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Name: Lukas BAUMGARTNER
Current position: PhD student (University Assistant) at ASC
Starting date: October 2022
Research group: Differential Equations and Dynamical Systems
Dissertation topic: Geometric Analysis of Multi-Parameter Singular Perturbation Problems
Supervisor: Prof. Peter SZMOLYAN

Many systems in nature display multiscale behaviour: some parts evolve quickly, others change only slowly. Each of these components can often be understood on its own, but when fast and slow processes interact, entirely new and fascinating phenomena can emerge. Mathematically, such systems are described by singularly perturbed differential equations, where “singular” roughly means “exceptional” or “difficult to analyse” and the underlying difficulties often resemble “division by zero”. In my thesis, I work on extending existing methods to cases, where the geometry and time-scale structure become significantly more intricate. A key technique I use is the blow-up method, a geometric way of “zooming in” near problematic points to uncover hidden structure and clarify how different time scales interact.

Alongside my research, I greatly value being part of the Vienna School of Mathematics (VSM), opens an external URL in a new window, a joint doctoral school of the University of Vienna and TU Wien. The VSM strengthens collaboration between the two universities and connects doctoral students across mathematical fields. I believe that fostering a supportive research environment is especially important for early-career scientists, so I contribute by co-organising both scientific and social activities within the VSM, such as colloquia
and student retreats.

In my daily life at the university, I also enjoy the opportunity to teach. I believe that teachers — both within and beyond university — have a serious responsibility to support young people in their personal and professional development. Throughout my own time in school and at university, I have often experienced how much of a difference good teachers can make. I hope that I can pass on some of that positive impact as well.

I discovered my enthusiasm for the qualitative analysis of differential equations during my master’s studies at the University of Vienna, particularly through work in evolutionary game theory and population dynamics. These areas—and my current project—share the common language of dynamical systems, and I hope to combine and build on these skills in my future work.

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