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.
Piecewise contraction maps and its applications
Abstract: Our talk concerns dynamical systems which are defined by piecewise contraction maps (PC maps). There is a large literature which deals with the dynamical behavior of PC maps defined on convex subsets of Euclidean spaces in different contexts. Our aim is to show that, under certain conditions, a typical PC map, in the measure theoretical sense of the parameter space, is asymptotically periodic which means that the map has finitely many periodic orbits and every orbit converges to a periodic orbit. Our setup is the following:...
Introducción al aprendizaje de máquinas y redes neuronales
Abstract: El objetivo de esta charla es presentar la disciplina de aprendizaje de máquinas (AM) y su una de sus herramientas fundamentales: redes neuronales. En la primera mitad de la charla veremos los orígenes del AM, su relación con otras disciplinas, su impacto en problemas actuales y campos de aplicación. Posteriormente, veremos una introducción a redes neuronales artificiales, donde comenzando por una motivación biológica presentaremos la estructura de una red, la importancia del número y configuración de sus neuronas, y...
Low distortion embeddings of metric graphs and linear properties of Banach spaces
Abstract: We will survey examples of metric graphs whose low distortion embeddability into a Banach space X implies various linear properties for X such as non-reflexivity, containement of $\ell_1$ or large Szlenk index. In some cases the implications can be reversed (up to a renorming).
Limit theorems for products of non-negative and tropical random matrices
Abstract: Tropical matrices are matrices with entries in $(\R\cup\{-\infty\}, \max,+)$, where $\max$ is seen as the “addition”. They appear as the limit of nonnegative matrices and in models from computer science/operations research, as they are strongly linked to weighted directed graphs. Their dynamical behavior is quite similar to nonnegative matrices, with a kind of Perron-Frobenius theorem but the limits are often reached, which allows some combinatorial studies. In this talk, I will present a common framework, known as...
Lipschitz-free spaces
Abstract: Let M be a pointed metric space and Lip0 (M ) the space of Lipschitz functions vanishing at 0. Endowed with the Lipschitz norm this space is a Banach space. Denote F(M ) the closed subspace of Lip(M )* spanned by the evaluation points and call it the Lipschitz-free space over M. After an introduction explaining how one can use these spaces in the context of non linear classification of Banach spaces, we will more particularly be interested in dual Lipschitz-free spaces and shortly explain there link with optimal...
Recent advances on the acceleration of first-order methods in convex optimization
Abstract: Let f : H → R ∪ {+∞} be a proper lower-semicontinuous convex function defined on a Hilbert space H (think of RN), and let (xk) be a sequence in H generated by means of a “typical” first-order method, and intended to minimize f. If argmin(f) ̸= ∅, then (xk) will converge weakly, as k → +∞, to a minimizer of f, with a worst-case theoretical convergence rate of f(xk) − min(f) = O(1/k). In the 1980’s Y. Nesterov came up with a revolutionary – yet remarkably simple! – idea to modify the computation of the iterates with...
ESTADÍSTICA TEMPRANA: EL CASO DE KINDER
Resumen: El currículo escolar chileno, coincidente con la tendencia internacional, ha introducido la Estadística y la Probabilidad a partir de los primeros años de escolaridad, lo que ha provocado desafíos en su enseñanza. El análisis exploratorio de datos (AED) y el ciclo investigativo PPDAC (problema, plan, datos, análisis y conclusiones al problema) como estrategias de enseñanza, permiten que los niños tengan experiencias de aprendizaje con datos y desarrollen el sentido numérico y el sentido del dato. El propósito de esta exposición es...
Incremental Proximal and Augmented Lagrangian Methods for Convex Optimization: A Survey
Abstract: Incremental methods deal effectively with an optimization problem of great importance in machine learning, signal processing, and large-scale and distributed optimization: the minimization of the sum of a large number of convex functions. We survey these methods and we propose incremental aggregated and nonaggregated versions of the proximal algorithm. Under cost function differentiability and strong convexity assumptions, we show linear convergence for a sufficiently small constant stepsize. This result also applies to distributed...
“Recovering a function from a subdifferential”
Abstract: The issue of recovering a function from its derivative or one of its directional derivatives is a central issue that dates back to the seminal work of Lebesgue (1904). The question of recovering a function from its subdifferential is more recent and has been the subject of intensive research in recent years, since the seminal work of Moreau and Rockafellar (1970) on convex functions, up to the many successive works of Thibault and his co-authors on increasingly broad classes of functions beyond the convex functions....
