This workshop is focused on the mathematical theory of PDE models arising from biology and social sciences, featuring a gradient flow structure or, more generally, formulated via an entropy minimization principle. The main scientific goal is reviewing latest advances on the collective behavior that such systems produce in their dynamics, such as finite time concentration, asymptotic formation of singular aggregates, stability of stationary patterns. Three main aspects seem to attract most of the interest of the community in the last years: the interplay between the continuum formulation of the model under study and its discrete counterpart (e. g. agent based), the formulation of models "with many species", and the interaction between gradient flows and their corresponding second order formulation.
A classical example are reaction-diffusion systems with many species, in which a fully coupled entropy structure yields systems with cross-interaction terms. Such systems arise for instance from population dynamics, chemistry, and neuroscience. They feature a formal gradient flow structure, but their mathematical theory is an extremely challenging topic. Another typical example arises in the continuum modeling of swarming, as well as in other models in biology and sociology with a "nonlocal interacting agents" based dynamics. The use of singular interaction potential, the stability of concentrated patterns, and the coupling with nonlinear diffusion are some of the topics currently under study in the literature.
Lecturers of the Mini Courses
- José Antonio Carrillo, Imperial College, UK
- Ansgar Juengel, Technische Universität Wien, Austria
- Theodore Kolokolnikov, Dalhousie University Halifax, Canada
- Alethea Barbaro - Case Western Reserve University, USA
- Li Chen - University of Mannheim, Germany
- Young-Pil Choi, Imperial College, London, UK
- Klemens Fellner - University of Graz, Austria
- Razvan Fetecau - Simon Fraser University, Canada
- Matthias Liero - WIAS Berlin, Germany
- Stephan Martin - RWTH Aachen University, Germany
- Johannes Zimmer - University of Bath, UK
- Marco Di Francesco, University of L’Aquila
- Pierangelo Marcati, GGSI and University of L’Aquila
Speakers will be accommodated at Hotel San Michele www.stmichelehotel.it; young funded participants will be accommodated at Hotel Castello www.hotelcastelloaq.com. Other participants willing to attend the workshop can find a list of hotels here.
Download the Slides of the lectures: