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.
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Number theory
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Arithmetic statistics
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Galois representations
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Siegel modular forms
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Weiss, A., and Zou, D. (2026).
Experiments on 3-isogeny Selmer groups of elliptic curves with a 3-torsion point.
Preprint, arXiv:2609.31330.
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Kumar, A., and Weiss, A. (2026).
Distinguishing Siegel modular forms.
Journal of the London Mathematical Society 114(4), e70726.
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Jarossay, D., Lilienfeldt, D. T.-B. G., Saettone, F. M., Weiss, A., and Zehavi, S. (2024).
Polylogarithmic motivic Chabauty–Kim for P1\{0, 1, 8}: the geometric step via resultants.
Algebra & Number Theory (to appear).
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Duan, L., Wang, X., and Weiss, A. (2026).
Five-dimensional compatible systems and the Tate conjecture for elliptic surfaces.
Advances in Mathematics 503, 111236.
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Ophir, A., and Weiss, A. (2027).
Maximal stable lattices in representations over discretely valued fields.
Journal of Algebra 713, 515–533.
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Kumar, A., Kumari, M., and Weiss, A. (2026).
On the Lang–Trotter conjecture for Siegel modular forms.
Mathematika 72, e70108.
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Shnidman, A., and Weiss, A. (2025).
Ranks of abelian varieties in cyclotomic twist families.
Algebra & Number Theory 19(1), 39–75.
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Ophir, A., and Weiss, A. (2024).
On Ribet’s lemma for GL2 modulo prime powers.
Research in the Mathematical Sciences 11, Article 9.
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Shnidman, A., and Weiss, A. (2023).
Rank growth of elliptic curves over N-th root extensions.
Transactions of the American Mathematical Society, Series B 10, 482–506.
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Shnidman, A., and Weiss, A. (2022).
Elements of prime order in Tate–Shafarevich groups of abelian varieties over Q.
Forum of Mathematics, Sigma 10, e98.
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Berger, T., and Weiss, A. (2022).
Lafforgue pseudocharacters and parities of limits of Galois representations.
Manuscripta Mathematica 168, 225–256.
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Weiss, A. (2022).
On the images of Galois representations attached to low weight Siegel modular forms.
Journal of the London Mathematical Society 106(1), 358–387.
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- 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
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