# Study of Automata and its Applications to Number Theory and Algebra

Finite-state automata play a fundamental role in theoretical computer science, but in recent years many advances in number theory, geometry, and algebra have been made by adopting an automaton-theoretic viewpoint. Just a few of their many applications are to noncommutative algebra, where they can often be used to find Groebner bases for finitely presented algebras; and to number theory, where they can sometimes be used to determine whether power series satisfy certain differential equations. This project involves graduate students and visitors to IRMACS, who have both done research on these areas and holded seminars. IRMACS facilities have been also used for undertaking computations.

### About Project Leader: Dr. Jason Bell

Dr. Jason Bell is an Associate Professor in the Department Mathematics at Simon Fraser University. Dr. Bell currently works in noncommutative algebra and its connections with number theory and combinatorics. His research interests span across several mathematical areas: algebra, number theory, automata and words, combinatorics, and algebraic geometry. Well known for his readiness to share his ideas and knowledge with fellow mathematicians, Dr. Bell has collaborated with some of the most prominent mathematicians of our time including A. Frankel, D. Djokovic, and P. Cameron for example, as well as some young talented mathematicians at the beginning of their careers, M. Coons and K. Casteels, for example.