01:15,879 but of course, what they were doing was framed in a different way nowadays. 550 01:01:15,880 --> 01:01:19,240 And so we must actually dismiss them. But no. 551 01:01:19,240 --> 01:01:22,360 So what was giving me? Most pleasure? 552 01:01:25,070 --> 01:01:29,550 Uh. Well, you know, I think. I think this. 553 01:01:31,510 --> 01:01:36,370 You know, the Higgs. I mean, I wrote this paper which started the Higgs bubble. 554 01:01:37,000 --> 01:01:47,550 What? And that was a paper which I just came in day by day and kept discovering new things about. 555 01:01:47,640 --> 01:01:51,370 I mean, I started it in a in a simple fashion. 556 01:01:51,390 --> 01:01:57,450 I, I knew that there was some infinite dimension, dimensional hyperscale quotient, 557 01:01:57,450 --> 01:02:02,430 which was going to give me a margin I space related to bundles under the surface. 558 01:02:02,580 --> 01:02:07,080 That was my starting point, just HyperCard and geometry. 559 01:02:07,860 --> 01:02:13,169 But then the more I looked at these these this particular object, the more I found. 560 01:02:13,170 --> 01:02:25,110 And then it was over a period of a few weeks, actually, that somehow every feature seemed to generate a new new result, new aspect. 561 01:02:26,460 --> 01:02:34,800 On the one hand, it was a new proof of uniform ization. Now, I could also imitate the loss theory approach to it. 562 01:02:34,800 --> 01:02:43,709 But I can do this. I can do that. It was that was very, very satisfying because it I mean, the paper took much longer to write, 563 01:02:43,710 --> 01:02:50,820 but still, ultimately, the the pieces, the components of it, they all fell together very quickly. 564 01:02:51,000 --> 01:02:54,270 Mm hmm. So you you knew. You knew pretty quickly. 565 01:02:54,270 --> 01:02:57,840 This was a really rich vein of ideas. Yeah, yeah, yeah. 566 01:02:58,070 --> 01:03:04,220 I didn't realise that it is so influential, but. But it was pretty clear that there was. 567 01:03:04,690 --> 01:03:07,950 There was something genuinely new there. So. 568 01:03:08,450 --> 01:03:14,760 So as we're chatting this, that and certain influences on you are obvious. 569 01:03:15,840 --> 01:03:24,120 But are there any influences we haven't touched on in people or sets of ideas that are less obviously influences on you? 570 01:03:27,170 --> 01:03:32,300 Uh. They're obvious individuals, you know? 571 01:03:32,330 --> 01:03:36,040 I mean, you know, people like my friend Tia is singer. 572 01:03:37,180 --> 01:03:44,860 I mean, the ones who facilitated the connection between physics and mathematics. 573 01:03:46,640 --> 01:03:50,600 Edward Whitten example. I mean, I'm not saying we haven't written any papers together, 574 01:03:50,600 --> 01:04:02,900 but the people have had the patience to understand that there are two languages and you need to explain in order to really make the relationship work. 575 01:04:03,440 --> 01:04:11,270 You have to explain things in the right formulas, even if you know, even if the original way of thinking about them is very different. 576 01:04:11,570 --> 01:04:15,770 Mm hmm. And so. So people like that. Who. 577 01:04:18,140 --> 01:04:29,150 Who make this interface between physics and mathematics work requires requires patience and understanding of both sides of the road. 578 01:04:29,780 --> 01:04:33,590 And those three are of three examples. 579 01:04:33,860 --> 01:04:40,100 People have rarely done that in my life. So. So you're retiring a civilian professor. 580 01:04:41,180 --> 01:04:44,200 You're not retiring as a mathematician? I imagine so. It's a bit. 581 01:04:44,240 --> 01:04:47,510 What? What do you want to do the next part of your life? 582 01:04:47,510 --> 01:04:53,570 What really interests you still? What? What mathematically and unknown mathematically did you hope to do next? 583 01:04:54,830 --> 01:04:59,959 Uh, I'm still I still got the momentum of what I was doing, you know, for the previous years. 584 01:04:59,960 --> 01:05:03,250 So I have been coming in virtually every day to the office. 585 01:05:03,270 --> 01:05:08,450 I have is I think that's going to change very much over the next year or so. 586 01:05:08,900 --> 01:05:14,809 Hmm. Um, there is, there are projects which I'm, I'm working on. 587 01:05:14,810 --> 01:05:22,879 I mean, this, this kind of infinite dimensional version of timeless space, which is intriguing me very much. 588 01:05:22,880 --> 01:05:23,870 And which I mean, 589 01:05:24,140 --> 01:05:31,910 Francois Barea is another kind of version of it and it's not at all clear about whether his is exactly the same as the one that I'm looking at. 590 01:05:32,930 --> 01:05:42,610 Um, so, and I'm not sure. So I, now I have one research student left and he will finish the end of. 591 01:05:43,310 --> 01:05:49,870 Of this academic year. Mm hmm. Um, I'm not quite sure how things will go. 592 01:05:49,910 --> 01:05:57,200 I don't. I mean, for the sake of the research students, I don't really want to have anymore, because it will be a divided supervision. 593 01:05:57,200 --> 01:06:03,740 And in any case, they need me to absorb new ideas. 594 01:06:03,920 --> 01:06:11,230 Mm hmm. So I'll. I'll carry on with. With the many of the projects that I have and hopefully learn some more. 595 01:06:11,240 --> 01:06:16,130 I mean, I go to conferences, that's, uh, a conference and. 596 01:06:17,150 --> 01:06:22,969 Well, actually, to be honest, uh, part of the work that I. 597 01:06:22,970 --> 01:06:29,030 So next month I'm giving some lectures in Brandeis and named lectures. 598 01:06:29,510 --> 01:06:35,600 So I have to think about what I'm talking about. This is, this is way off right now from I think, Oh, I've got to give some lectures. 599 01:06:35,600 --> 01:06:40,400 Let me think a little bit more about this topic. And then gradually maybe a paper comes out. 600 01:06:41,510 --> 01:06:47,150 And then then, okay. There are now all sorts of 60th birthday conferences from her, from a student. 601 01:06:47,390 --> 01:06:54,620 Right. I know that these are all coming out her these these are things which keep keep me going because I give a talk. 602 01:06:54,620 --> 01:07:01,160 You know, I think I need to think of something new to talk. And it's always something in the back that which I can I can work on. 603 01:07:01,610 --> 01:07:04,880 That was great. Nigel, thanks very much for talking to us today. My pleasure.