On subgroups of odd order in the plane Cremona group over the field of real numbers

The Cremona group is a group of automorphisms of the field of rational functions in $n$ variables over a field $k$. The classification of finite subgroups in the plane Cremona group over an algebraically closed field is a classical problem. Its most complete solution was obtained only for $n = 1,\ 2$ and $k=\mathbb{C}$. In this talk we present some results on the classification of subgroups of odd order in the plane Cremona group over the field of real numbers.