# POSTDOC SPOTLIGHT: SEVERIN SCHRAVEN

### SEVERIN SCHRAVEN

#### WHAT IS your educational background?

As a highschool student I was torn between the many possible subjects I could study. I was interested in many things and at some point I managed to reduce it to chemistry, physics, mathematics and German literature. My math teacher, Mrs. Grawehr, had encouraged me to go to the Junior Euler Society (JES), a program of the University of Zurich for children from grade 3 to grade 12 to engage in mathematics. At some point they decided that the older students could learn about knot theory. This was a great vehicle to teach somebody how to prove mathematical statements rigorously. It had the added bonus that motivation from both chemistry and physics were provided. In fact, Lord Kelvin had proposed back in the days to model atoms as vortices in the ether.

At the end of high-school, every student in Switzerland needs to complete a project and write a thesis. It's an opportunity to engage with a topic in more depth. I asked Prof. Beliakova, who organized JES together

with Prof. Kappeler, whether she could think of a suitable topic in knot theory. She told me to try to reprove Conway's fundamental theorem of rational tangles. They gave me a rough sketch of the prove and I was asked to fill in all the details. The proof requires one to pass through a couple of lengthy computations and one ends up with some complicated polynomials and need to find a specific complex number which reduces this complicated expression - the expression we are looking for. After a couple of months I finally figured out how to pick the correct number for everything to simplify. I was in a euphoric state for a couple of days and it became clear to me that I had to study mathematics.

#### What drew you to your work?

I studied mathematics with a minor in physics. Studying problems from physics in a rigorous mathematical framework was always close to my heart. When the time came to choose a topic for a master's thesis I had a hard time making up my mind. One Professor (Prof. Okonek), offered me Instantons (mathematically more in the realm of complex/algebraic geometry), and Prof. Kappeler offerred me nonlinear PDEs about th Korteweg-de Vries equation (KdV) which models shallow water waves.

It was essentially a coin toss and I went for the nonlinear PDEs. One of the key tools in the study of the KdV equation was the spectral theory of the one-dimensional SchrÃ¶dinger operator. When Prof. Kappeler retired

after I had finished my master thesis, he recommended me to ask Prof. Schlein for a PhD position. This was the natural continuation as Prof. Schlein's main focus is to study spectral properties of quantum many-body problems, which aligned with my own interests.

#### What initially drew you to UBC for your Postdoc fellowship?

Originally, I was interested in learning more about adiabatic theory. One way of picturing this is the following:

If we take a glass of water and tilt it, the water will sit parallel to the floor. On the other hand, if we put it on a tray and let a toddler run around with it, it will most likely splash. The adiabatic theorem tells us that if we are moving slowly, the water will remain close to the state it would be in if we only tilted the glass while not move at all.

Sven Bachmann, a Mathematical Physicist at UBC, is an expert in these types of questions in quantum mechanics. This is why I decided to apply to UBC.

#### Can you provide a brief overview of your doctoral research?

During my PhD I've studied the properties of the ultra-cold Bose gas together with Christian Brennecke and Benjamin Schlein. Due to the large number of particles exact computations are doomed to fail and one needs to find good approximations which capture the essential features of the system. For my postdoc I switched to studying the spectrum of SchrÃ¶dinger operators together with Richard Froese and Sven Bachmann. More precisely, I've searched for an effective way to count the number of states below a given energy (Lieb-Thirring, respectively Cwikel-Lieb-Rozenblum bounds). Similarly as for the Bose gas, it is hopeless to compute the exact result for a generic potential. However, one can construct a so-called effective potential, which encodes most of the relevant data and can be used to effectively compute approximations for any given energy. The key novelity in this work is that we were able to also obtain lower bounds on the number of eigenvalues too.

#### What are you doing now that your postdoctoral fellowship at UBC has ended?

I have just started my second postdoc at the Technical University of Munich under the guidance of Prof. Warzel. Again I'll be fighting the curse of dimensionality, however, the methods will be rather different. Namely, I'll be using some more (operator) algebraic methods to describe the ground states of certain quantum systems.

#### What was the highlight of being a postdoc at UBC?

I had a great time at UBC. This is mainly because I was surrounded by fantastic people. On a professional level, the math office staff and the IT-support have pulverized any administrative problem thrown my way in no time with a smile on their faces. More personally, I had the best office mates and an awesome extended work group. Over many lively lunches I've got educated, among many other topics, on the Gimli Glider, improvised water skiing and the Iranian New Year, topped off by the mandatory cookies at Blue Chip.

#### What is/are your long-term career goal(s)?

My goal is to keep doing research in mathematics. Thus, I aim to secure a professorship at a university.

#### Do you envision yourself returning to Vancouver?

A: While it would be great to become a professor at UBC, realistically the chances that there will be an opening in my field at the correct time are somewhat small. However, I will certainly come visit and eat a bunch of cookies at the Blue Chip Cafe.