Abstract:
In this seminar, I will discuss recent results on the static and dynamic behavior of complex systems within the framework of the calculus of variations. Such systems are typically characterized by intrinsic multiscale features arising from their microscopic structure. After briefly reviewing results on perforated domains, thin films, and phase transitions, I will present recent work on convolution-type energies with kernels having finite p-moments, with applications to periodic homogenization, functionals on point clouds, and limits of the associated gradient flows. I will then address evolutionary problems, including gradient flows with oscillatory potentials and nonlinear diffusion equations with degenerate mobility, studied in the Wasserstein framework. Throughout the talk, I will emphasize and compare the variational techniques used in both static and dynamic settings.
Biography:
Nadia Ansini is a mathematician specializing in multiscale problems in the calculus of variations. Her research focuses on the rigorous derivation of macroscopic models for complex systems through variational methods, with particular expertise in Γ-convergence and homogenization theory. She has contributed to the analysis of perforated domains, thin films, phase transitions, periodic structures, and variational evolution problems. She has held research positions at several leading European institutions, including SISSA (Trieste, Italy), Université Paris 6 (France), EPFL (Lausanne, Switzerland), and the University of Bath (UK). She was awarded two Marie Skłodowska-Curie Fellowships (2001–2003 and 2013–2015). From 2022 to 2025, she served as Lise Meitner Professor at Lund University (Sweden). Her current research focuses on gradient flows and the study of convolution-type functionals introduced in the book she co-authored https://link.springer.com/
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai
This event is open to the NYU Shanghai community and Math community.