Noticias en español
Regla de las fases de Gibbs para potenciales Hölder en la familia de Manneville-Pomeau.
RESUMEN: En esta charla daremos una clasificación de los potenciales Hölder para las dinámicas en la familia de Manneville-Pomeau. Esta clasificación depende de la propiedades termodinámicas de los potenciales. Mostraremos que cuando existen potenciales con transiciones de fase hay dos fases en el espacio de potenciales, cada fase es un abierto conexo, y la unión de estas dos fases es densa. También mostraremos que estas dos fases tienen una frontera común y que esta frontera es homeomorfa a un subespacio de codimensión 1.
Read MoreAlgebraic intersections in translation surface.
RESUMEN: The purpose of this talk is to discuss the maximal possible (algebraic) intersection of closed curves of a given length on translation surfaces. One way to quantify this is to define the so-called “interaction strength” of the surface. The (moduli) space of translation surfaces comes with a natural SL(2,ℝ)-action and we are interested in understanding the behaviour of the interaction stength under this action. After having introduced translation surfaces and the SL(2,ℝ)-action, we will give a few geometric ideas and focus on the case of the Golden L for which we can...
Read MoreFamilias test para comprobar la promediabilidad de grupos residualmente finitos.
RESUMEN: Un clásico resultado establece que un grupo numerable G es promediable (amenable), si y sólo si toda acción continua de G sobre un espacio métrico compacto admite medidas de probabilidad invariantes. Motivados por esta caracterización de promediabilidad, Giordano y de la Harpe mostraron que para testear promediabilidad de un grupo G, basta con estudiar las acciones continuas de G sobre el Cantor. En otras palabras, probaron que las acciones continuas sobre el Cantor son una familia test para la promediabilidad de un grupo numerable. Una aplicación directa del resultado de Giordano...
Read MoreCharacterisation 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.
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