agrega datos de conferencias, modificaciones de estilo a header y titulo de index page
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nombre: Mónica Clapp
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afiliacion: UNAM
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web: https://www.matem.unam.mx/fsd/mclapp
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- titulo: TBA
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abstract: ''
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- titulo: Herramientas de geometría algebraica en biología de sistemas
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abstract: Motivaré e introduciré algunos métodos y conceptos de la geometría algebraica que se están utilizando en los últimos años para analizar modelos estándar en biología molecular. La teoría algebraica de los sistemas de reacciones químicas tiene como objetivo comprender su comportamiento dinámico aprovechando la estructura algebraica inherente en las ecuaciones cinéticas, y no necesita la determinación de los parámetros a priori, que puede ser teórica o prácticamente imposible. También señalaré algunos de los desafíos matemáticos que surgen de esta aplicación.
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pdf: ''
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speaker:
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nombre: Alicia Dickenstein
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- categoria: Semiplenarias
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charlas:
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- titulo: Eigenfunction concentration via geodesic beams
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abstract: ''
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abstract: A vast array of physical phenomena, ranging from the propagation of waves to the location of quantum particles, is dictated by the behavior of Laplace eigenfunctions. Because of this, it is crucial to understand how various measures of eigenfunction concentration respond to the background dynamics of the geodesic flow. In collaboration with J. Galkowski, we developed a framework to approach this problem that hinges on decomposing eigenfunctions into geodesic beams. In this talk, I will present these techniques and explain how to use them to obtain quantitative improvements on the standard estimates for the eigenfunction's pointwise behavior, Lp norms, and Weyl Laws. One consequence of this method is a quantitatively improved Weyl Law for the eigenvalue counting function on all product manifolds.
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pdf: ''
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speaker:
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nombre: Yaiza Canzani
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afiliacion: Universidad de Chile
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web: http://www.uchile.cl/portafolio-academico/impresion.jsf?username=friedman
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- titulo: Estimates for spherical averages
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abstract: ''
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abstract: |
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The family of classical spherical means \(A = \{A_t\}_t>0\) is given by:
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$$A_t f(x) = \int_{S^{d−1}}f(x-ty)d\sigma(y)$$
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where \(d\sigma\) denotes the normalized surface measure on the unit sphere \(S^{d-1}\). E. M. Stein [1] (\(d\geq 3\)) and J. Bourgain [2] (\(d=2\)) proved that the spherical maximal function \(Sf(x):=\sup_{t>0}|A_{t}f(x)|\) defines a bounded operator on \(L^{p}(\mathbb{R}^{d})\) if and only if \(p>d/(d-1)\). Thus, for \(p\) in this range, we have \(\lim_{t\rightarrow 0}A_{t}f(x)=f(x)\) a.e. for all \(f\in L^{p}(\mathbb{R}^{d})\).
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We consider the variation operator, for all \(1\leq r<\infty\), defined by,
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$$V_{r}A:=\sup_{N\in \mathbb{N}}\sup_{t_{1}<\ldots<t_{N}, t_{j}\in (0,\infty)} \bigg(\sum_{j=1}^{N-1}|A_{t_{j+1}}f(x)-A_{t_{j}}f(x)|^{r}\bigg)^{1/r}$$
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Variation norms have received considerable attention in analysis as they are used to strengthen pointwise convergence results for families of operators. Variation norm inequalities have important consequences in ergodic theory and harmonic analysis. R. L. Jones, A. Seeger, and J. Wright proved [3] that \(V_{r}A\) is bounded in \(L^{p}(\mathbb{R}^{d})\) for all \(r>2\) if \(d/(d-1)<p\leq 2d\). The endpoint result \(r=p/d\) was left open.
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We show an endpoint result for \(V_{p/d}A\) in three and higher dimensions, and \(L^{p}\rightarrow L^{q}\) estimates for local and global \(r\)-variation operators associated to the family of spherical means. These can be understood as a strengthening of \(L^{p}\)-improving estimates for the spherical maximal function. The results imply associated sparse domination and consequent weighted inequalities.
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Joint work with David Beltran, Richard Oberlin, Andres Seeger, and Betsy Stovall.
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===
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[1] E. M. Stein, Maximal functions. I. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), 2176–2177.
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[2] J. Bourgain, Averages in the plane over convex curves and maximal operators, J. Analyse Math. 47 (1986), 69–85.
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[3] R. L. Jones, A. Seeger, and J. Wright, Strong variational and jump inequalities in harmonic analysis, Trans. Amer. Math. Soc. 360 (2008), 6711–6742.
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pdf: ''
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speaker:
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nombre: Luz Roncal
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@ -107,9 +107,10 @@ hr.separador{
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}
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.logo-container{margin-top:70px;}
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h2.subtitle{
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margin-top:180px;
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margin-top: 15px;
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margin-bottom:180px;
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text-shadow: #333 2px 2px 1px;
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color:white;
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font-weight: normal;
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{% extends "layout.html" %}
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{% block content %}
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<h1 id="welcome" style="font-size:170%;margin-bottom: 45px;"><strong>¡Bienvenidos al VI Congreso Latinoamericano de Matemáticos!</strong></h1>
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<h1 id="welcome" style="font-weight:bold;margin-bottom: 45px;"><strong>¡Bienvenidos al CLAM VI!</strong></h1>
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<p>
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El Congreso Latinoamericano de Matemáticos (CLAM) busca contribuir al desarrollo de la investigación matemática en América Latina y el Caribe, estimular su visibilidad y fomentar el intercambio entre profesionales de la región y de otras partes del mundo. Los congresos CLAM se realizan cada cuatro años y acogen a los premios UMALCA que reconocen a los más destacados jóvenes matemáticos de la región.
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</p>
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