Dr Williams

My research background

I consider myself equally an arithmetic geometer and number theorist, although I also dabble in arithmetic statistics, group theory, combinatorics, and lattice point counting in polytopes. I pretty much just like to count interesting objects over finite fields, finite rings, or the integers.

I have been fortunate to work with talented mathematicians from all over the country through various workshops. In particular, I attended Women in Numbers 2 (WIN2) at BIRS in 2011, and the awesome Research Experiences for Undergraduate Faculty (REUF) through AIM in 2014. I also attended the Undergraduate Faculty Program at the Park City Mathematics Institute (PCMI), a program of IAS, in 2017. I highly recommend any of these experiences (or anything similar), especially for grad students and young faculty!

I have also started working with undergraduate students here at JMU. Check out the submitted publications with recent students! If you're a current JMU student looking for a research advisor and are interested in number theory or finite matrix groups, come see me!

(If you're looking for my research on flipped classrooms and other classroom-related things, check out the Teaching page.)

Publications

Local heuristics and an exact formula for abelian varieties of odd prime dimension over finite fields. (with J Gerhard*.) Submitted. (Preprint)

Numerical secondary terms in a Cohen-Lenstra conjecture on real quadratic fields. (with C Lewis*.) Submitted. (Preprint)
Local heuristics and an exact formula for abelian surfaces over finite fields. (with J Achter.) Canadian Mathematical Bulletin, 58 (4) (2015).
Optimizing acquisition and retention spending to maximize market share. (with R Williams.) Journal of Marketing Analytics, 3 (3) (2015).
Newton polygons for a variant of the Kloosterman family. (with R Bellovin, S A Garthwaite, E Ozman, R Pries, and H J Zhu.) Proceedings of the WIN2 Conference, Contemporary Mathematics 606 (2013).
The Arithmetic and Geometry of Sudokus." (with M Beck, J Friedman, M Gagliardo, T Hunter, N Sieben, and S Wright.) In preparation.

(* indicates an undergraduate coauthor)

Selected conferences and talks

Here are some recent highlights of conference trips and talks about math.

Upcoming:

MAA MD-DC-VA Fall Section Meeting, Christopher Newport University, November 17-18, 2017
MASON II, Towson University, Spring 2018
SERMON XXXI, Spring 2018
MAA MD-DC-VA Spring Section Meeting, Washington and Lee University/Virginia Military Institute, April 13-14, 2018

Recent Talks about math:

Elon University PME Colloquium Series, March 2017
AMS Special Session on RE(UF)search in Graphs and Matrices (Invited Speaker), Joint Mathematics Meetings 2017, Atlanta
MASON I (Mid-Atlantic Seminar on Numbers), Towson University, October 29, 2016
University of Virginia Math Club, April 2016
Adelphi University Math & Computer Science Seminar, March 2016
Longwood University Colloquium Series, September 2015
PaNTS 22, South Carolina State University, September 2014
Hamden-Sydney College Colloquium Series, February 24, 2014
MAA Session on the Flipped Classroom, JMM 2014, January 2014
AMS Western Sectional, Special Session on Heights, Diophantine problems, and Lattices (Invited Speaker), November 2013
SIAM Conference on Applied Algebraic Geometry (Invited Speaker), August 2013
Journee Arithmetiques, Grenoble, France, July 2013

Recent Conferences and Workshops about math:

SERMON XXIX (Co-organizer), April 2016
MAA MD-DC-VA Spring Section Meeting, Montgomery College, April 2016
MAA MD-DC-VA Spring Sectional, Roanoke College, April 2015
SERMON XXIII, Winthrop University, March 2015
Arizona Winter School: Arithmetic Statistics, March 2014
PaNTS 20, Davidson College, September 2013
PaNTS 19, University of South Carolina, December 2012