Claus Scheiderer (Konstanz)
An elementary proof of Hilbert's theorem on positive ternary quartics.
Abstract: In 1888, Hilbert proved that every nonnegative ternary quartic form f(x,y,z) with real coefficients can be written as a sum of three squares of quadratic forms. In contrast with the elementary formulation of this theorem, Hilbert's proof is not easy at all. It uses several key arguments, e.g. topological ones, which are not of elementary nature. No easier approach to Hilbert's theorem is known so far. In recent years, Pfister started working on an elementary proof. By now it seems fair to say that his approach has been successful. In my talk I will try to give an account of this work.
