The foundations group will talk about its research.
Foundations Open House
Tue, Sep. 15 11pm (350)
Number Theory
Jamie Juul (Colorado State University)
X
Iterating a polynomial or rational function produces a tree of preimages of a point, and the Galois group of the resulting tower of fields acts on this tree by symmetries — a dynamical analogue of the Galois representations attached to elliptic curves, and a natural place to ask how large this group of symmetries can be. I will describe a general criterion, based only on the combinatorics of a map's critical orbits, that determines whether this group is as large as possible, and if not, exactly how it falls short at every level. Along the way I'll work out an explicit family of examples where all the critical orbits eventually collide, and describe how recent work of König, Neftin, and Rosenberg makes the criterion apply automatically to a broad class of polynomials.
Rational Functions with Large Iterated Monodromy Groups
Foundations Open House