• Darrin Doud
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Darrin Doud

314 TMCB Department of Mathematics Brigham Young University Provo, UT 84602

phone: (801)422-1204 fax: (801)422-0504 e-mail:

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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.

My past research has involved the study of deformations of Galois representations. In particular, in my thesis I generalized work of Barry Mazur and Nigel Boston on explicit calculations of two-dimensional Galois representations to compute explicit deformations of three-dimensional Galois representations. In the process, I also discovered some interesting S₄-extensions of Q which are ramified at only one finite prime.

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.