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Mathematical Society*, Vol. 138 (12), 2010, pp. 4217-4229 - Osculation points at the cusps of Drinfeld modular curves (unpublished note)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 the*IEEE 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