Noticias en español
Braiding groups of homeomorphisms of the Cantor set.
Abstract: In this talk we will discuss some recent work on groups which connect self-similar and Higman-Thompson groups to big mapping class groups via “braiding”. We will explain some results on the topological finiteness properties of the resulting groups, which are topological generalizations of the algebraic properties of being finitely generated and finitely presented. The talk will involve recent joint works with Xiaolei Wu (Fudan) and Matthew Zaremsky (Albany).
Read MoreMean equicontinuity – beyond minimality.
Abstract:: In this talk we present recent developments and new results in the study of mean equicontinuity and weak mean equicontinuity in the context of countable discrete amenable groups, such as a characterization in terms of spectral theory. It is known that the notions of mean eq. and weak mean eq. do not depend on the process of averaging (the Følner sequence), whenever the action is minimal, or the acting group is Abelian. However, we present an example of a (non-minimal, but transitive) action where mean equicontinuity and weak mean equicontinuity do depend on the process of...
Read MoreGroup actions with discrete spectrum and their amorphic complexity.
Abstract: Amorphic complexity, originally introduced for integer actions, is a topological invariant which measures the complexity of dynamical systems in the regime of zero entropy. We will introduce its definition for actions by locally compact sigma-compact amenable groups on compact metric spaces. Further, we will illustrate some of its basic properties and show why it is tailor-made to study strictly ergodic group actions with discrete spectrum and continuous eigenfunctions. This class of actions includes, in particular, Delone dynamical systems related to regular model sets obtained...
Read MoreConjugacy classes of germs near a hyperbolic fixed point in dimension 1.
RESUMEN: A famous linearization theorem of Sternberg claims that, in dimension 1, near a hyperbolic fixed point (i.e. a fixed point where the derivative differs from 1), a germ of C^r diffeomorphism is C^r conjugate to its linear part when r is greater than or equal to 2. This result fails to be true in lower regularity, even for C^1 diffeomorphisms with absolutely continuous derivative. We will explain how to construct whole continuous families of such germs with the same derivative at a common fixed point but which are not pairwise bi-Lipschitz conjugate, or which are pairwise bi-Lipschitz...
Read MoreGrupos Nilpotentes actuando en el intervalo.
RESUMEN: En esta charla vamos a estudiar las realizaciones de los grupos Nilpotentes como subgrupos del grupo de difeomorfismos del intervalo y presentar el siguiente problema: dado un grupo Nilpotente G, ¿Cuál es el parámetro óptimo r>0 para el cual G es un subgrupo del grupo de difeomorfismos de clase C^r del intervalo?, ¿Cuál es el vínculo entre r y la estructura algebraica de G? Si bien este problema está abierto en general vamos a ver respuestas parciales a estas preguntas.
Read MorePresión al infinito en shifts de Markov con alfabeto numerable.
RESUMEN: El principio variacional para la presión dice que la presión topológica es igual a el supremo de la presión de medidas invariantes. En analogía al principio variacional, definimos la presión al infinito, como el supremo de la presión de una sucesión de medidas que converge cero. En esta charla, hablaré de la presión al infinito para shifts de Markov numerables y potenciales uniformemente continuos. Discutiré algunas ideas generales y aplicaciones a la existencia de estados de equilibrio, medidas maximizantes y a resultados de gap dimensional.
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