Nonlinear diffusion and related PDEs in (non) Euclidean settings (26w5543)

The Banff International Research Station will host the "Nonlinear diffusion and related PDEs in (non) Euclidean settings" workshop in Banff from August 30 to September 4, 2026.

The analysis of nonlinear diffusion PDEs is a wide field of research that not only encompasses elliptic and parabolic equations, but also includes several functional-analytic tools that proved successful in the deep understanding of such equations: just to mention a few, we recall Hardy, Poincaré and Sobolev inequalities. The corresponding rigorous theory, at least in the Euclidean setting, has reached extremely high levels, both in the local and the nonlocal case, with many sharp results available by now. The general interest for such equations is motivated by the fact that they are of paramount importance in the description and modeling of a number of real-world phenomena (e.g., the flow of gases through a porous medium, water infiltration, heat dispersion, population dynamics, etc...).

In more recent years, various lines of research have moved to the Riemannian framework (roughly speaking: from flat to curved environments), as can be seen by the increasing number of scientific papers, whereas the theory in the graph setting seems to be still in its infancy. Because graphs are ubiquitous in many applied fields ranging from Physics and Engineering to Biology, Image and Signal Processing, an advance of the research in the continuous and discrete field would represent a significant breakthrough, not only on the pure mathematical level. This task calls for collaborations of internationally recognized experts working in all the above mentioned areas, as well as training the next generation of scientists. The proposed workshop aims at facilitating this process by putting in touch researchers, at different career stages, working on nonlinear equations and related functional-analytic tools on manifolds or graphs.