.: Summer Research Experiences program
The Summer Research Experiences program is aimed at undergraduate students who are interested in obtaining experience in number theory and machine learning research topics.
Summer 2026 program
** Applications open! **
Please submit your application via the Qualtrics link sent out to all 2nd/3rd year math major/honours students. Applications are due by 18th February.
Summer 2025 program
Perfect Numbers -- On the occurrence of prime factors and their exponents, run by N. Walji.
Undergraduate mentor: Mathew Drexel.
Elliptic Curves -- On the distribution of sign changes for traces of Frobenius, run by N. Walji.
Undergraduate mentor: Oliver Shen.
Topics in Machine Learning, run by L. Daniels.
Summer 2024 program
Matching densities for automorphic L-functions, run by N. Walji.
Graduate mentor: Kin Ming Tsang.
Natural language processing and machine learning, run by L. Daniels.
Summer 2023 program
On the distribution of traces of Frobenius for elliptic curves, run by N. Walji.
Graduate mentor: Kin Ming Tsang.
Summer 2022 program
On the distribution of coefficients of GL(2) automorphic L-functions, run by N. Walji.
Heuristics for a variant of the Lang-Trotter conjecture for elliptic curves, run by N. Walji.
Local to global principle for expected values over function fields, run by S. Schraven.
PDF summary
arXiv link to paper:
https://arxiv.org/abs/2212.00895
Published version in
INTEGERS, Volume 25 (2025):
Local to Global Principle for Higher Moments over Function Fields,
by Andy Hsiao, Junhong Ma Blackmer, Severin Schraven, and Ying Qi Wen
Summer 2021 program
Congruence class bias and the Lang-Trotter conjecture
For various families of elliptic curves over the integers, we demonstrate the existence of congruence class bias with respect to the Lang-Trotter conjecture. We also investigate such questions computationally for individual elliptic curves. Lastly, we show that the heuristics for the distribution of traces of Frobenius for elliptic curves are consistent with our observations of congruence class bias on average.
Paper: Congruence class bias and the Lang-Trotter conjecture for families of elliptic curves by S. Jarov, A. Khadra, and N. Walji.
Preprint version.
Published in Involve, Vol. 17 (2024), No. 4, 569–592.
.: Earlier Student Projects
Students have worked with me in areas related to:
• Elliptic curves
• L-functions
• Group theory
Past project topics have included:
• The Lang-Trotter conjecture
• Refinements of strong multiplicity one for automorphic L-functions
• Occurrence of Hecke eigenvalues for pairs of Maass forms.
