A research team consisting of Jesi Weed '16, Sara Rodgers '16, Nicole Soltz '17, Assistant Professor Kristen Mazur, and A.L. Hook Professor in Science & Mathematics Chad Awtrey published an article in the most recent issue of an international mathematics journal.
The article, “On Galois groups of degree 15 polynomials”, appears in volume 104, no. 3 of the International Journal of Pure and Applied Mathematics, pg. 407-420.
In it, the research team lays out theoretical and computational techniques that are helpful in computing the Galois group of a degree 15 polynomial. Their work extends prior research by focusing on polynomials whose coefficients are 5-adic numbers; previously, only results up to and including degree 14 were known.
Research on Galois groups of polynomials with p-adic coefficients plays an important foundational role in many areas of modern mathematics, some with applications to quantum physics and cryptography.
In addition to producing this publication, the team has given a total of five presentations on their results at national and regional conferences so far. Another foiur presentations will occur over the rest of the academic year, as the researchers continue their investigations to include the case of degree 15 polynomials with 3-adic coefficients.