This workshop is aimed at the participants in the Junior Trimester Program "Renewal Equations, PDEs and non-equilibrium systems in biological modelling". It is not possible to apply only for this workshop.
Organizers:
- Viktoria Freingruber
- Alexandra Holzinger
- Niccolo Tassi
- Inmaculada Benitez
Speakers:
- Josephine Evans (University of Warwick)
- Sara Merino Aceituno (University of Vienna)
- Grigorios Pavliotis (Imperial College London)
- Benoît Perthame (Sorbonne Université)
- Jonathan Touboul (Brandeis University)
Description:
Biological systems are inherently multiscale: complex collective behaviours emerge from the interactions of many individual agents. Depending on the modelling framework, agents may be described solely by mechanical variables such as position and velocity, or may additionally carry internal states. Mathematical models of such systems therefore naturally span several levels of description, ranging from stochastic interacting particle models of McKean type and individual-based models to kinetic equations and macroscopic partial differential equations.
This workshop focuses on the mathematical links between these modelling scales, with emphasis on kinetic theory and stochastic scaling limits — powerful tools to connect microscopic agent dynamics to continuum PDE descriptions. Applications include but are not limited to structured population dynamics, collective animal behaviour, neuronal networks, and coagulation–fragmentation processes.
A central objective of the workshop is to bring together researchers working on analytical, numerical and stochastic perspectives. By fostering dialogue between these communities, we aim to promote a deeper understanding of the connections between probabilistic particle systems, kinetic theory, and macroscopic PDE models. In particular, we will explore both classical and recent analytical, probabilistic, and numerical methods, including scaling limits, ergodicity and hypocoercivity methods.