## Columbia Mathematics Department Colloquium

The Łojasiewicz exponent in

analysis, algebra, and geometry

analysis, algebra, and geometry

by

# Bernard Teissier

## Institut de Mathématiques de Jussieu

Abstract:

I will survey some of the avatars of
the concept of Lojasiewicz exponent, originally a key tool in the proof
of the possibility to divide a distribution by an analytic function. I
will discuss its rationality and its meaning in algebraic geometry. and
interpret a recent result of Moret-Bailly in arithmetical algebraic
geometry as the existence of a Lojasiewicz exponent in an
infinite-dimensional space.