Susanna Zimmermann will speak on

Birational involutions of real conic fibrations

Every birational map of the complex plane is a composition involutions and these involutions were classified by Bayle-Beauville in 2000: they are either conjugate to linear maps or their conjugacy class is determined by their irrational fixed curve. They show on the go that involutions conjugate to automorphisms of conic bundles fix a hyperelliptic curve. In this talk I present the part of the classification over the real numbers. In particular, there are infinitely many non-conjugate involutions acting on a conic bundle and fixing a rational curve. This is a collaboration with I. Cheltsov, F. Mangolte and E. Yasinsky.