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Physical and Mathematical Sciences
Math
Faculty/Doud, Darrin.jpeg

Darrin Doud

Professor
Curriculum Vitae
Permanent Faculty
Website: https://math.byu.edu/~doud
Email: doud@math.byu.edu

Office: 214 TMCB

801-422-1204

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:

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

Publications:

  1. Highly reducible Galois representations attached to the homology of GL(n,Z), with Avner Ash, Proceedings of the AMS, 143 (2015), 3801-3813.
  2. 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.
  3. Reducible Galois representations and the homology of GL(3,Z), with Avner Ash, International Mathematics Research Notices, 2014 (2014), 1379-1408.
  4. Two-divisibility of coefficients of certain weakly holomorphic modular forms, with Paul Jenkins and John Lopez, The Ramanujan Journal, 28, (2012), 89-111.
  5. p-adic properties of coefficients of weakly holomorphic modular forms, with Paul Jenkins, International Mathematics Research Notices, 2010 (2010) 3184-3206.
  6. LLL reduction and a conjecture of Gunnells, with Russell Ricks, Proceedings of the American Mathematical Society 138 (2010), 409-415.
  7. Finding Galois representations corresponding to certain Hecke eigenclasses, with Meghan DeWitt, International Journal of Number Theory 5 (2009), 1-11.
  8. 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.
  9. Distinguishing contragredient Galois representations in characteristic two, Rocky Mountain Journal of Mathematics 38 (2008), 835-848.
  10. Supersingular Galois representations and a generalization of a conjecture of Serre, Experimental Mathematics 16 (2007), 119-128.
  11. 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.
  12. 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.
  13. Even icosahedral Galois representations with prime conductor, with Michael W. Moore, Journal of Number Theory 118 (2006), 62-70.
  14. Wildly ramified Galois representations and a generalization of a conjecture of Serre, Experimental Mathematics 14 (2005), 119-127.
  15. Wild ramification in number field extensions of prime degree, Archiv der Mathematik 81 (2003), 646-649.
  16. Galois representations with conjectural connections to arithmetic cohomology, with Avner Ash and David Pollack, Duke Mathematical Journal 112(2002), 521-579.
  17. Three-dimensional Galois representations with conjectural connections to arithmetic cohomology, in Number Theory for the Millennium, A.K. Peters, Boston, 2002, 365-375.
  18. S4 and S4-extensions of Q ramified at only one prime, Journal of Number Theory 75(1999), 185-197.
  19. A procedure to calculate torsion of elliptic curves over Q, Manuscripta Mathematica 95(1998), 463-469. 

Papers in Progress:

  1. 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.
  2. Octahedral Extensions with a common Cubic Subfield, with Kevin Childers, (2015), In Review.