Noticias en español
Global Existence and Long Time Behavior in the 1+1 dimensional Principal Chiral Model with Applications to Solitons.
Abstract: We consider the 1+1 dimensional vector valued Principal Chiral Field model (PCF) obtained as a simplification of the Vacuum Einstein Field equations under the Belinski-Zakharov symmetry. PCF is an integrable model, but a rigorous description of its evolution is far from complete. Here we provide the existence of local solutions in a suitable chosen energy space, as well as small global smooth solutions under a certain non degeneracy condition. We also construct virial functionals which provide a clear description of decay of smooth global solutions inside the light cone. Finally,...
Read MoreContinuity for maximal operators at the derivative level.
Abstract: Maximal operators are central objects in harmonic analysis. The oscillatory behavior of such objects has been an important topic of study over the last decades. However, even in the dimension one there are interesting questions that remain open. In this talk we will discuss recent developments and open questions about this topic, particularly about the boundedness and continuity for such operators at the derivative level.
Read MoreThe fibering method applied to the level sets of a family of functionals.
Abstract: Given an one-parameter family of C1-functionals, Φμ : X →R, defined on an uniformly convex Banach space X, we describe a method that permit us find critical points of Φμ at some energy level c ∈ R. In fact, we show the existence of a sequence μ(n,c), n ∈N, such that Φμ(n,c) has a critical level at c ∈ R, for all n ∈ N. Moreover, we show some good properties of the curves μ(n,c), with respect to c (for example, they are Lipschitz), and as a consequence of this analysis, we recover many know results on the literature concerning bifurcations of elliptic partial differential...
Read MoreMaximal function estimates and local well-posedness for the generalized Zakharov–Kuznetsov equation.
Abstract: In this talk we will discuss recent results regarding local well-posedness for the generalized Zakharov–Kuznetsov equation. We prove a high-dimensional version of the Strichartz estimates for the unitary group associated with the free Zakharov-Kuznetsov equation. As a by-product, we deduce maximal estimates which allow us to prove local well-posedness for the generalized Zakharov-Kuznetsov equation in the whole subcritical case whenever d\ge 4, k\ge 4 complementing the recent results of Kinoshita and Herr-Kinoshita. Finally, we use some of those maximal estimates in order to...
Read MoreAharonov–Casher theorem on manifolds with boundary and APS boundary condition.
Abstract: The Aharonov–Casher (AC) theorem is a result from 1979 on the number of the so-called zero modes of a system described by the magnetic Pauli operator in $\R^2$. In this talk I will address the same problem for the Dirac operator when $\R^2$ is exchanged by a certain two dimensional manifold with a boundary. More concretely I consider a plane, disc and sphere with a finite number of circular holes cut out. The magnetic field consists of two contributions; a smooth compactly supported field on the manifold, and Aharonov—Bohm solenoids generating magnetic field inside the holes....
Read MorePerturbations of interpolations formulas.
Abstract: In this talk we will discuss some problems related to the theory of Fourier interpolation. The goal is to talk about the general problem of how to obtain new interpolation formulas from a previously known one by some perturbation argument, and also mentions some recent developments in joint work with João Pedro Ramos (ETH Zürich). This talk is meant for a broad audience with basic knowledge in analysis.
Read More