Noticias en español
Seminars appear in decreasing order in relation to date. To find an activity of your interest just go down on the list. Normally seminars are given in English. If not, they will be marked as Spanish Only.
Boson stars and their linear stability.
Abstract: Boson stars composed of massive scalar fields are among the most promising exotic objects that may populate the universe. Even though they remain hypothetical they are frequently considered as candidates for black hole mimickers, massive compact objects, or even the core of the galactic halos in the context of dark matter. In this talk I will focus on static, spherically symmetric boson stars and first explain how they arise as solutions of a nonlinear eigenvalue problem which is obtained from the Einstein-Klein-Gordon system. This...
Non-Euclidean Differentially Private Stochastic Convex Optimization.
Abstract: Differentially private (DP) stochastic convex optimization (SCO) is a fundamental problem, where the goal is to approximately minimize the population risk with respect to a convex loss function, given a dataset of i.i.d. samples from a distribution, while satisfying differential privacy with respect to the dataset. Most of the existing works in the literature of private convex optimization focus on the Euclidean (i.e., $\ell_2$) setting, where the loss is assumed to be Lipschitz (and possibly smooth) w.r.t.~the $\ell_2$ norm over a...
El eje de Datos y Azar: un desafío pendiente en la Formación Inicial Docente después de más de una década en el currículo escolar chileno.
RESUMEN En Chile, el cambio curricular realizado en la década del noventa trajo consigo grandes desafíos a las instituciones formadoras y a los profesores en activo del sistema escolar en la asignatura de matemática. Con la introducción del eje de Datos y Azar el año 2009, se espera formar estudiantes con las habilidades de leer, comprender, tomar decisiones y ser críticos con la gran cantidad de información con la cual interactuamos diariamente. Además, se aspira que los profesores durante la formación inicial adquieran una...
Universality of the outliers in weakly confined Coulomb gases in dimension.
Resumen: In the talk, we will study two particle systems with a strong conection to statistical physics: on one hand a class of Coulomb gases (model which describes the positions of electrons in dimension 2, attracted by a positive distribution of charges), and on the other hand zeros of random polynomials. For both models, it is known that most particules cluster in a compact set (the empirical measures converge), and we will study the existence of particles outside of this compact. We will see that these outliers converge towards a...
The Dispersion Time of Random Walks on Finite Graphs.
Abstract: Consider two random processes on an n vertex graph related to Internal Diffusion-Limited Aggregation (IDLA). In each process n particles perform independent random walks from a fixed vertex until they reach an unvisited vertex, at which point they settle. In the first process only one particle moves until settling and then the next starts, in the second process all particles are released together. We study the dispersion time which is the time taken for the longest walk to settle. We present a new coupling which allows us to compare...
Dbar-approachability, entropy density and B-free shifts.
ABSTRACT: Let dbar denote the pseudometric on the full shift over a finite alphabet A given by the upper asymptotic density of the set of positions at which two A-valued sequences differ. Write H-dbar for the associated Hausdorff pseudometric for subsets of the full shift. We study which properties of shift spaces (shifts) are closed with respect to H-dbar. In particular, we study shifts, which are H-dbar limits of their Markov approximations. We call these shifts dbar-approachable. We provide a topological characterisation of chain mixing...
Oriented trees via chromatic number.
Resumen: It is folklore that every graph G contains every tree T whose order is at most \chi(G), the chromatic number of G. This is no longer necessarily true if G and T are oriented. In 1980, Burr conjectured that an arbitrary orientation of a graph G contains every oriented tree of order 1 + \chi(G)/2. We will present related questions and recent advances relating to this conjecture.
Rigidity and bifurcation of low energy solutions to semilinear PDEs in symmetric domains.
Abstract: Motivated by recent developments on the connections between the Allen-Cahn equation – which is ubiquitous in certain models of phase transitions and separation phenomena – and minimal hypersurfaces, we will discuss variational and geometric properties of low energy solutions to certain PDEs in the sphere and other symmetric domains. Furthermore, we will describe a geometric bifurcation result for solutions of the Allen-Cahn equation in the 3-sphere and point out some relations with the variational theory of minimal...
