Noticias en español
Characterisation of the Set of Ground States of Uniformly Chaotic Finite-Range Lattice Models.
RESUMEN: The study of statistical physics models allows mathematics to offer another perspective on empirically observable phenomena. A point of interest is in particular the behavior of these models when the temperature tends towards 0, analogous to the emergence of complex crystal structures in materials. A way to model that is to consider tiling defined by local rules where some matching rules can be broken proportionally to a parameter which is the inverse of the temperature. This correspond to the Gibbs measure of the system and we are interested to the stability of these measures when...
Read MoreMinimum expansion factors of orientation-reversing pseudo-Anosov maps.
RESUMEN: Pseudo-Anosov maps are prevalent among mapping classes of surfaces. Given a pA map, the expansion factor measures the complexity of its dynamics. It is a classical result that the set of expansion factors (viewed as a subset of the set of real numbers) among all pA maps defined on a fixed surface has a minimum element. This minimum expansion factor can be thought of as the systole of the moduli space for the Teichmüller metric. Its value is not known for the genus larger than three.
Read MoreUna versión abstracta de la desigualdad de Gronwall.
RESUMEN: ¿Es posible considerar el lema de Gronwall como un principio del máximo? En esta charla elemental presentaremos una versión abstracta del lema, en términos de la cota espectral de un operador definido en un látice de Banach. Como consecuencia, deduciremos versiones generalizadas del lema, así como aplicaciones a sistemas discretos y resultados de unicidad para problemas semilineales.
Read MoreDominios de Baker hiperbólicos y formalismo termodinámico.
RESUMEN: Aplicamos técnicas de formalismo termodinámico a una familia de funciones enteras que tiene dominios de Baker de tipo hiperbólico probando la existencia de medidas conformes y obteniendo una fórmula de tipo Bowen para la dimensión de Hausdorff de un subconjunto “dinámicamente bueno” del conjunto de Julia. (Este es un trabajo conjunto con I. Inoquio).
Read MoreMultiple ergodic averages along polynomials for systems of commuting transformations.
RESUMEN: The last 50 years have seen tremendous activity at the interface between ergodic theory, combinatorics and number theory that started with Furstenberg’s dynamical proof of the Szemerédi theorem from the 1970s. The goal of this line of research has been to prove new multiple recurrence results and then deduce combinatorial corollaries. To achieve this, one wants to understand the limiting behaviour of relevant multiple ergodic averages. Of particular interest are averages of commuting transformations with polynomial iterates: they play a central role in the polynomial Szemerédi...
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