Marcin Bilski

Title: Higher order approximation of analytic sets by algebraic sets

Abstract:
It is known that every germ of an analytic set is homeomorphic
to the germ of an algebraic set.  We show that the homeomorphism
can be chosen in such a way that the analytic and algebraic germs
are tangent with any prescribed order of tangency.
Moreover, the space of arcs contained in the algebraic germ approximates 
the space of arcs contained in the analytic one, in the sense that
they are identical up to a prescribed truncation order. This is joint
work with K. Kurdyka, A. Parusinski and G. Rond.