adding passports for when the
quotient genus is not 0
higher genus data
quotient actions
Books
Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics (edited with A. Wootton and A. Broughton). Contemporary Mathematics vol. 776. [endmatter]
Research Papers and Expository Articles
On non-normal subvarieties of the moduli space of Riemann surfaces (with R. Hidalgo, S. Reyes-Carocca, and A. Rojas). Submitted. [pdf] abstract
Group actions and Riemann surfaces. To appear.
[pdf]
(This article is aimed at upper level undergraduate students.) abstract
Maintaining a research career at a primarily undergraduate institution. Notices of the AMS, Vol. 70, no. 4. April 2023. [pdf]
A database of group actions on Riemann
surfaces. Birational Geometry, Kähler-Einstein Metrics and Degenerations. Springer Proceedings in Mathematics & Statistics, 409 (2023), 693--708. [pdf] This paper describes the mathematics behind data at
www.lmfdb.org/HigherGenus/C/Aut abstract
Future directions in automorphisms of surfaces, graphs, and other topics. (with A. Broughton and A. Wootton.) Contemporary Mathematics. 776 (2022). abstract
Algorithmically distinguishing irreducible characters of the symmetric group. (with T. Chow.) The Electronic Journal of Combinatorics. 28 (2021) no. 2, online. [pdf] abstract
Non-abelian simple groups act with almost all signatures. (with M. Carvacho, T. Tucker and A. Wootton.) Journal of Pure and Applied Algebra. 225 (2021), no. 4, [pdf] abstract
Using strong branching to find automorphism groups of n-gonal surfaces. (with S.A. Broughton, C. Camacho, R.
Winarski, and A. Wootton). Albanian Journal of Mathematics, Special issue in honor of Kay Magaard, Vol. 12,
(2018), no. 1, 89--129. [pdf] abstract
Completely decomposable Jacobian varieties in new genera. (with
A. Rojas). Experimental Mathematics 26 (2017), no. 4, 430--445. (Published online 02 September 2016.) [pdf]
and extra [data] abstract
Jacobian varieties of Hurwitz curves with automorphism group PSL(2,q). (with A. Fischer and
M. Liu, both undergraduates). Involve, a Journal of Mathematics 9-4 (2016), 639--655. [pdf]
Also [poster] from ANTS-XI. abstract
Elliptic factors in Jacobians of hyperelliptic curves with certain
automorphism groups. ANTS X: Proceedings of
the Tenth Algorithmic Number Theory Symposium. Mathematical Science
Publishers. Everett Howe and Kiran Kedlaya (Eds.), 2013. [pdf]
There is an error in some of the computations in this
paper [errata]. (Note this error does not impact my other work in Jacobian variety
decompositions.)
abstract
On the parity of k-th powers mod p: A generalization of a problem of
Lehmer. (with J. Bourgain, T. Cochrane, and C. Pinner). Acta Arith. 47, no. 2 (2011), 173 -
203. [pdf] abstract
The l-rank structure of a global function field. (with
L. Berger, J.-L. Hoelscher, Y. Lee, and R. Scheidler). Women in
Numbers: Research Directions in Number Theory. Fields
Institute Communications 60 (2011), 145-166. [pdf] abstract
Studio College Algebra at Kansas State University. (with
A. Bennett, R. Manspeaker, and R. Natarajan). Haver, W.E. and
S.L. Ganter (Eds.), Partner Discipline Recommendations for
Introductory College Mathematics and Implications for College
Algebra, MAA Reports, Washington, DC: Mathematical Association of
America. (2011), 99-105.
Decimations of l-sequences and permutations of even residues mod p. (with
J. Bourgain, T. Cochrane, and C. Pinner). SIAM Journal on Discrete Mathematics 23 (2009), no. 2,
842-857. [pdf] abstract
Decomposing Jacobians of curves with extra automorphisms. Acta Arith. 132 (2008),
no. 3, 231-244. [pdf] abstract
Other Work
Branching Data for Curves up to Genus 48. (2015) Computations of
monodromy using work of Thomas Breuer. Information about and data from this
project are [here]. abstract
Thesis, REU Paper, etc.
PhD Thesis: Elliptic factors in Jacobians of low genus curves.
University of Illinois at Urbana-Champaign,
(2007). [pdf]
Cwatset Isomorphism and Its Consequences. (with C. Girod, M. Lepinski, and
J. Mileti). Rose-Hulman Mathematical Sciences Technical Report Series, vol 1 (2000).
[pdf] abstract