Cremona groups over finite fields and Neretin groups

Cremona groups are the groups of birational transformations of the projective plane, whereas Neretin groups are the groups of almost automorphisms of rooted trees. While the first come from algebraic geometry, the second appear in low-dimensional topology. In this talk, I will introduce both of them and explain how Cremona groups embed as dense subgroups into Neretin groups if we work over a finite field. This point of view allows us to better understand both groups.