Degrees:
Ph.D., Univ. of Sheffield
MMath, Univ. of Cambridge
B.A., Univ. of Cambridge
Ariel Weiss is an algebraic number theorist specialising in arithmetic statistics and the arithmetic of Galois representations. He earned his B.A. and M.Math. from the University of Cambridge, before completing his Ph.D. at the University of Sheffield. Prior to joining Trinity, Ariel held postdoctoral positions at The Hebrew University of Jerusalem, Ben-Gurion University of the Negev, and The Ohio State University. His research explores the arithmetic of Galois representations, particularly those arising from Siegel modular forms, as well as questions in arithmetic statistics, including theorems and heuristics related to rational points on elliptic curves. In the classroom, Ariel strives to foster a supportive and interactive environment, where students feel comfortable making mistakes, and are encouraged to think critically and to build confidence as mathematical thinkers.
|
-
Algebraic number theory
-
Arithmetic statistics
-
Galois representations
-
Siegel modular forms
|
- Kumar, A., and Weiss, A. (2025). Distinguishing Siegel modular forms. Available at https://arxiv.org/abs/2506.22264.
- Jarossay, D., Lilienfeldt, D. T.-B. G., Saettone, F. M., Weiss, A.,
and Zehavi, S. (2024). Polylogarithmic motivic Chabauty-Kim for P^1 minus three points: the geometric step via resultants. Available at: http://arxiv.org/abs/2408.07400. Algebra & Number Theory (to appear)
- Duan,
L., Wang, X. and Weiss, A. (2024), Five-dimensional compatible systems
and the Tate conjecture for elliptic surfaces. Available at:
http://arxiv.org/abs/2406.03617.
- Ophir, A. and Weiss, A. (2024),
Maximal stable lattices in representations over discretely valued
fields. Available at: http://arxiv.org/abs/2401.10183.
- Kumar, A., Kumari, M. and Weiss, A. (2022), On the Lang–Trotter conjecture for Siegel modular forms. Available at: http://arxiv.org/abs/2201.09278.
- Shnidman, A. and Weiss, A. (2025), Ranks of abelian varieties in cyclotomic twist families. Algebra & Number Theory, Vol. 19 (2025), No. 1, 39-75.
- Ophir, A. and Weiss, A. (2024), On Ribet’s Lemma for GL(2) modulo prime powers, Research in the Mathematical Sciences 11, 9 (2024).
- Shnidman, A. and Weiss, A. (2023), Rank growth of elliptic curves over
N-th root extensions, Trans. Amer. Math. Soc. Ser. B 10 (2023), 482-506.
- Shnidman, A. and Weiss, A. (2022), Elements of prime order in Tate–Shafarevich groups of abelian varieties over Q, Forum of Mathematics, Sigma, 10, p. e98.
- Berger, T., Weiss, A. (2022), Lafforgue pseudocharacters and parities of limits of Galois representations. manuscripta math. 168, 225–256 (2022).
- Weiss, A. (2022), On the images of Galois representations attached to low weight Siegel modular forms. J. London Math. Soc., 106: 358-387.
|
- AMS-Simons Travel Grant, 2023
- Noriko Sakurai Award for outstanding postdoctoral research, Ben-Gurion University, 2023
- T.M. Flett Prize in pure mathematics, The University of Sheffield, 2019
|
|