Organizers.
Nathan Grieve: nathan.m.grieve@gmail.com (Contact organizer)
Antonio Lei: alantoniolei@gmail.com
Webpage of the Ottawa-Carleton Number Theory group:
Fall 2025
We will schedule a collection of virtual and in person talks. The defalut seminar time slot is Monday @ 09:00-10:00 Ottawa time (however this may vary from time to time). The Zoom link is: here. Email any of the organizers for the Zoom password hint. More information will be posted here in due time.
List of confirmed speakers:
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22 September, 2025
In person lecture (with Zoom live stream)
Brandon Hanson
Title: Arithmetic combinatorics from high-dimensional probability
Abstract: The use of probability in combinatorics was pioneered by Erdos, rather famously. Recently, techniques from high-dimensional probability have proved fruitful in attacking problems where sparsity is a prominent feature. I will highlight its role in work joint with Rudnev, Shkredov and Zhelezov on the sum-product problem, and if time permits, newer results joint with Waterhouse convolutions in the boolean cube.
Location: STEM-664
Time: 09:00-10:00
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29 September, 2025
In person lecture (with Zoom live stream)
Omer Avci (University of Ottawa)
Title: Torsion of Rational Elliptic Curves over the Galois Extensions of $\mathbb{Q}$
Abstract: Mazur's celebrated theorem gives a complete classification of the torsion subgroups $E(\mathbb{Q})_{\mathrm{tors}}$ for elliptic curves $E/\mathbb{Q}$. This result inspired the broader problem of classifying $E(L)_{\mathrm{tors}}$ for elliptic curves $E/L$, where $L$ is a field of characteristic zero. In this talk, I will first review results from the literature and some variants of this problem. I will then focus on the case where $L/\mathbb{Q}$ is a Galois extension, outlining our methods and presenting two families of results: when $L = \mathbb{Q}(\zeta_p)$ for a prime $p$, and when $L$ is a $\mathbb{Z}_p$-extension of a quadratic field $K$.
Location: STEM-664
Time: 09:00-10:00
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6 October, 2025
Virtual lecture (Zoom live stream)
Nic Banks (University of Waterloo)
Title: Classification results for intersective polynomials with no integral roots
Abstract: In this talk, I describe the contents of my recently-defended PhD thesis on strongly intersective polynomials. These are polynomials with no integer roots but with a root modulo every positive integer, thereby constituting a failure of the local-global principle. We start by describing their relation to Hilbert's 10th Problem and an algorithm of James Ax. These are fascinating objects which make contact with many areas of math, including permutation group theory, splitting behaviour of prime ideals in number fields, and Frobenius elements from class field theory.
In particular, we discuss constraints on the splitting behaviour of ramified primes in splitting fields of intersective polynomials, building on the work of Berend-Bilu (1996) and Sonn (2008). We also explain the computation of a list of possible Galois groups of such polynomials, which includes many examples and which supports some recent conjectures of Ellis & Harper (2024).
Time permitting, we end by discussing future work, including results from permutation group theory and from character theory.
Location: Zoom live stream
Time: 09:00-10:00
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20 October, 2025
In person lecture (with Zoom live stream)
Sara Sajadi (University of Toronto)
Title: A Unified Finiteness Theorem For Curves
Abstract: This talk presents a unified framework for finiteness results concerning arithmetic points on algebraic curves, exploring the analogy between number fields and function fields. The number field setting, joint work with F. Janbazi, generalizes and extends classical results of Birch–Merriman, Siegel, and Faltings. We prove that the set of Galois-conjugate points on a smooth projective curve with good reduction outside a fixed finite set of places is finite, when considered up to the action of the automorphism group of a proper integral model. Motivated by this, we consider the function field analogue, involving a smooth and proper family of curves over an affine curve defined over a finite field. In this setting, we show that for a fixed degree, there are only finitely many étale relative divisors over the base, up to the action of the family's automorphism group (and including the Frobenius in the isotrivial case). Together, these results illustrate both the parallels and distinctions between the two arithmetic settings, contributing to a broader unifying perspective on finiteness.
Location: STEM-464
Time: 09:00-10:00
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27 October, 2025
In person lecture (with Zoom live stream)
Charlie Wu (University of Toronto)
Title: Compactness and character varieties
Abstract: Let $X$ be an orientable genus $g$ surface with $n$ punctures. Relative character varieties are spaces parametrizing isomorphism classes of representations of $\pi_1(X)$ satisfying some local conditions around the punctures. When this space is a single point, some remarkable work of Katz shows that the unique representation in this space has interesting arithmetic and complex geometric properties - namely that it is defined over the ring of integers of a number field and it ``comes from geometry". We discuss the geometry of this space when it is larger than a point, and we give a classification of their compact components. This is joint work with Daniel Litt.
Location: STEM-664
Time: 09:00-10:00
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3 November, 2025
In person lecture (with Zoom live stream)
Felix Baril Boudreau (CICMA & Université du Luxembourg)
Title: Abelian varieties with homotheties
Abstract: Let $A$ be an Abelian variety defined over a number field $K$. The celebrated Bogomolov-Serre theorem states that, for any prime $\ell$, the image $G_\ell$ of the $\ell$-adic representation of the absolute Galois group of $K$ contains all $c$-th power homotheties, where $c$ is a positive constant. If $K$ is a global function field, the analogous statement fails in general, since Zahrin has shown the existence of ordinary Abelian varieties of positive dimensions defined over $K$, for which $G_\ell$ only contains finitely many homotheties. In this talk, I will discuss my ongoing joint work with Sebastian Petersen (University of Kassel), in which we prove, under suitable additional assumptions, an analogue of Bogomolov--Serre Theorem when $K$ is a finitely generated field of positive characteristic.
Location: STEM-664
Time: 09:00-10:00
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10 November, 2025
In person lecture (with Zoom live stream)
Luochen Zhao (Morningside Center of Mathematics)
Title: TBD
Abstract: TBD
Location: STEM-664
Time: 09:00-10:00
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17 November, 2025
In person lecture (with Zoom live stream)
Luochen Zhao (Morningside Center of Mathematics)
Title: TBD
Abstract: TBD
Location: STEM-664
Time: 09:00-10:00
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24 November, 2025
In person lecture (with Zoom live stream)
Ben Forras (University of Ottawa)
Title: TBD
Abstract: TBD
Location: STEM-664
Time: 09:00-10:00
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TBD
In person lecture (with Zoom live stream)
Romain Branchereau (McGill University)
Title: TBD
Abstract: TBD
Location: STEM-664
Time: TBD (Winter 2026?)
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TBD
Virtual lecture (Zoom live stream)
Flora Poon (NCTS, Taiwan)
Title: TBD
Abstract: TBD
Location: Zoom live stream
Time: TBD (Winter 2026)
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TBD
In person lecture (with Zoom live stream)
Sunil Lakshmana Naik (Queen's University)
Title: TBD
Abstract: TBD
Location: Zoom live stream
Time: TBD (Winter 2026)
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TBD
Virtual lecture (Zoom live stream)
Alessandro Fazzari (University of Montreal)
Title: TBD
Abstract: TBD
Location: Zoom live stream
Time: TBD (Winter 2026)
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