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.
Diversidad en la enseñanza de la matemática para los niños y niñas: dificultades de aprendizaje, superdotación y recursos TIC
Resumen Es muy común en matemática, asociar el alto rendimiento de los niños con superdotación, y el rendimiento más bajo en matemática con dificultades de aprendizaje. En este amplio espectro, surgen diversos aspectos y dudas, que repercuten en la forma en que se identifican, se trabajan y se asisten a estos niños y niñas. En la actualidad, existen líneas de investigación cuyo desarrollo ha permitido notables avances en ambas direcciones. Una de las herramientas que ha permitido grandes avances en el caso de las dificultades de...
Convexity and Duality in the Economics of Financial Equilibrium
Abstract In classical models of economic equilibrium with markets of goods, agents maximize quasi-concave utility subject to budget constraints based on the value of their initial holdings. When financial markets are added, there are serious complications because of uncertainties over future states which the model must reflect. In that context, the existence of prices that bring supply and demand into balance is far from assured, and current theory is unsatisfying. However, strong results about the existence of equilibrium have...
Non-topological condensates for the self-dual Chern-Simons-Higgs model
Abstract For the abelian self-dual Chern-Simons-Higgs model I will discuss existence issues of periodic vortex configurations — the so-called condensates– of non-topological type for small values of the Chern-Simons parameter k. We provide a positive answer for the existence of non-topological condensates with magnetic field concentrated at some of the vortex points (as a sum of Dirac measures) as k tends to 0. Joint work with M. del Pino, M. Musso and P. Figueroa.
EPI-SPLINES AND EXPONENTIAL EPI-SPLINES: PLIABLE APPROXIMATION TOOLS
Abstract: Approximation theory for functions was, at the outset, mostly concerned with finding best approximating functions that can be (totally) described by a finite number of parameters. This question took another dimension when the information about the function was limited, say its value at some points, but also included some knowledge of its global properties, typically smoothness level, which should be replicated in the approximating one. This gave rise to the theory of splines and its manifold implementations. But in an evolving range...
A stochastic model for speculative bubbles
Abstract: “One commonly says that the creation of speculative bubbles is the consequence of two phenomenons: the self-reinforcing effect of the investors and the tendency of these investors to follow the forecasting rule which consists in deciding that the price will increase if it has (strongly) increased in the past. Following these two rules, we build a model for speculative bubbles which is a Gaussian two-dimensional “turning” diffusion. Then, the main objective of the work is to obtain some sharp bounds for the...
Newton’s method for solving inclusions using set-valued approximations
Abstract Results on stability of both local and global metric regularity under set-valued perturbations are presented. As an application, we study (super-)linear convergence of the Newton-type iterative process for solving generalized equations. The possibility to choose set-valued approximations allows us to describe several iterative schemes in a unified way (such as inexact Newton method, non-smooth Newton method for semi-smooth functions, inexact proximal point algorithm, etc.). Moreover, it also covers a forward-backward...
Teaching algorithm, what for? Some new questions for mathematics and issues for proof learning.
Simon Modeste will present some aspects and results of his PhD work, defended in Institut Fourier, Grenoble, France. He will concentrate on the most important elements and give illustrations of the results. Here is the abstract of the thesis: Recently, the notion of algorithm has gained in importance in secondary school curricula, in France and abroad. Algorithm is strongly linked with computer science, mathematics and proof and its teaching raises many didactical questions. In this thesis, we propose an epistemological analysis of the...
Convergence of descent methods in non-smooth non-convex optimization
Résumé: Following recent advances, we present a large class of descent methods which converges strongly to a critical point of a non-smooth non-convex function, under the condition that it has a ‘good’ behavior around its critical points. More exactly we consider proper lower semi-continuous functions satisfying the so-called Kurdyka-Lojasiewicz inequality. It is satisfied in finite dimensions by tame functions (like semi-algebraic or bounded sub-analytic functions), while in infinite dimensions we know some useful examples in PDE, for...
Positive and sign changing solutions to a nonlinear Choquard equation
Abstract: (adjunto)
Las dificultades de aprender fracciones: cerebro, mente y aula.
El aprendizaje de fracciones constituye la primera gran extensión del concepto de número que se realiza en el sistema escolar. Tal cambio es un enorme desafío educacional, que lamentablemente en muchos casos no es exitoso: estudiantes y adultos de todas las edades cometen errores que sugieren que fracciones como a/b son tratadas como la yuxtaposición de los números enteros a y b, y no como la razón entre éstos. Por ejemplo, razonando que 2/5 es menor que 2/7 puesto que 5 es menor que 7. En esta charla, haremos una revisión de la literatura en...
