[INVITED LECTURE] Asst. Prof. Vanja Wagner
Assistant Professor, Department of Mathematics, Faculty of Science, University of Zagreb
"From Diffusion to Sudden Events: Jump Processes in the Natural Sciences"
Many natural systems do not evolve only through smooth, gradual change. Instead, they display jump-like behaviour, including bursts, resets, rare transitions, punctuated transport, and clustered events. Some examples in natural sciences include genes switching on in bursts, chemical reaction networks firing one event at a time, particles making intermittent long displacements, contaminants moving through heterogeneous subsurface pathways in irregular pulses, and earthquakes triggering cascades of aftershocks. This lecture gives an accessible introduction to jump processes as a mathematical language for such phenomena, focusing on what is gained when one moves beyond purely continuous diffusion-based descriptions.
Short Bio
Vanja Wagner is an Assistant Professor at the Department of Mathematics, University of Zagreb. Her research interests are in probability theory, Lévy processes, and potential theory of Markov processes, with a particular focus on nonlocal operators and jump processes. She obtained her PhD in Mathematics from the University of Zagreb in 2016, and has also held a research position at Bielefeld University. Alongside her research, she is active in professional and educational work. She has contributed to mathematical outreach and competition activities, serves within the Croatian Mathematical Society, and has also been involved in applied and interdisciplinary projects. Her work reflects a broad interest in both the theoretical foundations of stochastic analysis and the wider role of mathematics in contemporary science.