Seminars

Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in english. If not, they will be marked as Spanish Only.

 

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.

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...

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?...

Un modelo de enseñanza efectivo para fortalecer el pensamiento matemático en el nivel de transición utilizando juegos: evidencia preliminar.

Event Date: Dec 14, 2021 in Education, Seminars

RESUMEN Esta charla presenta avances del proyecto FONDEF ID19I10030 que busca crear un conjunto de herramientas educacionales para la evaluación y desarrollo de habilidades matemáticas tempranas en el nivel de transición de la educación parvularia. El marco teórico del proyecto sugiere que es posible crear juegos de tablero de manera que su diseño y dinámicas permitan la representación y manipulación de los dominios matemáticos objetivo (p.ej., patrones, series y números). Esta charla esboza teorías de analogías, teorías de razonamiento...

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,...

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...

Aharonov–Casher theorem on manifolds with boundary and APS boundary condition.

Event Date: Dec 02, 2021 in Differential Equations, Seminars

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...

Rough walks in random environments.

Event Date: Dec 01, 2021 in Seminario de Probabilidades de Chile, Seminars

Resumen:   We shall discuss functional CLTs for additive functionals of Markov processes and regenerative processes lifted to the rough path space. The limiting rough path has two levels of which the first one is a Brownian motion with a well-known covariance matrix. However, in the second level we see a new feature: it is the iterated integral of the same Brownian motion perturbed by a deterministic linear function called the area anomaly and characterized in terms of the model. With that one obtains sharper information on the limiting path....

Rigidez dinámica de conjuntos de Julia geométricamente rígidos.

Event Date: Nov 29, 2021 in Dynamical Systems, Seminars

ABSTRACT: Voy a hablar de un trabajo conjunto con Hongming Nie (Stony Brook University). En el contexto de dinámica sobre cuerpos no-arquimedianos, voy a discutir nuestra caracterización de los polinomios “mansos” que están en la clausura del locus del shift (polinomios cuya dinámica es conjugada a un “full shift”). Dicha caracterización es consecuencia de un resultado de “rigidez dinámica”, el que a su vez es consecuencia de un notable resultado de análisis rígido acerca de conjuntos analíticamente...