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.
Note: up to date details for speakers this term are here.This term (Spring 2019), the seminar will be hosted by UCL, and will be on Wednesdays at 4pm in room 505 of the maths department (25 Gordon St), starting 9th Jan. The organisers are Chris Birkbeck and Alex Torzewski. Up to date details are here. The seminar will be preceded by tea/coffee in the 6th floor common room.
09 Jan 2019  Adam Morgan (Glasgow)
Title: Parity of Selmer ranks in quadratic twist families.
Abstract: We study the parity of 2Selmer ranks in the family of quadratic twists of a fixed principally polarised abelian variety over a number field. Specifically, we prove results about the proportion of twists having odd (resp. even) 2Selmer rank. This generalises work of Klagsbrun–Mazur– Rubin for elliptic curves and Yu for Jacobians of hyperelliptic curves. Several differences in the statistics arise due to the possibility that the Shafarevich–Tate group (if finite) may have order twice a square.
16 Jan 2019  Helene Esnault (Freie Universität Berlin)
Title: Vanishing theorems for étale sheaves
Abstract: The talk is based on two results: Scholze’s Artin type vanishing theorem for the projective space, which I proved without perfectoid geometry (which implies in particular that it holds in positive characteristic), and a rigidity theorem for subloci of the ladic character variety stable under the Galois group over a number field (joint work in progress with Moritz Kerz).
23 Jan 2019  Adam Logan
Title: Automorphism groups of K3 surfaces over nonclosed fields
30 Jan 2019  Jan Kohlhaase (Universität DuisburgEssen)
Title: Fourier analysis on universal formal covers
Abstract: : The padic Fourier transform of Schneider and Teitelbaum has complicated integrality properties which have not yet been fully understood. I will report on an approach to this problem relying on the universal formal cover of a pdivisible group as introduced by Scholze and Weinstein. This has applications to the representation theory of padic division algebras.
06 Feb 2019  Mladen Dimitrov (Université de Lille)
13 Feb 2019  Yiannis Petridis (UCL)
Inaugural lecture
20 Feb 2019  Pankaj Vishe (Durham)
27 Feb 2019  Martin Gallauer (Oxford)
06 Mar 2019  Edgar Assing (Bristol)
13 Mar 2019  Jan Vonk (Oxford)
Title: Singular moduli for real quadratic fields and padic mock modular forms
Abstract: The theory of complex multiplication describes finite abelian extensions of imaginary quadratic number fields using singular moduli, which are special values of modular functions at CM points. I will describe joint work with Henri Darmon in the setting of real quadratic fields, where we construct padic analogues of singular moduli through classes of rigid meromorphic cocycles. I will discuss padic counterparts for our proposed RM invariants of classical relations between singular moduli and the theory of weak harmonic Maass forms.
20 Mar 2019  Alice Pozzi (UCL)
The seminar will be preceded by various study groups.
A list of previous seminar talks is here.
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