London Number Theory Seminar

UCL King's Imperial College

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 (Summer 2019), the seminar will be hosted by Kings College, and will be held on Wednesdays in KCL room K-1.56 (King's building, floor (-1)), starting at 1600. The organisers are Eran Assaf and James Newton.

The talks start on Wed 24th April and finish on 3rd July. The talks will be preceded by tea at 1530 in S5.21, the common room on the 5th floor. Important: The most up-to-date website for information on the talks this term is on Eran's website.

24th April 2019 - Jesse Jääsaari (University of Helsinki)
Title: Exponential Sums Involving Fourier Coefficients of higher rank automorphic forms
Abstract: In this talk I will describe various conjectures concerning correlations between Fourier coefficients of higher rank automorphic forms and different exponential phases. I will also discuss recent work (partly in progress) towards some of these conjectures.

01 May 2019 - Kazim Büyükboduk (UC Dublin)
Title: Rank-2 Euler systems for non-ordinary symmetric squares Abstract: According to Beilinson's conjectures, the leading term of an L-function at a "generic" non-critical point should be explained by special elements in the highest exterior power of the relevant motivic cohomology. p-adic (étale) realisations of these special elements would in turn give rise to (higher rank) Euler systems. I will report on joint work with A. Lei, where we obtain a rank-2 Euler system associated to the symmetric square of an eigenform at a non-ordinary prime p twisted by a Dirichlet character, whose non-triviality is accounted by p-adic L-values.

07-08 May 2019 - London-Paris Number Theory Seminar.

08 May 2019 - Ben Heuer (King's College London)
Title: perfectoid modular forms and a tilting isomorphism at the boundary of weight space
Abstract: Similarly to how complex modular forms are defined as functions on the complex upper half plane, Chojecki--Hansen--Johansson describe p-adic modular forms as functions on Scholze's perfectoid modular curve at infinite level. In this talk, we show that the appearance of perfectoid spaces in this context is not just a technical coincidence, but that this definition gives rise to 'perfectoid phenomena' appearing in the world of p-adic and classical modular forms. As an example of this, we discuss a tilting isomorphism of p-adic modular forms near the boundary of weight space which gives a new perspective on the space of T-adic modular forms defined by Andreatta--Iovita--Pilloni. This isomorphism can be explained by a theory of 'perfectoid modular forms' that we will also discuss in this talk.

15 May 2019 - No seminar, we're all at the p-adic Langlands Programme and Related Topics workshop.

22 May 2019 - Eva Viehmann (Technical University of Munich)
Title: Affine Deligne-Lustig varieties
Abstract: Affine Deligne-Lusztig varieties are defined as certain subschemes of affine flag varieties using Frobenius-linear algebra. They are used in arithmetic geometry to describe the reduction of Shimura varieties. Motivated by this relation, I will report on recent geometric results describing affine Deligne-Lusztig varieties, and applications.

29 May 2019 - Eugenia Rosu (University of Arizona)
Title: Special cycles on orthogonal Shimura varieties
Abstract: Extending on the work of Kudla-Millson and Yuan-Zhang-Zhang, together with Yott we are constructing special cycles for a specific GSpin Shimura variety. We further construct a generating series that has as coefficients the cohomology classes corresponding to the special cycle classes on the GSpin Shimura variety and show the modularity of the generating series in the cohomology group over C.

05 June 2019 - Paul Ziegler (University of Oxford)
Title: Geometric stabilization via p-adic integration
Abstract: The fundamental lemma is an identity of integrals playing an important role in the Langlands program. This identity was reformulated into a statement about the cohomology of moduli spaces of Higgs bundles, called the geometric stabilization theorem, and proved in this form by Ngô. I will give an introduction to these results and explain a new proof of the geometric stabilization theorem, which is joint work with Michael Groechenig and Dimitri Wyss, using the technique of p-adic integration.

12 June 2019 - Ramla Abdellatif (Université de Picardie Jules Verne)

19 June 2019 - Mikhail Gabdullin (Lomonosov Moscow State University)

26 June 2019 -

3 July 2019 - Christopher Frei (University of Manchester)
Title: Average bounds for l-torsion in class groups.
Abstract: Let l be a positive integer. We discuss average bounds for the l-torsion of the class group for some families of number fields, including degree-d-fields for d between 2 and 5. Refinements of a strategy due to Ellenberg, Pierce and Wood lead to significantly improved upper bounds on average. The case d=2 implies the currently best known upper bounds for the number of D_p - fields of bounded discriminant, for odd primes p. This is joint work with Martin Widmer. (The results presented here are different from those presented by Martin Widmer in his talk with a similar title in Jan 2018.)

The seminar will be preceded by various study groups.

A list of previous seminar talks is here.

There are two mailing lists for number theory in London:

This page is maintained by Kevin Buzzard.