# Moduli Invariants in Complex Dynamics

Abstract: To any rational map f of the Riemann sphere, we can associate a collection of invariants given by the eigenvalues of the associated pushforward operator on the space of quadratic differentials with simple poles.  Recently, Buff-Epstein-Koch proved that many of the resulting invariants are dynamical; in particular, they arise from multipliers of periodic cycles of f. We will discuss the possible dynamical significance of the remaining invariants, focusing on a family of quadratic rational maps.

Note: this talk is in Seminar room 1.37, Hanna Neumann Building, rather than the usual room.