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.
Thermodynamics of small systems through a reversible and conservative discrete automaton.
Abstract: The focus of this talk will be the Q2R model which is a reversible and conservative cellular automaton. The Q2R model possesses quite a rich and complex dynamics. Indeed, the configuration space is composed of a huge number of cycles with exponentially long periods, that we attempt to characterize. Furthermore, a coarse-graining approach is applied to the time series of the total magnetization, leading to a master equation that governs the macroscopic irreversible dynamics of the Q2R automata. The methodology is replicated for...
A new probabilistic interpretation of Keller-Segel model for chemotaxis, application to 1-d.
Resumen: The Keller Segel (KS) model for chemotaxis is a two-dimensional system of parabolic or elliptic PDEs. Motivated by the study of the fully parabolic model using probabilistic methods, we give rise to a non-linear SDE of McKean-Vlasov type with a highly non standard and singular interaction kernel. In this talk I will briefly introduce the KS model, point out some of the PDE analysis results related to the model and then, in detail, analyze our probabilistic interpretation in the case d=1. This is a joint work with Denis Talay...
Oportunidades de aprendizaje de matemáticas que se proporcionan a estudiantes con discapacidad intelectual: primeros resultados.
Resumen: En Chile los estudiantes con discapacidad intelectual (DI) asisten a escuelas especiales o a escuelas regulares con Programas de Integración Escolar. Aun cuando se cuenta con datos referidos a su acceso al sistema educativo, poco se conoce respecto a las oportunidades de aprendizaje (ODA) que se proporcionan a estos estudiantes, menos aún en matemáticas. Usando la metodología de estudio de casos múltiple se ha avanzado en una primera descripción de las ODA que se proveen en matemáticas a estudiantes con DI en escuelas especiales. Se...
INTRODUCTION TO FORMAL VERIFICATION
ABSTRACT: Software is pervasive. In particular, a lot of programs are nowadays produced to be executed in safety critical contexts. It is crucial to certify these programs. There are several methods of certification. By far the most used is testing. But testing can be costly, and more importantly, it only covers a finite number of cases. Formal verification is a vastly different approach: it aims at building a mathematical proof that the program meets its specification, thus covering all possible cases. To increase the level of...
Development and Evaluation of an Internet-Based Tutorial Module (i-TModule) For Statistics Learning Among Postgraduate Students
Abstract: Because students’ ability to use statistics, which is mathematical in nature, is one of the concerns of instructors embedding within an e-learning system the pedagogical characteristics of learning is ‘value added’. It could facilitate the traditional method of learning mathematics which is usually a teacher-centered. Nowadays, many different types of online learning platform and Learning Management Systems, LMSs, (such as Moodle) are used in the teaching and learning process especially in universities, but there is a lack of...
TOPOLOGICAL DYNAMICS OF PIECEWISE Λ-AFFINE MAPS OF THE INTERVAL
ABSTRACT: Let 0 < a < 1, 0 ≤ b < 1 and I = [0,1). We call contracted rotation the interval map φa,b : x ∈ I → ax+b mod1. Once a is fixed, we are interested in the dynamics of the one-parameter family φa,b, where b runs on the interval interval [0, 1). Any contracted rotation has a rotation number ρa,b which describes the asymptotic behavior of φa,b. In the first part of the talk, we analyze the numerical relation between the parameters a, b and ρa,b and discuss some applications of the map φa,b. Next, we introduce a generalization of...
Quantitative multiple recurrence for two and three transformations.
Abstract: In this talk I will provide some counter examples for quantitative multiple recurrence problems for systems with more than one transformation. For instance, I will show that there exists an ergodic system $(X,\mathcal{X},\mu,T_1,T_2)$ with two commuting transformations such that for every $\ell < 4$ there exists $A\in \mathcal{X}$ such that \[ \mu(A\cap T_1^n A\cap T_2^n A) < \mu(A)^{\ell} \] for every $n \in \mathbb{N}$. The construction of such a system is based on the study of “big” subsets of...
Recurrences for generating polynomials
Abstract: In this talk we consider sequences of polynomials that satisfy differential–difference recurrences. Our interest is motivated by the fact that polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete mathematics. It is, therefore, of interest to understand the properties of such polynomials and their probabilistic consequences. We will be primarily interested in the limiting distribution of the corresponding random variables....
Stability of Hamiltonian systems which are close to integrable : introduction to KAM and Nekhoroshev theory
Abstract: We give a panorama of classical theories of stability of Hamiltonian systems close to integrable which are of two kind : – Stability in measure over infinite time (KAM theory). – Effective stability over finite but very long time (Nekhoroshev theory)
Limit distributions related to the Euler discretization error of Brownian motion about random times
Resumen: In this talk we study the simulation of barrier-hitting events and extreme events of one-dimensional Brownian motion. We call “barrier-hitting event” an event where the Brownian motion hits for the first time a deterministic “barrier” function; and call “extreme event” an event where the Brownian motion attains a minimum on a given compact time interval or unbounded closed time interval. To sample these events we consider the Euler discretization approach of Brownian motion; that is, simulate the...
