**Office Hours: **N/A

**Class Schedule: **No Classes Spring/Summer 2023

**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.

**Degrees: **Brigham Young University, BS in Mathematics (1992), MS in Mathematics (1993), University of Illinois at Urbana-Champaign, MS in Teaching Mathematics (1999), PhD in Mathematics (1999)

**Graduate Students Supervised:**

Kevin Childers, M.S. 2015

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**Prizes and Awards:**

- Distinguished Teaching Award, Department of Mathematics, 2006
- Distinguished Citizenship Award, Department of Mathematics, 2008
- Alcuin Fellowship in General Education, 2009-2011
- Outstanding Teaching Award (3-10 years service), BYU College of Physical and Mathematical Sciences, 2009
- The Savage Distinguished Teaching Award from the department in November 2009

**Publications:**

- Highly reducible Galois representations attached to the homology of GL(n,Z), with Avner Ash,
*Proceedings of the AMS*,**143**(2015), 3801-3813. - Proof of a conjecture of Wong concerning octahedral Galois representations of prime power conductor, with Kevin Childers,
*Journal of Number Theory*,**154**(2015), 101-104. - Reducible Galois representations and the homology of GL(3,Z), with Avner Ash,
*International Mathematics Research Notices*,**2014**(2014), 1379-1408. - Two-divisibility of coefficients of certain weakly holomorphic modular forms, with Paul Jenkins and John Lopez,
*The Ramanujan Journal*,**28**, (2012), 89-111. - p-adic properties of coefficients of weakly holomorphic modular forms, with Paul Jenkins,
*International Mathematics Research Notices*,**2010**(2010) 3184-3206. - LLL reduction and a conjecture of Gunnells, with Russell Ricks,
*Proceedings of the American Mathematical Society***138**(2010), 409-415. - Finding Galois representations corresponding to certain Hecke eigenclasses, with Meghan DeWitt,
*International Journal of Number Theory***5**(2009), 1-11. - Local corrections of discriminant bounds and small degree extensions of quadratic base fields, with Sharon Brueggeman,
*International Journal of Number Theory***4**(2008), 349-361. - Distinguishing contragredient Galois representations in characteristic two,
*Rocky Mountain Journal of Mathematics***38**(2008), 835-848. - Supersingular Galois representations and a generalization of a conjecture of Serre,
*Experimental Mathematics***16**(2007), 119-128. - Bond-valence methods for pKs prediction. II. Bond-valence, electrostatic, molecular geometry, and solvation effects. Barry Bickmore, Kevin M. Rosso, Christopher J. Tadanier, Eric J. Bylaska and Darrin Doud,
*Geochimica et Cosmochimica Acta***70**(2006), 4057-4071. - Explicit Frobenius computations supporting a generalization of a conjecture of Serre, with Brian Hansen,
*JP Journal of Algebra, Number Theory and Applications*,**6**(2006), 381-398. - Even icosahedral Galois representations with prime conductor, with Michael W. Moore,
*Journal of Number Theory***118**(2006), 62-70. - Wildly ramified Galois representations and a generalization of a conjecture of Serre,
*Experimental Mathematics***14**(2005), 119-127. - Wild ramification in number field extensions of prime degree,
*Archiv der Mathematik***81**(2003), 646-649. - Galois representations with conjectural connections to arithmetic cohomology, with Avner Ash and David Pollack,
*Duke Mathematical Journal***112**(2002), 521-579. - Three-dimensional Galois representations with conjectural connections to arithmetic cohomology, in
*Number Theory for the Millennium*, A.K. Peters, Boston, 2002, 365-375. - S
_{4}and S_{4}-extensions of Q ramified at only one prime,*Journal of Number Theory***75**(1999), 185-197. - A procedure to calculate torsion of elliptic curves over Q,
*Manuscripta Mathematica***95**(1998), 463-469.

**Papers in Progress:**

- Relaxation of strict parity for reducible Galois representations attached to the homology of GL(3,Z), with Avner Ash,
*International Journal of Number Theory*, (2015),*to appear*. - Octahedral Extensions with a common Cubic Subfield, with Kevin Childers, (2015),
*In Review*.