Algebra and Combinatorics Seminar

Date: September 9, 2016

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Andrew Bridy, Texas A&M University

Title: Automatic Sequences and Curves over Finite Fields

Abstract: An amazing theorem of Christol states that a power series over a finite field is an algebraic function if and only if its coefficient sequence can be produced by a finite automaton, which is a limited model of a computer with no memory. The proof is straightforward, but it hides information about the representation theory of semigroups associated to automata, which are naturally realized as operators on the differentials of an algebraic curve. I make this explicit by proving a precise link between the complexity of the automaton and the geometry of the curve.