London Junior Number Theory Seminar
2025/2026
2025/2026
This is the webpage for the London JNT seminar of 2025/2026, organised by Simon Alonso, Lucie Gatzmaga, Haoran Liang, and Naina Praveen. Here you can find previous and upcoming talks. Last year's website can be viewed here.
This seminar provides a space for London-based PhD students in number theory to learn about the research of their peers, as well as having the chance to present their own work. The aim is to keep the talks at a understandable level, and to prepare students for the London number theory seminar. In addition, it is a chance for us to gather together, socialize, and enjoy the snacks!
Check out here for other seminars in London that may be of interest.
When: Tuesdays at 5:00pm (see talks for exact dates).
Where: Room KIN 616 (old name K6.63), Strand Building, Kings College London.
TBC
28 October 2025, Kenza Memlouk (Université de Strasbourg)
Abstract: TBC
A Brief Introduction to the Tamagawa Number Conjecture
21 October 2025, Wenhan Zhang (KCL)
Abstract: I shall briefly introduce the central problem in Special Value Conjectures: the Tamagawa Number Conjecture. After introducing the related concepts first, I shall give a statement of the conjecture. Then I shall introduce how this conjecture naturally renders a few familiar results/conjectures as its special cases. Finally (if time permits), I shall introduce the current development and works on this problem. This talk shall be a rather non-technical overview.
Recovering reduction types of elliptic curves through torsion
14 October 2025, Naina Praveen (UCL)
Abstract: The classification of an elliptic curve's reduction at a prime $p$ yields interesting arithmetic invariants. Classically, one can determine this reduction type via Tate's algorithm, a method that depends on explicit Weierstrass models. A more intrinsic approach is to use representation theory — the Néron-Ogg-Shafarevich criterion allows for a classification of potentially good reduction types for primes p>3. In this talk, I shall introduce another method that extends these results by incorporating the geometric configuration of the l-torsion points, specifically their p-adic distances. This approach extends the full classification to the case of p=3. I will then present a rough classification for p=2 and walk through the problems/examples that prevent a complete determination in that case, along with a sketch of the proof. If time permits, I might introduce how the above techniques could be generalised to genus 2 curves.
What is the Taylor-Wiles patching?
7 October 2025, Simon Alonso (Imperial)
Abstract: In this talk I will give a hopefully not too technical introduction to one of the techniques that allowed Taylor and Wiles to prove the modularity theorem that was the final step for proving Fermat's Last Theorem. After explaining how the patching works, I will present some generalisations of the method to different contexts. If time permits, I will also briefly explain how patching was used to produce a candidate for the $p$-adic local Langlands correspondence.
If you'd just like to attend, then you are welcome to just turn up! If you don't have access to KCL, then make a note of one of our emails,
firstname [dot] lastname [dot] 24 [at] ucl [dot] ac [dot] uk
in case you have trouble entering the university. Please note that Haoran's email address is slightly different from the format above — it is haoran.1.liang@kcl.ac.uk. To receive updates on the talks via email, join the mailing list: https://www.mailinglists.ucl.ac.uk/mailman/listinfo/juniornumbertheory.