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Interview with David Rydh

Published Dec 21, 2021

David Rydh, born and raised in Sweden, has been a member of KTH for almost 22 years. He first came to KTH to study Engineering Physics and, even prior to finishing his Master’s degree at KTH, he started his PhD studies under the supervision of Dan Laksov. After completing his doctoral education, David Rydh had a one-and-a-half-year postdoc at MSRI (Mathematical Sciences Research Institute) and UC Berkeley, before returning to KTH as an assistant professor. Today he is a full professor at KTH. During the fall semester, he has been dividing his time between KTH and the Mittag-Leffler Institute, where he has been an organizer of the three-month program Moduli and algebraic cycles.

David Rydh

We met David to talk about his time at KTH as well as his recent election as a member of the Royal Swedish Academy of Sciences.

You have been at KTH for several years both as a student and as a faculty member. How has KTH changed during your time here?

One big change with a mostly positive effect on the students and the teachers is digitalization. Back when I was a student, the internet had not yet had a big impact on the studies except for the possibility to obtain text books slightly cheaper. Registration for courses was done on paper, as were all our assignments, and of course there was far less course material available. That is the biggest difference when it comes to the teaching environment.

Access to information is the greatest change regarding research as well. As books and journal articles are offered online, one is able to access them anywhere. Of course, there is some part of the old environment that I miss; going to the library, digging up journals and books and having this nice feeling of sitting in the library to explore them. For me, access to more information has led to research being quicker but less thorough.

Another big change is internationalization, especially when it comes to PhD students and, more recently, faculty members.

What changes would you expect to make KTH more competitive at an international level?

I think that KTH needs to continue becoming more international in order to succeed more in research. Moreover, striving for excellence is also key to KTH’s international success.

Could you tell us more about your research area? What kind of problems do you enjoy working on?

I work in algebraic geometry. We study objects as basic as polynomial equations. However, there is a lot of structure involved and machinery used, often coming from category theory. There are also interactions with several other areas; number theory, algebraic topology, complex analysis, combinatorics, string theory are some of them.

My own research is focused on something called moduli theory, a subject that has been developed in the past 70 years. The idea is to organise various geometric objects, such as curves or surfaces, as points in a space. Such spaces are called moduli spaces and come with natural geometric structures. By studying the geometry of the moduli space, we gain new insight on the objects we classify. These objects often come with symmetries. To reflect this, the moduli space needs to be a so-called stack. One of my key results is a precise local description of such moduli stacks when the symmetry groups are infinite.

The area of algebraic geometry is perceived to be less popular among Swedish Universities compared to other parts of the world. What do you think is the reason for that and how do you expect the algebraic geometry community to develop in the coming years?

There is a very simple explanation for that. Swedish mathematicians used to work mainly in analysis and related subjects such as partial differential equations and dynamical systems. Subjects like algebraic geometry, algebraic topology and number theory were rarely studied.

Algebra started taking footholds in Stockholm, and also in Sweden, in the 1970s after Jan-Erik Roos came to Stockholm University and my supervisor, Dan Laksov, came to KTH. The latter had origins from Norway, which has had a long-time strength in algebra and algebraic geometry.

Thankfully, the algebraic geometry community in Stockholm has grown a lot in the last 20 years, both at KTH and SU, and we expect it to continue doing so.

You are one of the relatively few members of KTH that has been elected as a member of the Royal Swedish Academy of Sciences in the Class of Mathematics. Did you expect to be a candidate? How do you feel about your election?

To be honest, that came as a big surprise. I didn’t expect to be elected, especially after having received the Göran Gustafsson prize in the spring. There are several well-respected colleagues that could qualify for the election.

I look forward to working in the Royal Academy very much, and engage in tasks such as selecting award and prize recipients, which I expect to be fun as a process. It also provides a nice opportunity to meet other mathematicians working on different subjects across Sweden.

What are your current plans regarding the Göran Gustafsson prize that you received in the spring?

I am very excited that the Göran Gustafsson prize is going to start in January. In the following months, I am planning to recruit a PhD student and a postdoc to start in the fall. In some aspects, I think that I'm at a turning point of my career and about to explore many new directions.

Text: Danai Deligeorgaki