Describing developments in mathematical terms

Verena Schwarz came to Klagenfurt to join the FWF doc.funds doctoral programme on “Modeling – Analysis – Optimization of discrete, continuous, and stochastic systems”. We spoke with her about the origins of her passion for mathematics.

The mathematician Verena Schwarz came to Klagenfurt at the worst possible time. Shortly after she arrived in Klagenfurt in September, having come from southern Germany, a far-reaching curfew was declared. Verena Schwarz came here to participate in the doc.funds Doctoral School “Modeling – Analysis – Optimization of discrete, continuous, and stochastic systems” and is now one of 14 doctoral students from the fields of mathematics and statistics who are conducting research in Klagenfurt as part of the FWF-funded project.

Her particular research interest revolves around stochastic differential equations, which can be used to model temporal processes that are manipulated by various influencing variables. Real-life examples include share prices or energy prices. “These models become very complicated fairly quickly, to the point where you can’t calculate them explicitly,” she tells us during our interview. Verena Schwarz examines theoretical approximation methods and investigates how quickly they produce a sufficiently good approximation to achieve the best possible result.

Verena Schwarz has enjoyed mathematics since her school days. Even as a student at secondary school, she excelled at recognising mathematical structures. Soon, she also started to pass on her knowledge by tutoring others. “I always sought to get my students excited about the beauty of mathematics,” she remembers. Eventually, she decided to study Mathematics and Management in Ulm; a decision she does not regret to this day: “I am really happy with this choice.” She found out about the position in Klagenfurt through the call for applications.

She takes great pleasure in working in an academic environment: “I like working in a team and dealing with unsolved problems and the new questions they raise.”

A few words with … Verena Schwarz

What would you be doing now, if you hadn’t become a scientist?

When I first started my degree, I had plans to work in consulting, but then I became so fascinated by mathematics that this idea was shelved.

Do your parents understand what it is you are working on?

Not really, but they always give it their best shot.

What’s the first thing you do when you get to the office in the morning?

First I greet my colleagues, then I check my calendar and draw up a rough plan for the day.

Do you have proper holidays? Without thinking about your work?

I try, but often the ideas for solutions come to me precisely when I’m not thinking about my unresolved questions, and of course I have to note them down even while I’m on holiday.

What makes you furious?

To be honest, sloppy mathematical formulations. I cannot let these stand, I always correct them.

And what calms you down?

A relaxing evening on the sofa with a good novel.

Who do you regard as the greatest scientist in history, and why?

Norbert Wiener. He was the first to mathematically model the so-called Wiener Process, named after him, which plays an important role in my research.

What are you afraid of?

In terms of my doctorate, I worry about experiencing a moment when I realise that the work I’ve been doing for the last few weeks has been a waste of time because of a problem in the last stage of the proof that can’t be fixed. It’ s bound to happen at some point in the next few years, so I might as well prepare myself for it now.

What are you looking forward to?

I am looking forward to the time after Corona. Then I will have the chance to really get to know the city of Klagenfurt and the university.