April 2026 - Analysis-seminar - Mailing list — Dipartimento di Matematica, UniPI

seminar - Mattia Magnabosco - Tuesday, April 28, 10:00, Aula Seminari
by Alessandra Pluda 28 Apr '26

28 Apr '26

Dear all, we are pleased to announce the next appointment of the joint UNIPI-SNS Geometric Analysis Seminar. This week the speaker is Mattia Magnabosco, from University of Oxford. Tuesday, April 28, 10:00, Aula Seminari - Dipartimento di Matematica - UNIPI Title: New topological restrictions for spaces with nonnegative Ricci curvature Abstract: The topology of complete noncompact Riemannian manifolds with nonnegative Ricci curvature has been studied extensively since the earliest developments of Geometric Analysis. In dimension 3, a complete topological classification was only recently achieved by Gang Liu, with a strategy based on minimal surfaces methods. They proved that a 3-dimensional Riemannian manifold with nonnegative Ricci curvature either is homeomorphic to R^3 or the universal cover splits a line isometrically. In this talk, I present an alternative proof of Liu’s classification, which also works for nonsmooth RCD(0,3) spaces. This generalisation of Liu’s theorem yields, as a consequence, the full classification of non-collapsed RCD(0,3) spaces without boundary. Our strategy relies on two main building blocks of independent interest, which provide results that are new also in the smooth setting. In particular, we prove that, given a complete n-dimensional Riemannian manifold (M,g) with nonnegative Ricci curvature and first Betti number b_1(M) ≥ n-2, the universal cover splits R^{n-2} isometrically. Moreover, we show that every complete oriented n-dimensional Riemannian manifold with nonnegative Ricci curvature has vanishing simplicial volume. This is a joint work with Alessandro Cucinotta and Daniele Semola.

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Seminario fisica-matematica lunedì 27 aprile
by Luigi Forcella 21 Apr '26

21 Apr '26

Care tutte, cari tutti, Inoltro il seguente annuncio di un seminario di Fisica-Matematica che può essere di interesse anche per un pubblico più vasto. Lunedì 17 aprile 2026, ore 14, in Aula Seminari Matteo Gallone (Milano, La Statale) terrà un seminario<https://www.dm.unipi.it/seminario/?id=69e393af84f0900654e87dfa> dal titolo "Prethermalization and quasi-conserved quantities in Many-Body quantum systems with time-dependent Hamiltonians”. Trovate l’abstract qui sotto. A presto, Luigi ----------------------------------- Dear all, I am pleased to forward the announcement of an upcoming Math-Physics seminar that may be of interest to a broad audience. On Monday, April 27, 2 pm, in Aula Seminari Matteo Gallone (Milano, La Statale) will give a talk<https://www.dm.unipi.it/seminario/?id=69e393af84f0900654e87dfa> with title "Prethermalization and quasi-conserved quantities in Many-Body quantum systems with time-dependent Hamiltonians”. You will find the abstract below. See you soon, Luigi ----------------------------------- Speaker: Matteo Gallone (University of Milan, La Statale) Title: Prethermalization and quasi-conserved quantities in Many-Body quantum systems with time-dependent Hamiltonians Abstract: Understanding thermalization, i.e. the relaxation of a physical system to thermal equilibrium, is a central problem in statistical physics. It is now well established that the presence of non-trivial quasi-conserved quantities can significantly slow down this process, leading to long-lived quasi-stationary states known as prethermal states. The approach to such states is referred to as prethermalization. In many-body quantum systems, external driving provides a powerful mechanism to engineer and control prethermal states. In the absence of many-body localization, general theoretical arguments predict that time-dependent perturbations ultimately drive the system toward a featureless infinite-temperature Gibbs state. However, both rigorous results and experiments show that, under fast periodic driving, fermionic quantum lattice systems can exhibit exponentially long-lived prethermal regimes, largely independent of the regularity of the drive. The situation becomes even richer for quasi-periodic driving, i.e., when the system is driven by a superposition of incommensurate frequencies. In this case, the regularity of the driving plays a crucial role in determining the lifetime of the prethermal regime. In this talk, I will review the problem and survey recent rigorous results, focusing in particular on the case of finitely differentiable drivings. In this setting, the prethermal state persists for polynomially long times in the driving frequency. I will also explain how to determine the optimal exponents governing this behavior. The analysis combines techniques from Hamiltonian perturbation theory adapted to quantum lattice systems, cluster expansions, and Lieb–Robinson bounds. This is joint work with Beatrice Langella. ----------- Luigi Forcella, Associate Professor University of Pisa Department of Mathematics Largo Bruno Pontecorvo 5 57127 Pisa, Italy https://pagine.dm.unipi.it/forcella/index.html

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seminar by Davide Parise - 16 Apr, 16:30, aula Riunioni
by Alessandra Pluda 12 Apr '26

12 Apr '26

Dear all, we are pleased to announce the next appointment of the joint UNIPI-SNS Geometric Analysis Seminar. This week the speaker is Davide Parise, from Imperial College London. Thursday, April 16, 16:30, Aula Riunioni - Dipartimento di Matematica - UNIPI Title: From phase transitions to minimal submanifolds in low codimensions Abstract: Minimal submanifolds—critical points of the area functional—play a central role in geometric analysis, with deep connections to differential geometry, topology, and the calculus of variations. A major breakthrough in their existence theory came with Almgren’s min–max framework in the 1960s, which provides a powerful but technically intricate approach to constructing minimal submanifolds in great generality. In recent years, a new PDE-based perspective has emerged, inspired by models from phase transitions and superconductivity. The guiding principle is to realize minimal submanifolds as limits of nodal sets of critical points of elliptic functionals. In this talk, I will first give an overview of this variational–PDE framework. Using ongoing series of works with collaborators as examples, I will show how it can offer new conceptual insights and, in some settings, greater flexibility than classical min–max techniques. In codimension one, I will focus on the Allen–Cahn functional and explain how it can be used to construct minimal hypersurfaces with free boundary, i.e. meeting the ambient boundary orthogonally. We will then move to higher codimensions (specifically codimensions 2 and 3), where the theory is much less developed. Here, I will discuss the abelian and non-abelian Yang–Mills–Higgs functionals as natural higher codimension analogues and present recent progress in this setting. I will highlight other successes of this theory, and point to some open problems. The content of this talk is based on joint works with Martin Li, Lorenzo Sarnataro, Alessandro Pigati, and Daniel Stern.

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