ABOUT THE SCHOOL

The emergence of complex spatial structures is a phenomenon encountered in several fields of the life sciences, ranging from biological morphogenesis to population dynamics. This school aims to provide a comprehensive framework that connects the rigorous mathematical analysis of parabolic PDEs and systems with the most advanced techniques of Mathematical Analysis and scientific computing.

By combining theoretical lectures delivered by world-leading experts with practical sessions, the school offers a multidisciplinary perspective to model  and investigate the complexity of natural systems.

The program is structured around four fundamental pillars:

Analytical Foundations: The course introduces the concepts of Turing instability and cross-diffusion systems, analyzing the qualitative and quantitative properties of the destabilization of steady-state solutions (Prof. L. Desvillettes).

Biological Modelling: Participants will examine specific case studies such as striped patterns in tulips, deterministic chaos in chemotaxis, and "go-or-grow" models, providing a deep understanding of how natural phenomena are translated into mathematical language (Prof. T. Hillen).

Complex Geometries and Growing Domains: Part of the school is dedicated to the numerical simulation of patterns on stationary and growing domains, as well as evolving surfaces, addressing the computational challenges posed by geometric changes during biological processes (Prof. A. Madzvamuse and Prof. I. Sgura).

The school is free of charge but the registration is mandatory before the 25th of July 2026 at the Registration page.

The event is organized within the activities of thematic semester on "PDE: Models, Analysis and Numerical Analysis",
Funded by Dipartimento di Eccellenza Project CUP B83C23001390001

The workshop "From PDEs to Life & Social Sciences" is organized the week before the school (September 7-9, 2026).

ORGANIZERS

Alessandro Alla · Giulio Galise · Corrado Mascia · Luca Rossi

SPONSORS

Department of Mathematics within Excellence Departments 2023-2027