Responsable : Leonid Vainerman
Résumé : The Continuum Problem is in general asking us to determine the place of the cardinality of the real line R in the hierarchy of cardinal numbers \aleph_\alpha. In particular, it asks us whether this cardinality takes its minimal possible value \aleph_1. Ever since its appearence on Hilbert's 1900 list of mathematical problems for the twentieth century the problem has generated a great interest and important research contribution especially in the field of Set Theory. In fact Set Theory is a field of mathematics that greatly profited from this research. We shall review this research but will concentrate on analyzing modern views on this important problem of Georg Cantor.
Résumé : Dynamical systems, both discrete and continuous, permeate vast areas of mathematics, physics, engineering, and computer science. In this talk, we consider a selection of natural decision problems for linear dynamical systems, such as reachability of a given hyperplane. Such questions have applications in a wide array of scientific areas, ranging from theoretical biology and software verification to quantum computing and statistical physics. Perhaps surprisingly, the study of decision problems for linear dynamical systems involves techniques from a variety of mathematical fields, including analytic and algebraic number theory, Diophantine geometry, and real algebraic geometry. I will survey some of the known results as well as recent advances and open problems.
Ce document a été mis à jour le 25 janvier 2017.