### Monday March 4, 2001

**Speaker**: Laurent Berger

**Title**: Approximation by polynomials with integral coefficients

**Abstract**: If K is a compact subset of the real numbers R, then a theorem of
Weierstrass says that every continuous function f : K -> R is a uniform
limit of polynomials. But which functions are limits of polynomials with
integral coefficients? For example, if 0 is in K, then f(0) must be an
integer. We will see that the general answer depends on arithmetical and
geometric properties of K.