Awtrey publishes with alumni, gives invited talks
A.L. Hook Associate Professor Chad Awtrey publishes a research paper with alumni Taylor Cesarski '17 and Peter Jakes '17 in the latest issue of an international number theory journal.
Alumni Taylor Cesarski '17 and Peter Jakes '17 published a paper with A.L. Hook Associate Professor Chad Awtrey titled "Determining Galois groups of reducible polynomials via discriminants and linear resolvents" in the latest issue of the JP Journal of Algebra, Number Theory, and Applications (volume 39, issue 5, pages 685-702).
Their results add to the growing body of literature concerning algorithms for computing Galois groups (symmetries) of polynomials. Galois groups are structures that encode many important arithmetic properties of the corresponding polynomial, and they play a fundamental role in current research pursuits in the mathematical fields of algebra, geometry, and number theory.
Most results concerning Galois group computations focus on polynomials that cannot be split apart into polynomials of smaller degree; such polynomials are called irreducible. But there is growing interest in understanding the ones that can be split apart into irreducible pieces since their Galois groups are intimately connected to the symmetries of the irreducible pieces. For these reducible polynomials, Awtrey, Cesarski and Jakes have developed new theory and techniques for determining Galois groups using minimal data. Their particular algorithm contains novel methods which have broad applications to computing general characteristics of polynomials.
Cesarski now teaches high school mathematics in North Carolina, and Jakes works as an actuary in Chicago, Illinois.
Awtrey also recently delivered an invited talk on Nov. 16 at Roanoke College in Virginia as part of the college's Mathematics, Computer Science and Physics Conversation Series. Awtrey, whose visit was sponsored by the national mathematics honor society Pi Mu Epsilon, spoke on recent research results he obtained with his undergraduate students. This talk marks the fifth and final such invited presentation Awtrey delivered this calendar year. The previous were two talks at the University of Nebraska-Omaha on February 16-17, and two talks at Christopher Newport University in Virginia on March 22-23.