# Seminar talk, 5 October 2016

The talk will discuss the Lie problem on point classification of ordinary differential equations of second order ${\displaystyle y''=F(x,y)}$ and a new approach to the study of infinite dimensional subgroups of the Cremona group.
The approach is based on an unexpected relation between differential equations and algebraic geometry. Namely, the group of point symmetries of differential equations of the form ${\displaystyle y''=F(x,y)}$ with rational right-hand side is a subgroup of the Cremona group.