Continuity for maximal operators at the derivative level.

Event Date: Jan 06, 2022 in Differential Equations, Seminars

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.

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Quantum Decoherence for probabilists.

Event Date: Dec 15, 2021 in Seminario de Probabilidades de Chile, Seminars

Resumen:  Quantum decoherence (QD) is today one cornerstone in the development of quantum computing (QC). This refers to the collapse of a quantum state into a classical one. From a mathematical point of view, its modelling has also been a major problem, motivating the development of new research in open systems theory. One could classify today this phenomenon at the interface between non-commutative and commutative probabilities. The general question is: how a quantum evolution becomes classical? Is this inevitable? Shall QC live with that? The talk will provide a panorama on the...

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The fibering method applied to the level sets of a family of functionals.

Event Date: Dec 16, 2021 in Differential Equations, Seminars

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 bifurca- tions of elliptic partial differential...

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Maximal function estimates and local well-posedness for the generalized Zakharov–Kuznetsov equation.

Event Date: Dec 09, 2021 in Differential Equations, Seminars

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...

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La severidad de los incendios forestales: parámetro clave en las decisiones de gestión pre y post incendio.

Event Date: Dec 13, 2021 in Ciclo de Seminarios quincenales de la Alianza Copernicus-Chile, Seminars

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Denjoy-Kocsma y la convergencia de sumas de Birkhoff para difeomorfismos del círculo.

Event Date: Dec 06, 2021 in Dynamical Systems, Seminars

ABSTRACT: Una herramienta fundamental en el estudio de los difeomorfismos del círculo es la desigualdad de Denjoy-Kocsma, explotada incansablemente por Herman en su célebre tesis. Hace una década, Avila-Kocsard probaron una versión más fina de esta que incluye la convergencia (y no solo la mayoración) de las sumas de Birkhoff para potenciales suficientemente suaves en los tiempos de recurrencia. Este resultado fue mejorado después por Navas-Triestino, llegando hasta a una clase de diferenciabilidad casi optimal. En esta charla explicaré un argumento reciente y completamente elemental que...

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