# Seminars

## Development and Evaluation of an Internet-Based Tutorial Module (i-TModule) For Statistics Learning Among Postgraduate Students

Event Date: Apr 26, 2017 in Education, Seminars

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 innovation to adopt effective instructional approaches...

## Quantitative multiple recurrence for two and three transformations.

Event Date: Apr 10, 2017 in Dynamical Systems, Seminars

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 $\mathbb{N}^2$ and $\mathbb{N}^3$  satisfying...

## Limit distributions related to the Euler discretization error of Brownian motion about random times

Event Date: Mar 28, 2017 in Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars

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 Brownian motion on a discrete and equidistant times...

## Stability of Hamiltonian systems which are close to integrable : introduction to KAM and Nekhoroshev theory

Event Date: Mar 29, 2017 in Optimization and Equilibrium, Seminars

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)

## TOPOLOGICAL DYNAMICS OF PIECEWISE Λ-AFFINE MAPS OF THE INTERVAL

Event Date: Apr 17, 2017 in Dynamical Systems, Seminars

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 contracted rotations. Let −1 < λ < 1 and f...