Doud, Darrin

Email: doud@math.byu.edu
Office: 214 TMCB
Phone Number: (801) 422-1204
Fax Number: (801) 422-0504
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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 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. In addition, in recent research with Avner Ash, we have proven the conjecture in many reducible cases. My research also includes work with Paul Jenkins on modular forms, as well as work on discriminant bounds for number fields. Other interests include computational number theory, elliptic curves, and class field theory.
Joseph Adams, M.S. 2014
Wil Cocke, M.S. 2014
Vinh Dang, M.S. 2011
Ka Lun Wong, M.S. 2011
Brian Hansen, Ph.D. 2010
Wayne Rosengren, M.S. 2008
Jon Blackhurst, M.S. 2006
Heather Florence, M.S 2005
Brian Hansen, M.S. 2005
Glen Simpson, M.S. 2004
Michael W. Moore, M.S. 2004