***I stopped updating this website in June 2023 – see my new site ***

(Note: Papers published with undergraduate mentees are listed separately toward the bottom.)

Under Review

(with N. Hung and C. Vallejo) Principal blocks with six ordinary irreducible characters. Submitted 2023. Preprint:  Preprint Here

(with L. Ruhstorfer) Navarro’s Galois–McKay conjecture for the prime 2. Submitted 2022. Preprint Here.

(with G. Malle, G. Navarro, and P.H. Tiep) Brauer’s Height Zero Conjecture. Submitted 2022. Preprint Here.



(with N. N. Hung) On Héthelyi–Külshammer’s conjecture for principal blocks.  Algebra & Number Theory, 17:6 (2023),   Preprint Here.

(with N.N. Hung and C. Vallejo) Height zero characters in principal blocks. Journal of Algebra, 622 (2023), 197–219. Preprint Here. 

(with G. Navarro and N. Rizo) Principal blocks for different primes, II.  Vietnam J. Math. Special issue dedicated to Pham Huu Tiep on the occasion of his 60th birthday (2022). Preprint Here.

(with G. Navarro and N. Rizo) Principal blocks for different primes, I. Journal of Algebra. 610 (2022), 632-654. Preprint Here. Published form here. Addendum Here.

(with J. Taylor) Galois Automorphisms and Classical Groups.  Transformation Groups.  28, (2023), 439–486Preprint Here.  Published form here.

(with L. Ruhstorfer) The inductive McKay–Navarro conditions for the prime 2 and some groups of Lie type.   Proceedings of the American Mathematical Society, Ser. B (2022), 204–220. Open Access – Available Here. Corrections to Section 2 Available on arXiv here.

Galois-equivariant McKay bijections for primes dividing q-1.   Israel Journal of Mathematics. 247, 269–302 (2022).  Preprint Here.  Published form here.

(with E. Giannelli and J. M. Martínez) Character degrees in blocks and defect groups.   Journal of Algebra. Vol. 594 (2022), 170-193.   Preprint Here.

(with N. Rizo and C. Vallejo) Principal blocks with 5 irreducible characters.  Journal of Algebra. Vol. 585 (2021), 316-337.  Preprint Here.

(with M. Cabanes and B. Späth) On the inductive Alperin-McKay conditions in the maximally split case.  Mathematische Zeitschrift. Vol. 299 (2021), 2419–2441.  Preprint Here.

(with G. Navarro, N. Rizo, and C. Vallejo) Characters and generation of Sylow 2-subgroups.  AMS Representation Theory. Vol. 25 (2021), 142–165.

(with N. Hung, E. Giannelli, and C. Vallejo) Characters of π’-degree and small cyclotomic fields.  Annali di Matematica Pura ed Applicata. Vol. 200 (2021), 1055–1073.  Preprint Here.

(with E. Giannell, N. Rizo, and B. Sambale) Groups with Few p’-Character Degrees in the Principal Block. Proceedings of the American Mathematical Society.  148:11 (2020), 4579-4614. Preprint Here.

(with N. Rizo and C. Vallejo) Galois Action on the Principal Block and Cyclic Sylow Subgroups.  Algebra and Number Theory. 14-7 (2020), 1953–1979.   Preprint Here.

(with J. Brough) Radical Subgroups and the Inductive Blockwise Alperin Weight Conditions for PSp(4, q).  Rocky Mountain Journal of Mathematics. 50:4 (2020), 1181-1205.  Preprint Here.

(with N. N. Hung, H. Tong-Viet, and C. R. Vinroot) On the Number of Irreducible Real-Valued Characters of a Finite Group.   Journal of Algebra.  Vol. 555 (2020), 275-288.  Preprint Here.

(with E. Giannelli and N. Rizo) Groups with Few p’-Character Degrees.  Journal of Pure and Applied Algebra.  224 (2020) no 8.  Preprint here.

(with E. Giannelli and C. Vallejo) Characters of π’-Degree.  Proceedings of the American Mathematical Society. 147 (2019) no. 11, 4697-4712.  Preprint Here.

(with C. R. Vinroot) Fields of Character Values for Finite Special Unitary Groups. Pacific Journal of Mathematics.  Vol. 300 (2019), No. 2, 473–489.  Preprint Here.

Action of Galois Automorphisms on Harish-Chandra Series and Navarro’s Self-Normalizing Sylow  2-Subgroup Conjecture. Trans. Amer. Math. Soc. 372  no. 1 (2019), pp. 457-483.  Preprint Here.

(with J. Taylor) Principal  2-Blocks and Sylow  2-Subgroups.  Bull. Lond. Math. Soc., 50 (2018), 733-744.

(with J. Taylor) On Self-Normalizing Sylow  2-Subgroups in Type A . J. Lie Theory (2018), 28:1, 139-168.

(with C.R. Vinroot) Real Classes in Finite Special Unitary Groups. J. Group Theory (2016), 19:5, 735-762.

Odd-Degree Characters and Self-Normalizing Sylow Subgroups: A Reduction to Simple Groups. Communications in Algebra (2016), 44:5, 1882-1904. Preprint Version Here.

(with H.N. Nguyen, and M.L Lewis) Finite Groups with an Irreducible Character of Large Degree. Manuscripta Mathematica (2016), 149:3, 523-546.

Sp(6, 2^a) is `Good’ for the McKay, Alperin Weight, and Related Local-Global Conjectures. J. Algebra 401 (2014), 13-47

Cross-characteristic Representations of Sp(6, 2^a) and their Restrictions to Proper Subgroups. J. Pure Appl. Algebra 217 (2013), no. 8, 1563-1582.

(with K. Lux and C. R. Vinroot) Strong Reality Properties of Normalizers of Parabolic Subgroups in Finite Coxeter Groups. Comm. Algebra. 40 (2012), no. 8, 3056-3070.

(with G. Haynes, L. Mitchel, C. Park, and J. Webster) Orthogonal Vector Coloring. Electronic Journal of Combinatorics (2010), v 17.

Ph.D. Thesis

Irreducible representations of finite groups of Lie type: On the irreducible restriction problem and some local-global conjectures. PhD dissertation. The University of Arizona, Tucson, AZ, USA. (2013). Available here.  PDF Here..

Papers with Undergraduates

 (students A. Peña and F. Pryor) Galois action and cyclic defect groups for Sp(6,2^a). To Appear in Involve, a Journal of Mathematics (2023). Preprint Here.

(students K. Albee, M. Barnes, A. Parker, E. Roon) On Irreducible Character Restrictions in Low-Rank Classical Groups. Involve, a Journal of Mathematics 12-4 (2019), 607–631. DOI 10.2140/involve.2019.12.607

(student E. Roon) That Strikes a Chord! An Illustration of Permutation Groups in Music Theory.  The Rowdy Scholar: A Journal of Undergraduate Research and Creative Works (2019), v. 1.  Available Here