Il se tient le mardi à 16h30, une à deux fois par trimestre.

**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.