Research
My research is in low-dimensional topology and number theory. Here is a copy of my cv. Here is some information about research projects.
Math Publications
(with A. Tsvietkova) Representations of Knot Groups (preprint)
(with J. Leach) Symmetries and Surfaces Detected by the Character Variety (submitted)
(with N. Hoffman) Small PSL(2,F) representations of Seifert Fiber Space Groups (submitted)
(with C. D. Sinclair) Equidistribution of Elements of Norm One in Cyclic Extensions (accepted Publicationes Mathematicae Debrecen)
(with J. Sellers) Partitions Associated to Class Groups of Imaginary Quadratic Number Fields (to appear Aequationes Mathematicae 2023)
(with L. Eldredge) Minimal Mahler Measure in Cubic Number Fields Int. J. Number Theory 19 (2022), no. 10, 2157-2169.
(with A. Reid) Gonality and Genus of Canonical Components of Character Varieties. Characters in low-dimensional topology, 263-292, Contemp. Math., 760, Amer. Math. Soc., Providence, RI, 2020.
(with S. Holmin, N. Jones, P. Kurlberg, and C. McLeman) Missing class groups and class number statistics for imaginary quadratic fields Exp. Math. 28 (2019), no. 2, 233-254.
(with S. Akhtari, K. Aktas, K. Biggs, A. Hamieh, and L. Thompson) Lower bounds for heights in relative Galois extensions. Women in numbers Europe II, 117, Assoc. Women Math. Ser., 11, Springer, Cham, 2018.
(with A. Tran) Character Varieties of Double Twist Links Algebr. Geom. Topol. 15 (2015), no. 6, 3569-3598.
The A-polynomial of a Family of Two-Bridge Knots. NY Journal of Math. Volume 21 (2015) 847-881.
Arithmetic Groups and Lehmer's Conjecture. Institut Mittag-Leffler preprint series, Workshop on Mahler Measure and Growth in Geometry and Topology (2013). (expository article)
(with K. Baker) Character Varieties of Once-Punctured Torus Bundles with Tunnel Number One. Internat. J. Math., 24 (2013), No. 06. 1350048, 57pp.
(with M. R. Murty) A Bombieri-Vinogradov Theorem for All Number Fields. Trans. Amer. Math. Soc. 365 (2013), no. 9, 4987-5032.
(with M. R. Murty) The Euclidean Algorithm for Number Fields and Primitive Roots. Proc. Amer. Math. Soc. 141 (2013), 181-190.
(with L. Fukshansky) On Well-Rounded Ideal Lattices. Int. J. Number Theory Vol 8 (2012) Issue 1:189-206.
(with M. Macasieb and R. van Luijk) Character Varieties of a Family of Two-Bridge Knots. Proc. London Math. Soc. (2011) 103(3): 473-507
(with C. D. Sinclair) Equidistribution of Algebraic Numbers of Norm One in Quadratic Number Fields. Int. J. Number Theory Volume: 7, Issue: 7(2011) pp. 1841-1861.
(with M. R. Murty) The Generalized Artin Conjecture and Arithmetic Orbifolds. Groups and symmetries, 259--265, CRM Proc. Lecture Notes, 47, Amer. Math. Soc., Providence, RI, 2009.
Counting Cusps of Subgroups of PSL2(OK). Proc. Amer. Math. Soc. 136 (2008), 2387-2393
(with C. D. Sinclair) Conjugate Reciprocal Polynomials with all Roots on the Unit Circle. Canad. J. Math. (2008) 60, no. 5, 1149-1167.
One-Cusped Congruence Groups of Bianchi Groups. Mathematische Annalen (2007) 338, no 2, 249 - 282.
One-Cusped Congruence Subgroups of PSL2(OK) , PhD dissertation. University of Texas, May 2005.
Other Publications
Non-Profit Alternatives to Commercial Academic Journals: Success Stories from Mathematics. Political Geography Volume 31, Issue 5, June 2012, Pages 263-265
(with N.C. Craig and D. C. McKean) Vibrational and Quantum Chemical Studies of 1,2-Difluoroethylenes: Spectra of 1,2-13 C2H2F2 Species, Scaled Force Fields, and Dipole Derivatives The Journal of Physical Chemistry A, (2002) Vol. 106, No. 26, pp. 6358-6369