Chad Awtrey, assistant professor of mathematics, presented a research talk at the joint meetings of the American Mathematical Society and the Mathematical Association of America, in Boston, Mass., on Jan. 7, 2012.
In his talk, “Dihedral p-adic fields,” Awtrey described results from a recent paper, coauthored with mathematics major Trevor Edwards (’11), concerning computational Galois theory for p-adic fields. In particular, the paper completely classifies p-adic fields of prime degree q which have the property that their symmetries are the same as the symmetries of the regular polygon with q sides.
This result is part of Awtrey’s ongoing research program that aims to completely classify all p-adic fields through their arithmetic invariants. A complete understanding of p-adic numbers would have tremendous impact not only in mathematics, but also in physics and cryptography.