Seminari in programmazione durante l'anno accademico 2025-2026

Michele Caselli  (SNS Pisa)

Saddle-type solutions to phase-transition models

28 ottobre 2025 alle ore 11:00: in aula 1BC45

In this talk, we will provide an overview of results on entire saddle-type solutions to phase transition models, as the Allen–Cahn equation in codimension one or the Ginzburg–Landau system in codimension two, highlighting similarities and differences. Then, we will present a new result, obtained in a joint work with Nicola Picenni, regarding the existence of an entire saddle solution of the complex Ginzburg–Landau system in 3D whose zero set is a union of two orthogonal, intersecting lines.

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Eugenio Bellini  (Università di Padova)

Curvature measures and the sub-Riemannian Gauss-Bonnet Theorem

8 ottobre 2025 alle ore 12:30: in aula 1BC45

 It is not uncommon for curvature to concentrate at the singularities of geometric spaces. In this talk, we show how this phenomenon occurs for surfaces immersed in 3D contact sub-Riemannian manifolds. Adopting a measure-theoretic viewpoint on the Riemannian approximation scheme, we prove that the Gaussian curvature measure of such a surface is singular and supported on its isolated characteristic points. We identify natural geometric conditions under which this behavior occurs, namely when the surface admits characteristic points of finite order of degeneracy.

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Isabeau Birindelli  (Università di Roma Sapienza)

Fully nonlinear equations in thin domains, à la Evans

25 settembre 2025 alle ore 11:30: in aula 2AB45

We will present some recent works and works in progress with Ariela Briani and Hitoshi Ishii, where we consider the asymptotic behaviors of solutions of equations in family of domains which "lose" one dimension at the limit. Starting from new proofs for old results and obtaining new insights in particular for general oblique boundary conditions. The analysis is done through the perturbed test function approach à la Evans.

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Luca Capogna  (Smith College)

The Neumann problem in metric measure spaces and  applications to non-local p-Laplacians

18 settembre 2025 alle ore 12:30: in aula 1BC50

We review the ongoing program joint with Gibara, Korte, and Shanmugalingam, aimed at extending the Caffarelli-Silvestre approach to non-local operators from the Euclidean space to general doubling metric measure spaces. An integral component of this program is the study of the well-posedness of the Neumann problem in uniform domains in metric measure spaces that satisfy a Poincare' inequality and a doubling condition.

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