Noticias en español
Sphere Packings with Forbidden Distances.
Abstract: We will introduce the sphere packing problem, survey past and recent developments, the breakthrough work of Viazovska, and report on recent work of mine.
Read MoreExtensiones libres de subshifts.
RESUMEN: Dado un grupo G, un subgrupo H y un H-subshift X, la extensión libre de X a G es el G-subshift cuyas configuraciones son aquellas cuya restricción a cada clase lateral de H correponde a un elemento de X. En ésta charla les contaré sobre la motivación detrás de la definición de extensión libre, las interesantes propiedades que satisfacen y les mostraré un resultado reciente que muestra que satisfacen una fuerte propiedad de universalidad cuando G es el producto directo de H con un grupo no promediable.
Read MoreA second-order descent method with active-set prediction for group sparse optimization.
Abstract: In this talk, we propose a second-order algorithm for the solution of finite and infinite dimensional group sparse optimization problems. Group sparse optimization has gained a lot of attention in the last years due to several important classification problems requiring group sparse solutions. The most prominent application example is the group LASSO problem, which consists in minimizing a least-squares fitting term together with the group sparsity l1/l2 norm. The method is built upon the steepest descent directions of the nonsmooth problem, which are further modified by using...
Read MorePartially non-convex minimax theorem and applications to remotal sets.
Abstract: Given a convex subset B A of a locally convex space Y X; and a function f : Y X ! R such that B is compact and f (y; ); y 2 Y; are concave and upper semicontinuous, we establish in a Örst step a minimax inequality of the form maxy2B infx2A f (y; x) infx2A supy2B0 f (y; x); where B0 is the set of points y 2 B such that f (y; ) is proper and convex. The main di§erence with the classical minimax theorem is that, here, the set B0 does not need to be convex or compact. We use this result to give a new proof of the characterization of remotal sets, relying on the convexiy of the set...
Read MoreA gluing construction of singular solutions for a fully non-linear equation in conformal geometry.
Abstract: We study construction of a complete non-compact Riemannian metrics with positive constant σ2-curvature, on the sphere Sn with a prescribed singular set Λ given by a disjoint union of closed submanifolds whose dimension is positive and strictly less than n−√n−22 . This is a fully non-linear problem, nevertheless, we show that the classical gluing method of Mazzeo-Pacard for the scalar curvature still works in this setting since the linearized operator has good mapping properties in weighted spaces. A necessary condition is that 2 ≤ 2k < n.
Read MoreLa estructura de sistemas simbólicos de complejidad baja.
RESUMEN: En el contexto de dinámica simbólica, la clase de “subshifts de complejidad lineal” es de particular relevancia, ya que ocurre en una variedad de áreas, tales como sistemas dinámicos geométricos, teoría de lenguajes, teoría de números y sistemas de numeración, entre otros. Durante el intenso estudio de este tema en los noventa, fue propuesto que una descomposición jerárquica basada en secuencias S-ádicas que caracterice a los subshifts de complejidad lineal sería útil para entenderlos. El problema de encontrar tal caracterización fue llamado la “conjectura...
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