Dia: Dimecres 3 de setembre de 2025
Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Kathrin Padberg-Gehle, Leuphana Universitaet Lueneburg
Títol: From trajectories to transport: network-based approaches for coherent sets and scalar mixing in turbulent flows
Resum: Understanding, quantifying and controlling transport and mixing processes are central in the study of fluid flows. Many different Lagrangian approaches have been proposed for detecting organizing flow structures, including recent data-based methods that aim to identify such coherent objects directly from simulated or measured tracer trajectories. Among these approaches are Lagrangian flow networks, where trajectories serve as network nodes and the links are weighted according to spatio-temporal distances between trajectories. Spectral clustering as well as simple network measures such as node degrees or clustering coefficients can be used to identify flow regions of different dynamical behavior. In this talk, we propose some extensions to the network-based framework that allow us
Dia: Dimecres 10 de setembre de 2025
Lloc: Aula T2 (segon pis), Facultat de Matemàtiques i Informàtica, UB.
A càrrec de: Dongchen Li, Imperial College
Títol: Symplectic blenders near whiskered tori and persistence of saddle-center homoclinics
Resum: A blender is a hyperbolic basic set such that the projection of its stable/unstable set onto some central subspace has a non-empty interior and thus has a higher topological dimension than the set itself. We show that, for any symplectic Cr-diffeomorphism (where r is sufficiently large and finite, or r=∞,ω) of a 2N-dimensional (N>1) symplectic manifold, symplectic blenders can be obtained by an arbitrarily small symplectic perturbation near any one-dimensional whiskered KAM-torus that has a homoclinic orbit. Using this result, we prove that non-transverse homoclinic intersections between invariant manifolds of a saddle-center periodic point (i.e., it has exactly one pair of complex multipliers on the unit circle) are persistent in the following sense: the original map is in the Cr closure of a C1 open set in the space of symplectic Cr diffeomorphisms, where maps having such saddle-center homoclinic intersections are dense. These results also hold for Hamiltonian flows in the corresponding settings.
Dia: Dimecres 17 de setembre de 2025
Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Przemysław Berk, Nikolaus Copernicus University in Toruń
Títol: Disjointness of rescalings of surface flows.
Resum: We consider certain classes of flows on compact surfaces such as locally Hamiltonian or translation flows, and we are investigating the relation of these flows with their rescalings, that is, their linear accelerations. I will show that in certain well parametrized classes of such flows, a typical one is disjoint (spectrally or in the sense of Furstenberg) with its rescalings (rational or real, depending on the class), i.e. it is non-isomorphic to an extreme degree. This talk is based on an article with Adam Kanigowski and an ongoing project with Corinna Ulcigrai.
Dia: Dimecres 1 d'octubre de 2025
Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Robert Cardona, Universitat de Barcelona
Títol: Beyond helicity: dynamical invariants of 3D volume-preserving flows and a conjecture of Arnold and Khesin
Resum: Volume-preserving flows on 3-manifolds arise naturally in fluid dynamics and plasma physics, where the vorticity or magnetic field is transported by the motion of the fluid. A central role is played by the helicity, a classical invariant introduced by Woltjer and Moffatt that measures the average linking of flow lines. Helicity is the best-known “coadjoint invariant” of a volume-preserving flow, which implies that it is preserved under the natural symmetries of the fluid equations, and it enjoys important uniqueness properties among such invariants. In this talk, which is meant to be accessible, I will first explain and motivate the relevant notions, and then focus on the question of how far the uniqueness of helicity really goes. In particular, I will show that the Ruelle invariant is, in a precise sense, everywhere independent of helicity in the 𝒞 ¹-topology. This gives a strong negative answer to the 𝒞 ¹-case of a conjecture of Arnold and Khesin.
This is joint work with Julian Chaidez (University of Southern California) and Francisco Torres de Lizaur (Universidad de Sevilla).
Dia: Dimecres 15 d'octubre de 2025
Lloc: Aula S04, Facultat de Matemàtiques i Estadística, UPC. Pau Gargallo,14 BCN.
A càrrec de: Otto Vaughn Osterman, University of Maryland
Títol: Length Spectrum Rigidity in Dispersing Billiard Systems
Resum: The problem of spectral rigidity in dispersing billiard systems is that of determining whether the perimeters of periodic orbits uniquely determine the billiard table up to isometry. We consider this problem for the class of dispersing billiard systems consisting of three convex scatterers in the plane satisfying the non-eclipse condition. We show that the perimeters of a particular set of periodic orbits for two such systems are identical if and only if their collision maps are locally analytically conjugated to each other near a particular homoclinic orbit.
Last updated: Mon Oct 20 17:42:11 2025