Making Connections, Physically and Theoretically, with PIMS PDF Reinier Kramer
by Robyn Humphreys, Communications and Event Assistant
Reinier Kramer describes himself as a bit of an algebraic geometer and a bit of a mathematical physicist. He likes employing tools from different parts of mathematics and theoretical physics.
Having an interest in both maths and physics made doing a double degree at the University of Amsterdam an ideal bachelor program for him. Very soon Reinier discovered that maths at university was far more fun than the high school material he’d learned, so his focus shifted to maths over physics.
Reinier continued at the University of Amsterdam and began a two-year masters in mathematical physics. But after his first year, his zest for the mathematical sciences took him to the University of Cambridge where he decided to do a one-year masters in math. The flexibility of the program at Cambridge allowed him to take more courses that interested him. Reinier then returned to Amsterdam to work on his thesis.
Since moving to Edmonton at the end of September, Reinier has quickly got to work, “on my very first day, Vincent Bouchard, my PDF supervisor, and a master student of his, Quinten Weller, told me about an extension of topological recursion to essential singularities to understand some limit procedure. These essential singularities are a common occurrence for Hurwitz-type problems, but usually, we can ignore them. The particular case they studied sounded familiar to me, and I suggested it could explain the difference between completed cycles and Atlantes Hurwitz numbers. We checked a few things, and this seems to be true. We still have to prove it, though.”
Tell us about the connections you’ve made through your mathematical journey and the knowledge you’ve gained working with them?
I got to know Sergey Shadrin when he supervised my master’s thesis. When I started looking for a Ph.D. position, Sergey asked me to do one with him, on relations between moduli spaces of curves, integrable hierarchies, and Hurwitz numbers. These were subjects I didn’t know much about, but I liked Sergey as a supervisor, so I accepted. Most of my first year consisted of getting to understand all of these new subjects, which was quite hard. Luckily, Sergey is very approachable, and he had two more experienced Ph.D. students at the time, so I could ask many questions.
My knowledge of these subjects increased in my second year and I started producing results in many collaborative compositions. Most of my work during my Ph.D. was on working towards topological recursion for different kinds of Hurwitz numbers. I also investigated other related topics, such as classifying deformations of bi-Hamiltonian pencils of hydrodynamic type — giving rise to systems of PDEs which Hurwitz numbers may satisfy.
While working on my Ph.D., I also did a side project on the transfer of quantum states. A friend of mine working on such problems came up to me at a party asking if I knew about the solution to some mathematical issue he encountered. I didn’t really, but together with his sister, who is also a mathematician, we figured it out using a process called STIRAP. STIRAP can be described via weighted graphs and had only been found for odd chains or odd grids. We generalized it to semi-bipartite graphs.
I enjoy being part of the topological recursion research community and got to know it well through research collaborations with Sergey and conferences I attended. I met Gaëtan Borot when he visited Amsterdam a few times, and we wrote a paper together, so it was natural to do a postdoc with him at the Max Planck Institute for Mathematics (MPIM) in Bonn after my Ph.D. I continued to work on Hurwitz problems, but also investigated the theory of topological recursion itself, including a more algebraic perspective. Unfortunately, the pandemic affected my work in Bonn as Gaëtan moved to Berlin halfway through my postdoc, and while I had opportunities to work with new people, I did not have quite as many interactions as I had hoped.
Through several conferences, I got to know Vincent Bouchard, my current supervisor in Edmonton. Vincent also works on topological recursion and has worked on Hurwitz numbers, the original conjecture linking Hurwitz numbers and topological recursion is partially due to him. We certainly have common mathematical interests, and we had talked a few times, both about maths and non-maths. When I started looking for a new postdoc I contacted Vincent, and he told me about the possibility of applying for a PIMS PDF— which is where you can find me now.
You were in Bonn, Germany, at the onset of the Pandemic? How did you adapt to working from home during the lockdown?
The first lockdown for me was in March 2020. The first month was really hard and then I went to stay with my mother for about three months. When I returned to Bonn, I mostly worked from home. I was allowed to come to MPIM but was discouraged.
I adapted to working from home well and established a routine. I worked from 10 am–5 pm typically but if I was feeling productive, I would work till 7:30 pm. Weather permitting, I would have lunch on the fire escape stairs of my apartment. One thing I learned from working at home is that it is best to just stop working for the day if you feel you are not doing anything productive anymore.
During the lockdown, I missed the informal research discussions my colleagues and I would have over coffee or lunch. I was not teaching at the time, the MPIM is not affiliated with a university, and all our seminars moved online, which is less fun and less productive. Nevertheless, I organized an online reading group for fellow postdocs and Ph.D. students, which was at least a way to keep structure in the week. I would have a chance to talk with the speaker before their presentation, and most participants gave at least one talk. As a result, I knew the audience and we had a lot of questions during presentations. Interaction with the audience can be hard during online lectures, but we somewhat circumvented this.
How do you spend your time outside of work? What do you do to balance your research and life?
I try not to think about research after dinner or on weekends. Instead, I enjoy various activities such as swimming, cycling, bouldering, and yoga. These vary a bit as I have not set up a routine in Edmonton yet.
I also really like skiing, but never lived close to mountains until now. Before I always had to go on holiday to the Alps, while now I can go to the Rockies for a weekend. I look forward to that.
Furthermore, I read quite a lot in my free time. Mostly literature, but also philosophy. I have a book club with a group of Dutch friends, which is currently online due to the pandemic, so I can still participate.
And I spend time with friends, eating and drinking, playing board games and video games.
Publications
You can find Reinier’s papers on MathSciNet and Zentralblatt MATH.
Reinier Kramer studied physics and mathematics at the Universities of Amsterdam and Cambridge. In 2019, he obtained a PhD at the University of Amsterdam with Sergey Shadrin, and from 2019 to 2021 he held a postdoctoral fellowship at the Max Planck Institute of Mathematics in Bonn, in the group of Gaëtan Borot. Currently, he is a postdoctoral fellow with Vincent Bouchard at the University of Alberta. He works in the areas of mathematical physics and algebraic geometry, and is mainly interested in using topological recursion to calculate intersection-theoretic and enumerative-geometric objects, with a focus on Hurwitz numbers.
Reinier will be speaking at the PIMS Emergent Research Seminar Series, on November 24, 2021, at 9:30 AM Pacific. Details on his talk, Hurwitz Numbers via Topological Recursion, can be found here.
