Aleksandra Nowel
Title: Effective methods for calculating some invariants of real polynomial mappings
Abstract:
The development of the Gröbner basis theory and Hironaka's results on resolution
of singularities benefited to growing importance of effective methods for studying
invariants associated with objects of algebraic geometry. The rapid development
of computers has enabled the practical use of algorithms which had been worked out.
I will present the use of classic results for counting the number of roots of polynomials
("trace formula" - Pedersen, Roy, Szpirglas, Becker, Wörmann) and the local topological
degree (Eisenbud, Levine, Khimshiashvili, Szafraniec, Łęcki) using signature of a square
form to calculate some invariants of real polynomial mappings.