It is an excellent opportunity for young researcher Tamás Kátay to continue his work at UCLA in Los Angeles in the autumn. This is the occasion for this interview, in which he talks about why he applied for the job, what professional development it could bring him and what new perspectives it could open up in the field he is most interested in.
- I'm working mainly in descriptive set theory, although it's still in its formative stages, because I'm very young, 29 years old, I've just finished my PhD and I'm really looking for my field. During my PhD the biggest topic, which I wrote my dissertation on, was the study of generic properties of different objects, more specifically we studied generic behaviour in spaces of different mathematical objects. This can be many things...
If you had to explain it to someone - not a mathematician - could you give a concrete example? Surely it's not the first time I've been asked to do this...
- A significant part of my dissertation was concerned with generic properties of groups and topological groups in the sense of Baire's category. I am asked from time to time how to make this tangible, to explain it, it is not easy. Essentially, we are studying a class of certain mathematical objects and we want to know what is the typical behaviour within this class. Is a property true for many or few objects of this class? Somehow we can imagine this by putting all our objects into a big hat, and if I randomly pick one of them, what will it look like? I think of a property, and if I randomly pick one, will I see that as typical or not? Of course, it's a bit misleading when I say randomly because people usually think of probability, but what we're dealing with is a different concept, topologically speaking, of magnitude-likeness. So, from a very bird's eye view, you can think of it like this: what does a randomly chosen object look like, like a group, or a graph, or a set, or a function... You can look at any kind of object really.
How long have you been working at the Rényi Institute?
- I've been at Rényi for 10 months, starting in September, and I'm basically in a two-year predoctoral position, which - now that I've done my thesis - has been transformed into a junior researcher position. So, as it happens, I went from being an assistant to a staff member.
How did the opportunity abroad come about, which is now changing your position, and indeed your life, significantly?
- I applied for jobs abroad in many places in the autumn and a year earlier. The motivation was mainly professional. I was not driven by a desire to try what it would be like to live in Los Angeles. But really, everyone says it's very rewarding professionally to go abroad for at least a few years, and of course it's financially rewarding. After all, this January I got two offers, one from UCLA and one from UC Irvine, both in California. I took the first one...
How is it done when you apply, what criteria are used to decide who gets in and how prestigious is it to be accepted?
- I don't really know what they decide on, I don't see behind the scenes. These are completely publicly advertised jobs collected on a portal, obviously it's not all the opportunities in the world, but you can actually see information about a lot of jobs here, it's called mathjobs.org. I've applied for maybe 10-15 jobs there, and two of them have just come in. So I'm going to Los Angeles to UCLA, I got an offer for three years, which is really cool. It's relatively rare nowadays to be offered a three-year position right away, typically they're more likely to offer you one or two years with a potential extension. But I was very happy about that, because now I don't have to look for a job for a long time. And my answer to the question of how much prestige value it has is that I think it's a very good place. I don't know exactly where UCLA itself ranks in the overall rankings, but when I looked it up, I remember it was 14th in the world in mathematics.
What can this job bring professionally, what is the most attractive thing about it?
- The person I will be working with, Anton Bernshteyn, is a fantastic young researcher. He's not that much older than me, maybe seven or eight years older than me, but he's working on really hot topics. What he's researching is of great interest globally...
...and is he in the same field as you?
- In a medium broad sense, yes, because he is mainly working on Borel combinatorics, which is a frontier area of descriptive set theory that I would like to research in the longer term. I don't have a paper on this narrower topic yet, but I have been thinking about moving in this direction for a few years. In Hungary, Zoltán Vidnyánszky is the main expert in this field, and he has a grant at the ELTE.
Can you tell us about what you expect the work to be like, researching, teaching, what will you be doing for these three years?
- I will definitely teach, because that is a requirement. At UCLA, it's quarters, it will be in my contract that I have to teach four quarter courses in a year. Then, exactly how much time I will have for research and what Antón and I will end up doing, I don't know. I really hope it will be a productive period. My contract is supposed to start from 1 July, but I fly in August and have to teach from the end of September.
I understand that you don't see your timetable yet, but do you have a concrete idea, as a mathematician, what you expect from these three years?
- I expect a lot. For example, my English and my lecturing skills will definitely improve a lot, teaching twelve courses completely independently in three years is no small task. And I can only really hope to come close to what Anton Bernshteyn is doing. Cutting edge or state of the art, these are the words used to describe this kind of research, and I hope to learn them. It could be published in excellent places, it's in the spotlight, and it's one of the most active areas of descriptive set theory at the moment...
... but why is there so much interest in it now, is there a demand for it from the application side?
- No, what we are doing is quite theoretical basic research, and therefore the motivation should certainly not come from the fact that there is an industrial application that directly affects our research. Rather, it means that there have been some interesting results that have linked descriptive set theory with other areas of mathematics, and along these links a more serious work has started. Areas such as dynamical systems, as well as group effects, measurable group theory - which, by the way, is something that a lot of people here at the Rényi Institute are working on, as well as random graphs - but there are also links with, for example, distributed computing. It's very exciting that the issues of Borel and measurable combinatorics seem to be closely related to certain problems and models that computer scientists have studied. Suppose you have a large network of computers, and they want to solve some problem together in such a way that one computer cannot see the whole network, but can only communicate with some neighbouring computers in the network. Or, for example, there is some kind of limit to how far you can see on this network, and you have to solve different problems with such constraints. It turns out that these so-called local problems are closely related to Borel combinatorics and descriptive set theory. These are theoretical problems, so the answer to what you asked is that the driving force here is purely scientific curiosity.