Notice Board

Guest: Zheng Zhu - University of Calgary

Topic: Galois Groups on Preimage Trees: Stability and Finite Index for Rational Maps

Date: Monday, Nov. 16 at 1 p.m. Room M1060 (Markin Hall)

In this talk, I will discuss a connection between this finite-index problem and eventual stability, which asks whether the number of irreducible factors of f n (x) = α remains bounded. Under suitable hypotheses on the critical orbits and geometric monodromy, we establish an equivalence between eventual stability and finite index. The result is conditional on the abc conjecture over number fields and unconditional for non-isotrivial rational maps over characteristic-zero function fields