Siegfried Van Hille
Hi there! I am a Postdoctoral Fellow at McMaster University. My supservisor is professor Patrick Speissegger.
Research interests
My research lies within the intersection of real algebraic geometry and applied model theory, o-minimality to be precise. More specifically:
Parametrizations and applications to point counting
Preparation theorems
Pfaffian functions
Latest
Work in progress: power series of pfaffian functions, with Mickaël Matusinski
Publication: The symmetric function theorem via the Faà di Bruno formula. (arXiv)
The symmetric function theorem states that a polynomial that is invariant under permutation of variables, is a polynomial in the elementary symmetric polynomials. We deduce this classical result, in the analytic setting, from the multivariate Faà di Bruno formula. In two variables, this allows us to completely determine all coefficients that occur in the inductive equations.
Recorded talk
Parametrizations and complexity of preparation, Introductory Workshop on Tame Geometry, Transseries and Applications to Analysis and Geometry, Fields Institute