Moved to the next session of the seminar.

The fixed point set of an anti-holomorphic involution on a compact Riemann surface X, say of genus g, consists of at most g+1 circles. If this bound is attained, one calls X maximal. More generally, an algebraic variety X with an anti-holomorphic involution is called maximal if the sum of the mod-2 Betti numbers of X is equal to the corresponding sum for the fixed point set.

Recently, Biswas and D'Mello have shown that the n-th symmetric product of a maximal curve is again maximal provided that n <= 3 or n >= 2g-1. In this talk, we will explain how to generalize this result not only to all n and to other maximal varieties, but even beyond the realm of algebraic geometry.