# Doud, Darrin

**Email:**doud@math.byu.edu

**Office:**322 TMCB

**Phone Number:**(801) 422-1204

**Fax Number:**(801) 422-0504

Click Here to View Doud, Darrin's Curriculum Vitae

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**Prizes and Awards:**

**Publications:**

*Proceedings of the AMS*,

**143**(2015), 3801-3813.

*Journal of Number Theory*,

**154**(2015), 101-104.

*International Mathematics Research Notices*,

**2014**(2014), 1379-1408.

*The Ramanujan Journal*,

**28**, (2012), 89-111.

*International Mathematics Research Notices*,

**2010**(2010) 3184-3206.

*Proceedings of the American Mathematical Society*

**138**(2010), 409-415.

*International Journal of Number Theory*

**5**(2009), 1-11.

*International Journal of Number Theory*

**4**(2008), 349-361.

*Rocky Mountain Journal of Mathematics*

**38**(2008), 835-848.

*Experimental Mathematics*

**16**(2007), 119-128.

*Geochimica et Cosmochimica Acta*

**70**(2006), 4057-4071.

*JP Journal of Algebra, Number Theory and Applications*,

**6**(2006), 381-398.

*Journal of Number Theory*

**118**(2006), 62-70.

*Experimental Mathematics*

**14**(2005), 119-127.

*Archiv der Mathematik*

**81**(2003), 646-649.

*Duke Mathematical Journal*

**112**(2002), 521-579.

*Number Theory for the Millennium*, A.K. Peters, Boston, 2002, 365-375.

_{4}and S

_{4}-extensions of Q ramified at only one prime,

*Journal of Number Theory*

**75**(1999), 185-197.

*Manuscripta Mathematica*

**95**(1998), 463-469.

**Papers in Progress:**

*International Journal of Number Theory*, (2015),

*to appear*.

*In Review*.

**Research Interests:**

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.

**Graduate Students Supervised:**

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