mercoledi' 21-06-2006 (15:00) - Sala dei Seminari Jesus Ruiz (Universitad Complutense Madrid) : Open questions concernings Hilbert's 17th Problem for analytic curves
Abstract The Hilbert 17th Problem asks when a psd function is a sum of squares, and of how many.
For real analytic curves this reduces to the local problem for germs at singular points. For those germs, the problem splits into the consideration of their irreducible branches.
Now, irreducible curve germs are classically discussed using the semigroup of values: all irreducible curves with fixed semigroup form a "moduli" algebraic set in some finite dimensional affine space.
There, Pythagoras numbers, positive semidefinite germs, sum of squares provide semialgebraic mappings on and stratifications of the "moduli" set.
The understanding od these semialgebraic data is a difficult matter that has surprising connections with classical concepts (for instance, Arf curves and Pythagorean curves are one and the same thing).
************************* Segreteria Didattica Giulia Curciarello tel- 050 2213219 *************************
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