Il giorno Martedi 10 Giugno alle ore 15 in Sala Seminari il prof. J.M.Ruiz dell'Universita' Complutense di Madrid terra un seminario dal titolo:

"On the finiteness of Pythagoras numbers of real meromorphic functions"

Abstract:

We consider the 17th Hilbert Problem for global real analytic functions in a modified form that involves infinite sums of squares. Then we prove a local-global principle for a real analytic function to be a sum of squares of real meromorphic functions. We deduce an affirmative solution to the 17th Hilbert problem for global real analytic functions implies the finiteness of the Pythagoras number of the fields of real meromorphic functions and of real meromorphic germs. This measures the difficulty of the 17th Hilbert problem in the analytic case.