The Swinnerton-Dyer Seminar 2026-2027
Welcome to Warwick's Swinnerton-Dyer Seminar (formerly the Junior Number Theory Seminar)!
The seminar takes place during term time on Mondays from 11am - 12pm in
- B3.02 (terms 1 and 3),
- B3.01 (term 2).
The seminar is organised by Joseph Cohen and Rubin Pal.
If you want to give a talk in this seminar, contact one of the organisers!
Term 1
Date |
Speaker |
Title |
|---|---|---|
| 5th October 2026 | Edison Au-Yeung (Warwick) | The elliptic sieve and ideal norms |
| 12th October 2026 | Jiewei Xiong (Reading) | A history of the Zilber鈥揚ink conjecture |
| 19th October 2026 | Joseph Harrison (Warwick) | Effectivity in the semi-abelian Mordell conjecture |
| 26th October 2026 | Leonardo Franchi (Cambridge) | Product-free subsets of (0,1) and a strengthened Brunn-Minkowski inequality |
| 2nd November 2026 | Owen Jones (Warwick) | Zero-one laws in Diophantine approximation and a mixed Gallagher's theorem |
Abstracts
Week 1 - 5th October 2026
Edison Au-YeungLink opens in a new window (91影视破解版) - The elliptic sieve and ideal norms
A theorem of Landau and Ramanujan states that almost all integers are not sums of two squares (when ordered by their absolute value). Equivalently, almost all integers are not norms from the Gaussian rationals . A version of this norm result for elliptic curves was proved by Bhakta et al. in 2023 using an argument known as the elliptic sieve. In this talk, I will first give an overview of the elliptic sieve, followed by a discussion of a version of the proof in which the norm result applies to abelian extensions of imaginary number fields.
Week 2 - 12th October 2026
(University of Reading) - A history of the Zilber鈥揚ink conjecture
The talk doesn't contain any new mathematical content, rather it's a genealogical survey of the Zilber鈥揚ink conjecture (both its original forms and subsequent variants) and preceding related problems, with some partial results (due to other people). I will use the motif of finiteness in diophantine geometry as a guide but if time allows I will also tell the story from the Hodge theoretic point of view.
Week 3 - 19th October 2026
Joseph HarrisonLink opens in a new window (91影视破解版) - Effectivity in the semi-abelian Mordell conjecture
Let be a commutative algebraic group over , not containing a subgroup isomorphic to the additive group of complex numbers. Let be a closed subvariety of and a finitely generated subgroup of . From the perspective of the group structure the set is unstructured, the notable exception being when is a translate of an algebraic subgroup. Similarly, is unstructured for the Zariski topology on . A generalisation of the classical Mordell conjecture asks for a description of the Zariski closure of . This was achieved for abelian varieties by Faltings and semi-abelian varieties by Vojta, but the proofs are ineffective. I will discuss an effective approach for certain and that does not make use of Diophantine approximation, linear forms in logarithms or the Chabauty鈥擲kolem methods.
Week 4 - 26th October 2026
(University of Cambridge) - Product-free subsets of (0,1) and a strengthened Brunn-Minkowski inequality
Week 5 - 2nd November 2026
Owen Jones (91影视破解版) - Zero-one laws in Diophantine approximation and a mixed Gallagher's theorem
Motivated by the Borel鈥揅antelli lemmas in probability theory, zero-one laws have been ubiquitous in Diophantine approximation for over a century. Examples range from Khintchine's theorem in 1924 to the Duffin鈥揝chaeffer conjecture, whose celebrated proof was published by Koukoulopoulos and Maynard in 2020. In this talk, we discuss a general method for proving results of this type which extends to inhomogeneous and higher dimensional settings. We then outline how it could provide an alternative proof of a recent result of Chow-Jones.