Laureano Gonzalez-Vega
  Title:
    Using Quantifier Elimination to solve the Birkhoff Interpolation 
    Problem

  Abstract:
    This talk is devoted to show how to use Quantifier Elimination to
    solve some particular instances of the Birkhoff Interpolation Problem.
    In particular, this problem is completely solved for degrees smaller or
    equal than 3 and any number of nodes and several instances of degrees 4
    and 5 by computing all the incidence normal poised matrices  with such
    characteristics. The special structure of the first order formulae
    involved in the Birkhoff Interpolation Problem allows to apply in a very
    efficient way different features of several Quantifier Elimination
    Methods: Sturm-Habicht Sequences, manipulation of formal inequalities
    "a la BenOr-Kozen-Reif", etc.