Seminars

On the 3D Ginzburg-Landau model of superconductivity

Event Date: Apr 02, 2018 in CAPDE, Seminars

Abstract: The Ginzburg-Landau model is a phenomenological description of superconductivity. A crucial feature is the occurrence of vortices (similar to those in fluid mechanics, but quantized), which appear above a certain value of the applied magnetic field called the first critical field. We are interested in the regime of small ɛ, where ɛ>0 is the inverse of the Ginzburg-Landau parameter. In this regime, the vortices are at main order codimension 2 topological singularities.  In this talk I will present a quantitative 3D vortex approximation construction for the Ginzburg-Landau...

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Existence of solutions to a pure critical elliptic system in a bounded domain

Event Date: Apr 02, 2018 in CAPDE, Seminars

Abstract:   http://capde.cl/past-seminars/  

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A maximal nondegenerate sign-changing solution for the Yamabe problem

Event Date: Apr 16, 2018 in CAPDE, Seminars

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Gagliardo-Nirenberg-Sobolev inequalities in domains

Event Date: Apr 16, 2018 in CAPDE, Seminars

Abstract:  Our objective is to estimate constants for a type of Gagliardo-Nirenberg-Sobolev inequalities in domains in euclidean space. We obtain a rough bound valid for bounded convex domains in dimension 3 and higher. When the domain is a cube, we obtain an improved bound in any dimension. In one dimension, the sharp constant is simply related to the sharp constant of the inequality on the real line and I will comment on the open question whether this holds true in higher dimensions.

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Linear inviscid damping and enhanced viscous dissipation of shear flows by the conjugate operator method

Event Date: May 28, 2018 in CAPDE, Seminars

Abstract: We will show how we can use the classical Mourre commutator method to study the asymptotic behavior of the linearized incompressible Euler and Navier-Stokes at small viscosity equations  about shear flows. We will focus on the case of the mixing layer. Joint work with E Grenier, T. Nguyen and A. Soffer

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Intertwinings and Stein’s factors for birth-death processes

Event Date: May 28, 2018 in CAPDE, Seminars

Abstract: In this talk, I will present intertwinings between Markov processes and gradients, which are functional relations relative to the space-derivative of a Markov semigroup. I will recall the first-order relation , in the continuous case for diffusions and in the discrete case for birth-death processes, and introduce a new second-order relation for a discrete Laplacian. As the main application, new quantitative bounds on the Stein factors of discrete distributions are provided. Stein’s factors are a key component of Stein’s method, a collection of techniques to bound the distance...

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