“Pure logic, which surprises me again and again”

Kathrin Spendier is one of the first doctoral students to participate in the FWF doc.funds doctoral programme on “Modeling – Analysis – Optimization of discrete, continuous, and stochastic systems”. She talked to us about the fascination mathematics holds for her, and what goals she wants to achieve with her research.

The topic of Kathrin Spendier’s doctoral thesis is theoretical and not readily comprehensible to the layperson: At the centre of her work are stochastic differential equations, which are used to model time-dependent processes that are exposed to stochastic disturbance factors as well as deterministic influences. Mathematicians and statisticians use them to describe phenomena such as unstable stock prices or physical systems subject to thermal fluctuations. Specifically, the focus is on stochastic differential equations with irregular coefficients, where the drift term is discontinuous or grows superlinearly. Intensive research is currently being carried out into these on account of their high practical relevance. There is no general approach to identifying the solution; in some cases it is only possible to verify the solution by calculating the derivative. Often, no closed form of the solution can be achieved. The aim of Kathrin Spendier’s doctoral thesis is to consider and develop numerical discretization methods to approximate these stochastic differential equations and to study the convergence of the respective method. Neural networks, which are used in artificial intelligence, also constitute a new approach. In this context, it is important to keep computational time – and with it the consumption of resources – as low as possible.

In other words, Kathrin Spendier conducts basic research that forms the foundation for subsequent fields of application. We enquire about her typical working day and learn the following: “I read numerous scientific articles and I use mind maps to summarise the approaches taken and the results achieved by fellow researchers. Based on this, I then attempt to outline my problem and develop my own approach, which I then try to prove.”

Kathrin Spendier has been working on her doctoral thesis since May this year, supervised by Michaela Szölgyenyi, co-supervised by Elena Resmerita and her international mentor Andreas Neuenkirch. The bulk of her work has been performed under the constraints of the prevailing pandemic. But those who believe that a mathematican doesn`t care whether she works alone or not are mistaken: The exchange with colleagues is important in order to find new approaches to your own thoughts. A weekly meeting with her supervisor Michaela Szölgyenyi, currently held online, helps her with this, as does the structure of the FWF doc.funds doctoral programme on “Modeling – Analysis – Optimization of discrete, continuous, and stochastic systems”, which was recently launched. A total of 14 doctoral students from various mathematical disciplines are carrying out research within this programme.

Kathrin Spendier’s passion for mathematics dates back to her school days. As she tells us, her enthusiastic mathematics teacher at the BG/BRG Mössingerstraße Klagenfurt helped her to unravel the proverbial “knot” while she was still in lower school. “From that point on I suddenly found everything in mathematics to be perfectly logical. Even then, I knew that I wanted to study this subject later on. At first, I experienced a bit of a culture shock at university, because academic mathematics has new and different approaches, but then I began to enjoy the subject more and more”, Kathrin Spendier explains. For her, mathematics is “pure logic, which surprises me again and again”.

The Department of Statistics at the University of Klagenfurt is headed by the young professor Michaela Szölgyenyi, who is just 32 years old and whose career has already been distinguished by numerous major scientific successes. She is an important role model for Kathrin Spendier: “At our department, as well as at the department of mathematics, women are encouraged to believe in themselves and not be deterred by the traditionally male-dominated scientific environment. We have absolutely no disadvantages compared to men and we are given strong support.” For Kathrin Spendier, the notion of pursuing an academic career once she has completed her doctorate is definitely attractive, though she is not averse to taking other paths. The main thing, she tells us, is that she “can work on problems where the solution can be a basis for innovations developed by others.”