The projective translation equation: where topology, algebraic geometry, differential equations, and number theory meet

A flow is a bivariate function (the first variable belongs to a
certain space while the second is a "time") which satisfies a natural
iterative functional equation. The aim of this talk is to describe a new
field of projective flows and its manifold aspects, including topology,
combinatorics (Polya urns), number theory (elliptic curves, elliptic and
abelian functions), linear PDEs, birational geometry (Cremona groups),
algebraic geometry, projective flows over finite fields, and group
representations (symmetries of flows).