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Name: Lukas ANZELETTI
Current Position: Postdoc
Starting date: October 2023
Research group: Prof. Mate GERENCSER
Research area: Stochastic differential equations, regularization by noise

Why mathematics? As frustrating as the many days without any progress are, the feeling of solving a complex problem on which one has worked for hours, days, weeks, or months is simply unique. Second but not least: the collaboration and exchange on equal footing with like-minded people from all around the world; just as in sports or music, it is also beautiful in mathematics to share a passion with other people and to be able to convey it in teaching.

Area of research? As part of my postdoc, I study systems or equations that are subject to a mixture of deterministic and random influences. These are mostly motivated by physics and financial mathematics. I am particularly interested in situations in which the deterministic influences are singular or “rough” and yet, through randomness, a stable or predictable behavior emerges. A central part of my work is to find out when such systems, despite all randomness, have a unique evolution and how different kinds of random motions contribute to this. Once this is ensured, I study the numerical approximation of the unique solution. Although these equations originate from applications, I deal solely with the abstracted version of these problems, formulated as stochastic differential equations.

What's next? I think it helps to provide some context before answering the question. A former chancellor supposedly already dreamed in the sandbox of one day pulling the strings of the republic from Ballhausplatz. Well … until a visit to an education fair at the age of 16, I didn’t even know that one could study mathematics. The decision was made on the spot (for the University of Vienna; unfortunately, I overlooked the TU Wien booth, mea culpa!). During the first two years of my studies, a career in research was never on my radar. In hindsight, my bachelor’s thesis was the initial spark, in which I could study fine properties of Brownian motion in detail. Then, by chance, I stumbled across an advertisement of a PhD thesis in Paris on stochastic differential equations and I stuck with them after finishing the thesis. By the way: among my friends, it’s a running gag that I of all people now do research on differential equations; in my first course on differential equations, my performance was anything but outstanding…

As one can probably tell, the path into research was largely “flying blind”, and so far the approach worked out quite well. That’s why I try (sometimes with limited success) not to stress too much about what the future will bring. As long as I enjoy it, I want to stay in research and/or teaching, and at the moment I still enjoy it a lot.