|322 TMCB |
Department of Mathematics
Brigham Young University
Provo, UT 84602
My current research deals with actions of Hecke algebras on the cohomology of arithmetic groups, and relations of these actions to Galois representations. In particular, in joint research with Avner Ash and David Pollack, I have recently generalized an important conjecture of Serre relating certain two-dimensional Galois representations to arithmetic cohomology from the two-dimensional case to the n-dimensional case. We have developed techniques and software to compute the relevant cohomology groups in the three-dimensional case, and have found many computational examples to support the conjecture. Several of my recent papers have proved cases of the conjecture.
Other areas in which I am interested include the study of number fields with limited ramification, elliptic curves, expicit class field theory, and Galois cohomology.