Seminars

Operator algebras, compact operators, and the essential spectrum of the N-body problems

Event Date: Jul 23, 2018 in CAPDE, Seminars

Abstract:  I will begin by reviewing a general method to determine the essential spectrum of Schrodinger-type operators. The method is based first on the fact that an operator is Fredholm if, and only if, it is inversible modulo the compacts (Atkinson’s theorem). This reduces the study of certain quotients by the compact operators. To study the invertibility in these quotients, one uses, following Georgescu, Mantoiu, and others, a determination of the spectrum of a suitable operator algebra and of the action of the translation group on its spectrum.   I will give an example of how...

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Sensitive dependence of geometric Gibbs measures at positive temperature

Event Date: Jul 23, 2018 in Dynamical Systems, Seminars

ABSTRACT:   In this talk we give the main ideas of the construction of  the first example of a smooth family of real and complex maps having sensitive dependence of geometric Gibbs states at positive temperature. This family consists of quadratic-like maps that are non-uniformly hyperbolic in a strong sense. We show that for a dense set of maps in the family the geometric Gibbs states diverge at positive temperature. These are the first examples of divergence at positive temperature in statistical mechanics or the thermodynamic formalism, and answers a question of van Enter and Ruszel....

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Uso de Datos satelitales y drones para seguimiento de volúmenes de cosecha

Event Date: Jul 23, 2018 in Ciclo de Seminarios quincenales de la Alianza Copernicus-Chile, Seminars

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The singular Yamabe problem and a fully nonlinear generalization & Vortex desingularization for the 2D Euler equations

Event Date: Jul 17, 2018 in CAPDE, Seminars

(16:00 hrs.) Title: The singular Yamabe problem and a fully nonlinear generalization  Abstract: I will begin with an overview of the work of Loewner-Nirenberg on constructing complete conformal metrics of constant negative scalar curvature on domains in Euclidean space, and its extension to Riemannian manifolds with boundary.  I will then describe some fully nonlinear generalizations.  Finally, I will discuss a certain geometric invariant of solutions, called the renormalized volume, and some recent work with Robin Graham on computing closed formulas for these invariants in dimension four....

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Morse theory for the action functional and a Poincare-Birkhoff theorem for flows

Event Date: Jul 09, 2018 in Dynamical Systems, Seminars

ABSTRACT: The goal of this talk is twofold. Firstly I would like to explain how pseudo-holomorphic curves can be used to study Morse theory of the action functional from classical mechanics. Then I will move to applications, focusing on a generalization of the Poincare-Birkhoff theorem for Reeb flows on the three-sphere.  

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Analogies between the geodesic flow on a negatively curved manifold and countable Markov shifts

Event Date: Jul 09, 2018 in Dynamical Systems, Seminars

ABSTRACT: By the work of Bowen and Ratner it is known that the geodesic flow on a compact negatively curved manifold can be modeled as a suspension flow over a subshift of finite type. Unfortunately, a symbolic representation is not available if the manifold is non-compact. In this talk I will briefly explain some recent developments on the study of the thermodynamic formalism of the geodesic flow on non-compact negatively curved manifolds. Surprisingly some of the methods used to understand the geodesic flow have consequences to the theory of countable Markov shifts. I will explain such...

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