Swan-Like Results Over Finite Fields

Speaker: David Thomson (Carleton University, Canada)

Time: 4:00PM
Date: Mon 28th February 2011

Location: Mathematical Sciences Seminar Room

Swan-like results give the parity of the number of irreducible factors of polynomials over finite fields. These give simple necessary conditions on irreducibility when proving irreducibility is hard. Swan's result (Pac. J. Math - 1962) gives the parity of the number of irreducible factors of trinomials over GF(2). In this talk, I give an overview of Swan-like results appearing over the last decade, and give necessary conditions on the irreducibility of binomials and trinomials over finite fields of odd characteristic. Special emphasis will be placed on the bottleneck of current methods which provide some interesting open problems in the area.

(This talk is based on joint work with Brandon Hanson (University of Toronto) and Daniel Panario (Carleton University).)

(This talk is part of the Algebra/Claude Shannon Institute series.)