London Number Theory Seminar

The London Number Theory Seminar is held weekly, on Wednesdays, during term time. The location of the seminar cycles between KCL, Imperial College and UCL.

This term (Autumn 2015), the seminar will be hosted by Imperial College, and will be held on Wednesdays from 4pm to 5pm in room 140 in the Huxley Building. The seminar is organized by David Helm, and starts on 7th October.

The talks will be preceded by tea/coffee in Imperial's common room (room 549 Huxley) from around 3:30.

07/10/15 Martin Orr (Imperial)
Title: A bound for rational representations of isogenies in the fundamental set
Abstract: Let z and z' be two points in the standard fundamental set in the upper half-plane. If the corresponding elliptic curves are related by an isogeny of degree N, then there is a 2x2 matrix with integer coefficients and determinant N which maps z to z'. As an ingredient in their work on unlikely intersections, Habegger and Pila proved that the entries of this matrix are bounded by a uniform polynomial in N. I will discuss the generalisation of this result to moduli of abelian varieties and beyond, to Riemannian symmetric spaces of non-compact type.

14/10/15 Stephane Bijakowski (Imperial)
Title: The partial degrees of the canonical subgroup
Abstract: If the Hasse invariant of a p-divisible group is small enough, then one can construct a canonical subgroup inside its p-torsion. I will first present an alternative approach to this problem, assuming the existence of a subgroup satisfying some simple conditions. A key property is the relation between the Hasse invariant and the degree of the canonical subgroup. When one considers a p-divisible group with extra structures, more information is available. I will define the partial Hasse invariants, the partial degrees, and relate them for the canonical subgroup.

21/10/15 Yiwen Ding (Imperial)
Title: L-invariants and local-global compatibility for GL2
Abstract: Let F be a totally real number field, w a prime of F above p, V a 2-dimensional p-adic representation of the absolute Galois group G_F of F which appears in etale cohomology of quaternion Shimura curves. When the restriction Vw of V to the decomposition group of G_F at w is semi-stable non-crystalline in Fontaine's sense, we can associate to Vw the so-called Fontaine-Mazur L-invariants, which are invisible in classical local Langlands correspondance. We show that these L-invariants can be found in the completed cohomology group of Shimura curves.

28/10/15 Rob Kurinczuk
Title: TBA

04/11/15 Paul Ziegler
Title: TBA

9/11/15 London-Paris Number Theory Seminar (in Paris)

11/11/15 Laurent Berger
Title: TBA

18/11/15 Julien Hauseux (Kings)
Title: TBA

25/11/15 TBA
Title: TBA

2/12/15 Jacques Benatar (Kings)
Title: TBA

9/12/15 TBA
Title: TBA

16/12/15 TBA
Title: TBA

The seminar will be preceded by the Study Groups, which this term will run 1200-1330 (p-adic Langlands) and 1400-1530 (the yoga of weights).

A list of previous seminar talks is here.

There are two mailing lists for number theory in London:

This page is maintained, poorly, by Kevin Buzzard. If anyone thinks they can do better they're welcome to offer.