Chad Awtrey, assistant professor of mathematics, gave an invited research talk at the University of North Carolina-Greensboro on Wednesday, Feb. 29, 2012.
Awtrey’s talk, “Computing Galois-theoretic invariants of p-adic fields,” provided an overview of his research program concerning computational algebraic number theory. In addition to providing a brief history of certain problems related to p-adic numbers, the talk also addressed several of Awtrey’s recent research papers.
Of particular interest to audience members was his most recent paper, “Dodecic 3-adic fields,” which has been accepted for publication in International Journal of Number Theory. This paper completely classifies the set of numbers which arise from roots of certain polynomials of degree 12 whose coefficients are 3-adic numbers. Essential in this classification is a new algorithm for computing the Galois groups of these polynomials.
Awtrey is currently conducting research with three undergraduates on individual projects, all of which are related to either p-adic numbers, Galois groups, or both.