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.
Dynamics of strongly interacting 2-solitons for dispersive equations
Abstract: The theory of linear dispersive equations predicts that waves should spread out and disperse over time. However, it is a remarkable phenomenon, observed both in theory and practice, that once there are nonlinear effects, many nonlinear dispersive equations (for example: NLS, gKdV, coupled NLS,…) admit special “compact” solutions, called solitary wave or solitons, whose shape does not change in time. A multi-soliton is a solution which is close to a superposition of several solitons. The problem we address is...
Sistemas Dinámicos de Santiago Dynamical Day
Primera Sesión: 14:30 hrs. Speaker: Mike Todd (University of St Andrews, United Kingdom). Title: Phase transitions and limit laws. Abstract: The `statistics’ of a dynamical system is the collection of statistical limit laws it satisfies. This starts with Birkhoff’s Ergodic Theorem, which is about averages of some observable along orbits: this is a pointwise result, for typical points for a given invariant measure. Then we can look for forms of Central Limit Theorem, Large Deviations and so on: these are about how...
Desvíos rotacionales para mapas del toro y aplicaciones.
ABSTRACT: El número de rotación de Poincaré es sin duda alguna el invariante más importante en el estudio dinámico de homeomorfismos del círculo (que preservan orientación). En general, estos sistemas exhiben lo que llamamos “desvíos rotacionales uniformemente acotados”, es decir, cualquier órbita de un homeomorfismo de este tipo siempre se mantiene a distancia uniformemente acotada de la órbita de la rotación rígida correspondiente. Esta importante propiedad tiene implicaciones profundas en dinámica unidimensional. En...
On breather solutions of some hierarchies of nonlinear dispersive equations
Abstract: In this talk I will briefly introduce hierarchies of some nonlinear dispersive equations, namely KdV, mKdV and Gardner hierarchies. We will see that some of these hierarchies have soliton and breather solutions, suited to the level of the hierarchy. I will show that these soliton and breather solutions satisfy the same nonlinear ODE characterizing them for any member of the hierarchy and I will present a stability result for breather solution of some higher order mKdV equations.
Maintaining Perfect Matchings
Abstract: We investigate the minimum-cost perfect matching problem in metric spaces with two stages. In the first stage, an algorithm is confronted with a set of points from a metric space and ought to find a perfect matching among them. Subsequently, an adversary can announce new points after which the algorithm has to give a perfect matching on the extended set. However, for every arrived point, the algorithm can only do a constant number of reallocations with respect to the old matching. We call an algorithm for this problem (two-stage)...
Process-Based Measurement Toward Understanding Learning with Applications
Resumen: Process data arise from measuring a construct over time to better understand how a learner achieves some outcome (i.e., explain or predict outcome performance). It is useful for instructional or assessment purposes. For example, it may be used to adapt and individualize instruction. It may provide feedback to the learner or the instructor. It may also diagnose strengths and weakness in learning. We first motivate the analysis of process data with a project in the area of simulation training of medical professionals. We then...
Scaling limits for a slowed random walk driven by symmetric exclusion
Abstract: Consider a simple symmetric exclusion process in one dimension, and a random walk on the same space. When on top of particles, the walker has a drift to the left, when on top of holes it has a drift to the right. Under weakly asymmetric scaling, we prove a law of large numbers and a functional central limit theorem for the position of this random walk. The proof uses techniques from the field of hydrodynamic limits to study the fluctuations of the number of particles of the in large boxes around the walker.
Semiclassical Trace Formula and Spectral Shift Function for Schrödinger Operators with Matrix-Valued Potentials.
Abstract: In this talk, I will present some recent results on the spectral properties of semiclassical systems of pseudodifferential operators. We developed a stationary approach for the study of the Spectral Shift Function for a pair of self-adjoint Schrödinger operators with matrix-valued potentials. A Weyl-type semiclassical asymptotics with sharp remainder estimate for the SSF is obtained, and under the existence condition of a scalar escape function, a full asymptotic expansion for its derivatives is proved. This last result is a...
