A new solution to $\Delta u+u^p-u=0$ on the entire space.

Event Date: Sep 08, 2020 in Differential Equations, Seminars

Abstract: In this talk we develop some techniques to construct solutions of certain semilinear elliptic equations which are periodic in some variables, decaying in others, and quasiperiodic in one variable. These solutions, which are found near ground states of a lower-dimensional problem, are constructed using spatial dynamics and results from the KAM theory. The use of a suitable KAM-type theorem provides hypotheses for homogeneous equations which rely on simple scaling arguments, applying in particular to $\Delta u+u^p-u=0$ with $p>1$ Sobolev subcritical.

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Dimension theory for continued fractions.

Event Date: Sep 02, 2020 in Dynamical Systems, Seminars

ABSTRACT: Every real number can be written as a continued fraction. There exists a dynamical system, the Gauss map, that acts as the shift in the expansion. In this talk, I will comment on the Hausdorff dimension of two types of sets: one of them defined in terms of arithmetic averages of the digits in the expansion and the other related to (continued fraction) normal numbers. In both cases, the non compactness that steams from the fact that we use countable many partial quotients in the continued fraction plays a fundamental role. Some of the results are joint work with Thomas Jordan and...

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Generalized Newton Algorithms for Tilt-Stable Minimizers in Nonsmooth Optimization.

Event Date: Sep 02, 2020 in Optimization and Equilibrium, Seminars

Abstract: This talk aims at developing two versions of the generalized Newton method to compute local minimizers for nonsmooth problems of unconstrained and constraned optimization that satisfy an important stability property known as tilt stability. We start with unconstrained minimization of continuously differentiable cost functions having Lipschitzian gradients and suggest two second-order algorithms of the Newton type: one involving coderivatives of Lipschitzian gradient mappings, and the other based on graphical derivatives of the latter. Then we proceed with the propagation of these...

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“Monitoreo satelital y reportería automatizada de ubicación de Centros de Engorda de Salmones con SAR”.

Event Date: Aug 31, 2020 in Ciclo de Seminarios quincenales de la Alianza Copernicus-Chile, Seminars

Participación en Linea: Use Explorer, Firefox o Safari.

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Kac’s model with thermostats and rescaling.

Event Date: Sep 01, 2020 in Differential Equations, Seminars

Abstract: In this introductory talk we present Kac’s model in statistical mechanics that involves N identical particles undergoing collisions. Kac introduced this model in 1956 to derive the Kac-Boltzmann equation: a one particle equation. Kac’s approach in obtaining this equation is now known as ”propagation of chaos”. We also introduce thermostats and see their role in speeding up approach to equilibrium. Finally, we introduce a rescaling mechanism for the thermostated Kac model, and establish uniform in time propagation of chaos (with explicit rates) for this...

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Chemostats and epidemics: competition for nutrients/hosts (2013)

Event Date: Jul 29, 2020 in Seminarios Lectura Papers COVID19, Seminars

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