Math majors & faculty give talks at sectional meeting of the American Mathematical Society

​Robin French ’15 presented a contributed talk, “A new algorithm for Galois groups of quintic polynomials”, which was mentored by Assistant Professor Chad Awtrey. The work offers an improvement of previous research in 1991 by D. Dummit, as it illustrates a new approach to studying the symmetry properties of solutions to degree five polynomial equations.

Nicole Soltz ’17 discussed aspects of her research in the contributed talk “Counting Roots and Galois Groups,” also mentored by Awtrey.  Soltz’s work extends frontiers of research in p-adic numbers by completely classifying all “distinct” polynomial equations of degree 15 whose coefficients are 5-adic numbers. She also spoke on joint work with Elon undergraduate Sara Rodgers ’16 that aims to compute the symmetry properties of these polynomials’ roots.

Awtrey gave an invited talk “Degree 14 2-adic fields”.  This research project, which was joint work with Elon students Nicole Miles ’15, Chris Shill ’14, and Erin Strosnider ’14 and with UNCG doctoral student Jonathan Milstead, gives a classification of all possible degree 14 polynomials whose coefficients are 2-adic numbers.  

The results of the research appear in a paper of the same name which has been accepted for publication in the journal “Involve”, a high-quality mathematics research journal that publishes original contributions by faculty-student research teams.

Awtrey also co-organized two special sessions of talks, “Algorithms for Local Fields” and “Galois Theory and Its Interactions with Algebra and Number Theory.”  The first session was co-organized with mathematician Sebastian Pauli (UNC-Greensboro) and the second with mathematician Michael Bush (Washington and Lee University).  Between the two sessions, a total of 19 mathematicians gave talks related to p-adic numbers and Galois theory, two active areas of current mathematical research in number theory.