2025 CMS Winter Meeting
Toronto, Dec 5 - 8, 2025
Number Theory by Early Career Researchers
Org: Jérémy Champagne, AJ Fong and Zhenchao Ge (University of Waterloo)
[PDF]
Org: Jérémy Champagne, AJ Fong and Zhenchao Ge (University of Waterloo)
[PDF]
- ALI ALSETRI, University of Kentucky
- FÉLIX BARIL BOUDREAU, CICMA & Université du Luxembourg
- HYMN CHAN, University of Toronto
- JOSE CRUZ, University of Calgary
- NIC FELLINI, Queen’s University
- KEIRA GUNN, Mt Royal University
- FATEMEH JALALVAND, University of Calgary
- NICOL LEONG, University of Lethbridge
- ISABELLA NEGRINI, University of Toronto
Rigid Cocycles and the p-adic Kudla Program [PDF]
- FÉLIX BARIL BOUDREAU, CICMA & Université du Luxembourg
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Rigid cocycles, introduced by Darmon and Vonk in 2017, offer a promising framework to extend complex multiplication theory to real quadratic fields, suggesting a theory of “real multiplication.” They exhibit striking parallels with modular forms and are central to the emerging p-adic Kudla program. While the classical Kudla program studies the theta correspondence between automorphic forms on different groups, the p-adic version appears to replace automorphic forms with rigid cocycles. Although a theory for a p-adic theta correspondence has yet to be developed, recent results suggest its existence. In this talk, I present some of these p-adic results, draw comparisons to the classical setting, and discuss the evidence for an underlying p-adic theta correspondence.
- EMILY QUESADA-HERRERA, University of Lethbridge
- FATEME SAJADI, University of Toronto
- GIAN CORDANA SANJAYA, University of Waterloo
- KYLE YIP, Georgia Institute of Technology
Diophantine tuples and Diophantine powersets [PDF]
- FATEME SAJADI, University of Toronto
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Let $k,n$ be integers with $k\geq 2$ and $n \neq 0$. A set $A$ of positive integers is a Diophantine tuple with property $D_{k}(n)$ if the product of $ab+n$ is a perfect $k$-th power for every $a,b\in A$ with $a\neq b$. These Diophantine tuples have been studied extensively. In this talk, I will discuss some recent progress on ``Diophantine powersets" (first studied by Gyarmati, S\'{a}rk\"{o}zy, and Stewart), where we allow $ab+n$ to be a perfect power instead of a perfect $k$-th power for some fixed $k$. Joint work with Ernie Croot.
- XIAO ZHONG, University of Waterloo