Those who are interested can download my curriculum vitae, or my PhD thesis.
Papers and preprints:
- Some Results on Two Conjectures of Schützenberger (with M. Desgroseilliers, B. Larose and C. Malvenuto)
Canadian Mathematical Bulletin, Vol. 53 (3), 2010, pp. 453-465 - Drinfeld modular forms modulo P
Proceedings of the American Mathematical Society, Vol. 138 (12), 2010, pp. 4217-4229 - Osculation points at the cusps of Drinfeld modular curves (unpublished note)
- On the trace and norm maps from Gamma0(P) to GL2(A)
Journal of Number Theory, Vol. 142, 2014, pp. 18-43 - Appendix for Galois representations attached to moments of Kloosterman sums and conjectures of Evans by Z. Yun
Compositio Mathematica, Vol. 151, 2015, pp. 68-120
Here is the code for the computation and a list of Fourier coefficients - Weierstrass points on the Drinfeld modular curve X0(P)
Research in the Mathematical Sciences, Vol. 2 (10), 2015 - Zeta functions of a class of Artin-Schreier curves with many automorphisms (with I. Bouw, W. Ho, B. Malmskog, R. Scheidler and P. Srinivasan)
Directions in Number Theory, Assoc. Women Math. Ser., 3, Springer, 2016, pp. 87–124 - Constructing genus 3 hyperelliptic Jacobians with complex multiplication (with J.S. Balakrishnan, S. Ionica and K. Lauter)
LMS Journal of Computation and Mathematics, Vol. 19 (A), 2016, pp. 283-300.
Here is a link to the repository where the code is held - A characterization of the U(Omega,m) sets of a hyperelliptic curve as Omega and m vary
Advances in the Mathematical Sciences, Assoc. Women Math. Ser., 15, Springer, 2018, pp. 79-95 - Modular invariants for genus 3 hyperelliptic curves (with S. Ionica, P. Kilicer, K. Lauter, E. Lorenzo Garcia, M. Massierer and A. Manzateanu)
Res. Number Theory, Vol. 5 (1), 2019, 22 pp. - Appendix for An inverse Jacobian algorithm for Picard curves by J.-C. Lario and A. Somoza,
Res. Number Theory, Vol. 7 (2), 2021, 23 pp. - A robust implementation for solving the S-unit equation and several applications (with A. Alvarado, A. Koutsianas, B. Malmskog, C. Rasmussen, and M. West)
Arithmetic geometry, number theory, and computation, a volume of the Simons Symposia series by Springer, 2021, pp. 1-41 - Isogeny classes of abelian varieties over finite fields in the LMFDB (with T. Dupuy, K. Kedlaya, and D. Roe)
Arithmetic geometry, number theory, and computation, a volume of the Simons Symposia series by Springer, 2021, pp. 375-448 - Efficient Differentially Private Secure Aggregation for Federated Learning via Hardness of Learning with Errors (ordered author list: T. Stevens, C. Skalka, C. Vincent, J. Ring, S. Clark, J. Near)
32st USENIX Security Symposium (USENIX Security 22), 2022, pp. 1379-1395 - Counterexamples to a conjecture of Ahmadi and Shparlinski (with T. Dupuy, K. Kedlaya, and D. Roe)
Experimental Mathematics, vol. 32 (3), 2023, pp. 540-544. - Determining the primes of bad reduction of CM curves of genus 3 (with S. Ionica, P. Kilicer, K. Lauter, E. Lorenzo Garcia, and A. Manzateanu)
The Quarterly Journal of Mathematics, vol. 75 (1), 2024, pp. 239-276. - Failing to hash into supersingular isogeny graphs (with J. Booher, R. Bowden, J. Doliskani, T. B. Fouotsa, S. D. Galbraith, S. Kunzweiler, S.-P. Merz, C. Petit, B. Smith, K. E. Stange, Y. B. Ti, J. F. Voloch, C. Weitkämper, L. Zobernig)
The Computer Journal, vol. 67 (8), August 2024, pp. 2702-2719. - Foldable recursive proofs of isogeny computation with reduced time complexity (with K. Maughan and J. Near)
accepted for publication in the program of theIEEE International Conference on Quantum Computing and Engineering -- QCE24.
Theses I have advised
- Garvin Gaston, Hilbert Class Fields of Imaginary Quadratic Fields and Reflex Fields of Certain Sextic CM Fields,
MSc, August 2017 - Rosie Steinberg, Enumerating Curves of Genus 2 over Finite Fields,
BA, May 2018 - Grace Brill, Maximal Artin-Schreier Curves for Coding Theory,
BS, December 2019 - Alec Critten, Characterizing Insecure Error Distributions for Various RLWE Problems,
BS, May 2021 - Marcus Elia, Loss of Precision in Implementations of the Toom-Cook Algorithm,
PhD, May 2021 - Annie Zhang, An Analysis of a Linear Algebra Based Group Key Exchange Protocol,
MSc, August 2023 - Sarah Days-Merrill, Ring Learning with Errors,
PhD, May 2024 - Jesse Franklin, Computing the Canonical Ring of Certain Stacks,
PhD, May 2024; co-advised with Taylor Dupuy
Presentations
- Slides from my presentation on The Number theory behind cryptography at UVM Math Day 2017