Nonlinearity, Complexity and Foundations in Mathematics - 12 settembre 2024

Nonlinear phenomena in partial differential equations have long fascinated the mathematical community. On one hand, it is possible to address them mathematically using topological and critical point techniques that allow a strong geometric intuition when dealing with these problems. On the other hand, they are linked to complex physical phenomena, and they occasionally exhibit surprising behaviors which require a rethinking of the mathematical approach from the very foundations. This conference aims to bring together experts in these topics, including not only analysts who work on the more classical aspects of solution studies, but also physicists, mathematical physicists, engineers, and computer scientists who are engaged with the applications of these problems, and logicians and philosophers of science who attempt to rethink the foundations of the theory to obtain a mathematics which is better suited for the study of complex systems.

Angela Pistoia, On the generic properties of critical points of functions 00:00
Angelo Di Garbo, Dynamical behaviour of a polynomial two dimensional nonlinear oscillator 40:04
Marco Forti, A Euclidean comparison of the sizes of sets 1:17:14
Matteo Tanzi, Selfconsistent Transfer Operators: Existence and stability of fixed points in presence of strong coupling 2:00:53
Philip Ehrlich, Integration on the Surreals 2:43:05
Monica Clapp, Limiting profiles for a Schrödinger equation with a shrinking region of attraction 3:14:25
Isabella Ianni, New solutions for the lane-emden problem in planar domains 3:52:48
Stefano Ruffo, Burgers equation and the Fermi-Pasta-Ulam-Tsingou lattice 4:28:57

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