### Algebra Seminar The Arboreal Finite Index ProblemAndrew Bridy (Yale University)

Wednesday, September 11, 2019
11:15am – 12:05pm

Storrs Campus
Monteith 313

Let $$K$$ be a global field, $$f$$ in $$K[x]$$, and $$b$$ in $$K$$. Let $$K_n$$ be the splitting field of $$f^n(x)−b$$, where $$f^n$$ denotes $$n$$-fold composition. The projective limit of the groups $${\rm Gal}(K_n/K)$$ embeds into the automorphism group of an infinite rooted tree. A major problem in arithmetic dynamics, motivated by Serre's open image theorem, is to determine when the index is finite. I discuss the solution of the problem for quadratic, cubic, and unicritical polynomials by classifying all obstructions to finite index, and the issues that arise in trying to apply the same ideas to polynomials in general.

Contact:

Mihai Fulger, mihai.fulger@uconn.edu

Algebra Seminar (primary), UConn Master Calendar