### Research

My research area is in algebraic number theory with connections to arithmetic geometry, algebraic topology, and group theory. I am specifically interested in Galois actions.
### Publications and preprints

R. Davis, R. Pries, V. Stojanoska, and K. Wickelgren ** The Galois action and cohomology of a relative homology group of Fermat curves**, submitted October 2016. See the Magma files of computuations for the paper.

A.C. Cojocaru, R. Davis, A. Silverberg, and K.E. Stange, ** Arithmetic properties of the Frobenius traces defined by a rational abelian variety,** with two appendices by J-P. Serre. International Mathematics Research Notices (2016).

R. Davis, R. Pries, V. Stojanoska, and K. Wickelgren **Galois Action on the Homology of Fermat Curves** to appear in the WIN3 proceedings volume. November, 2014.

R. Davis ** Images of metabelian Galois representations associated to elliptic curves** Proceedings of the WIN2 Conference, Contermp. Math 606 (2013).

A. Brouwer, R. Davis, A. Larkin, D. Studenmund, and C. Tucker ** Intrinsically S^1 3-Linked Graphs and Other Aspects of S^1 Embeddings** Rose-Hulman Institute of Technology Undergraduate Math Journal (2007).