Sonstige

Gaëtan Borot studied at the ENS Paris and finished his PhD with Bertrand Eynard in theoretical physics at CEA Saclay in 2011. After two years as postdoc in Geneva and a visit of MIT, he joined the Max Planck Institute for Mathematics in 2014 as Advanced Researcher (W2). In the Fall of 2020 he has moved to a chair at the Humboldt University in Berlin. He is working on the combinatorial and algebraic structures of quantum field theory and is best known for his contributions to topological recursion for which he has received the Dubrovin Medal of 2020. Christian Blohmann had a conversation with him about his new position and his time in Bonn.

Blohmann: How is your new job?

Borot: Very different. I realize how much I was taken care of at MPIM in terms of all that is external to research, and had time to really devote myself to science. This is not critical of my university, which is a big machine, a big factory, in which the math department is just one droplet. The organization cannot be the same. Every little thing for the office I had to find out how to get it according to the rules, which have their own reason to be. The people I’ve met here are nice but because of Corona, its like starting to work in the underground and wait for the days when we are able to go outside. The department of mathematics is not big, but there are interesting people to talk to, and so I’m looking forward to when I will be settled in and when Corona will be over so that we can start to have a scientific life again.

Blohmann: Do you already have a new group in Berlin?

Borot: I am in the process of building it. On my homepage I have also included the PhD students and postdocs who are still in Bonn. One of them is moving to Berlin soon. I have a new PhD student from Italy and one postdoc who is not yet living in Berlin for Corona reasons. And I am planning to hire two more postdocs this year with my startup funds. So I’m slowly trying to redo what I had at MPIM. Maybe within 2 or 3 years I will have a group of 4 or 5 people around, but then it has to be sustained by external funding.

Blohmann: Was it hard to get a good job? How was your application process?

Borot: In general, finding a job in Germany is not easy and there’s also the special situation that I do pure mathematics but have a PhD in theoretical physics. For some people I’m still considered as a physicist but in front of physicists it’s hard to defend that I do theoretical physics. In my head I don’t make this separation, but the university structure and the job market are more categorized. Since my PhD I have always been in the math department. I’m really inside mathematics with the things I do and questions I ask. But sometimes I still see some resistance, which comes from the dichotomy between physics and mathematics.

Blohmann: Can you tell us how you got to MPIM?

Borot: My first position after the PhD was in Geneva. I had just finished writing my thesis day and night for three months and was eager to meet new people and learn new things. So I went to a conference on knot theory, where I met Don [Zagier]. He told me many things about knots, his ideas on the Jones polynomial, the Bloch group, and introduced me to Tudor Dimofte who told me about quantization of Chern-Simons. I saw some similarities to topological recursion, but at that time it was too fuzzy. So I worked through “The 1-2-3 of Modular Forms” Don had told me about. A few months later I found a connection which explained some calculations of theoretical physicists on perturbative knot invariants, so I had something concrete to show to him. A year later, when I was already set to move to Boston for my next postdoc at MIT, I received a call from Don who told me about a five-year position at MPIM. I had been to MPIM for short visits but knew nothing about the German system and W2 positions. So I applied and five days later, just when I was about to fly to Boston, Don called me and told me that I got the position. I felt extremely lucky because I didn’t have to look for the position, it just came to me. When I arrived at the Max Planck Institute, I was totally free and I didn’t have to worry about what to do next. I really had the space just to try something interesting. I also came with this feeling that I have to pay back the trust that the people put in me by doing something that’s worth in mathematics.

Blohmann: That sounds like a classic story about Don getting math talent to MPIM. In some sense, this is the ideal Max Planck Society style recruiting. Now that your time at MPI is over, did you realize the goals you had when you started?

Borot: I usually start with modest goals, first try things that one can actually do, which are still interesting. When I came to the MPIM, there were several things I wanted to understand, but I didn’t have the faith that I’m going to solve that. I just wanted to learn and, in the process, maybe find something where I can say something which is not totally trivial. What I really benefited from in Bonn were the talks. I didn’t go to many talks at the MPIM because I needed time locked in my office to work. But the talks I went to, maybe once in a month, a bit more when there was a conference, were extremely helpful and that happened without me wanting it consciously. Just by diffusion I learned a lot of geometry, about algebraic geometry, in the talks from the group of Peter Teichner about factorization algebras, about higher categories in quantum field theory, or got better acquaintance in topological strings by discussing with Albrecht Klemm at Bonn University. There was this little sheet of paper in front of my office with my category number (the level of your category that you can think about without having a headache). When I arrived in Bonn, it was perhaps 1, after a year in it was 2, and after 5 years in Bonn I was not far from infinity.

Blohmann: Infinity is the next simple number after 2. Nobody ever says, you know, 37.

Borot: Exactly (laughs)! That’s something that happened just by going to talks from time to time discussing with people. When I arrived at Bonn, topological recursion was not geometric in the sense that it produced out of some data an object that depends on two integers g and n, that were in applications often related to the genus of a surface and the number of punctures or boundary components, but it was not clear why. So when I discussed from time to time with Peter Teichner and other people, they were always asking “Why is g the genus?” and “Why is n related to the number of boundaries?” When I arrived in Bonn this was not known. Topological recursion was just in the process of being cast in a purely mathematical framework. So, what I found, with Jørgen Andersen and Nicolas Orantin, is a way to obtain topological recursion from a geometric construction that is finer than topological recursion. And this can be used in practice. The assumptions are not too hard to check. When I did that, for what it’s worth, I thought that my years at the Max Planck were not wasted.

Blohmann: How was your life outside of math during your time in Bonn? Bonn is not Paris or Berlin and, as I know, you’re a cultured person?

Borot: I must say, I was extremely happy to get away from Paris and didn’t even consider to return. I come from a small village in the center of France. I'm not too attracted by big towns. Before Bonn, I was in Geneva, which was really a beautiful place for nature, so when I arrived to Bonn, for the first 2 years, it was hard. It felt gray at the time. I had some changes in my personal life, I knew nobody, I was not very social, and I was travelling a lot. In my first year I spent more than half of my time away for conferences and to work with people. But then I volunteered to give a course at the University, so I had to be there every week. For 6 months I didn’t travel much and only went to events which were really essential. Then I started to meet some people, some friends. This happened randomly because of a guest at the institute who was organizing a cineclub. I went there once and that’s where I met some of the persons that later became very close friends, which gave me a different access to Bonn. From that point I started to enjoy it. I didn’t see it gray anymore. The Rhine is very nice, the green is not far with the Siebengebirge, the Rheinaue, the Hofgarten, all these things, and that you can walk everywhere! Once you know to enjoy it, it is really pleasant. Later I got married and my wife came to Bonn as well, so I was exploring the space even more.

Blohmann: Is there something particular you miss about Bonn or MPIM?

Borot: Of course, the last months in the MPI were very special. It was a bit sad that I couldn’t meet people [due to Corona]. One thing I miss from Bonn is this rich environment of lectures, talks, visitors, which is really making this place extremely enjoyable because you are exposed to a lot of different mathematics, and just by diffusion you learn a lot from this. That’s perhaps the thing that is unique or rare that the MPIM has, which will be much harder to recreate at other places like at the university. Right now, everything is shut down. But I will keep this experience in mind. If I am later in a position to take decisions or to recreate something, I can find some inspiration from what happened in Bonn.

Blohmann: This is a good plan. As you know from MPIM history, we exist because Hirzebruch liked the IAS in Princeton so much. Did you find the language and culture in Bonn difficult to get used to?

Borot: No, I never had this kind of prejudices in Germany that some people may have. I could speak German before. In fact, I spoke way better German before I arrived to Bonn. I must say my German has declined during my 7 years in Bonn.

Blohmann: Now you have to brush it up?

Borot: I'm taking courses, because I have to teach in German next year.

Blohmann: Come on Gaëtan, your German is so good, you’re beyond courses! You should read books in German.

Borot: I read books without any problems since 10 years. However, it is speaking which has always been difficult for me, and I never did math in German. Even for a simple sentence, like explaining a proof in German, I don’t have the vocabulary.

Blohmann: I see. But that’s the same for me. At MPIM I haven’t talked math in German for a long time. What are your big goals for the next step of your career?

Borot: I'm not a person who works on big problems. I am more interested in constructions, ideas, connecting several things. One of my goals is to understand some constructions coming from quantum field theory in a more unified way. This is not about the physics itself, but many current constructions in geometry have a quantum field theory flavor. Physicists have a lot of success in making predictions that interest geometers because they can jump from one thing to another by steps that are not well-defined or rigorous, so they can forsee that this is going to be connected to that, and can use ideas from there to solve problems here, or use some dualities which convert a hard problem into an easy one. For example with mirror symmetry or in geometric Langlands. I would like to make such relations into concrete mathematics. This often brings interesting and new results.

Blohmann: Thank you for the enjoyable and interesting conversation, Gaëtan. We certainly miss you here! But I am sure that we will see you in Bonn often and that you will bring mathematics at the Humboldt University and in Bonn closer together. And this is what the Max Planck Institute for Mathematics is about.