Number Theory Seminars 201112
 The seminars are held on Mondays at 15:00 in Room B3.03 – Mathematics Institute
Organiser: Damiano Testa
201112 Term 3
 23 April 2012 — Carlos de VeraPiquero (Barcelona, visiting Warwick)
Title: Galois representations over fields of moduli and rational points on Shimura curves
Abstract
 30 April 2012 — No seminar
 7 May 2012 — Bank holiday (No seminar)
 14 May 2012 (in MS.03) — Chris Smyth (Edinburgh) **Note unusual room**
Title: Sequences and congruences related to Ramanujan's tau function.
Abstract: I discuss some sequences arising from the tau function, and resulting congruences. These differ from the classical ones.
 17 May 2012 (in MS.03 at 3pm) — Otmar Venjakob (Heidelberg) **Note unusual date**
Title: From the Birch and Swinnerton Dyer Conjecture to the GL_2 Main Conjecture for elliptic curves.
Abstract: Starting from the BSDconjecture we try to motivate the formulation of the noncommutative Iwasawa Main Conjecture and survey the known results in this context. The talks trys to be rather elementary and is directed to nonexperts.
 21 May 2012 — James McKee (Royal Holloway)
Title: Salem graphs: What? Why? Whither?
Abstract: Certain classes of algebraic integers can be studied fruitfully by associating them with combinatorial objects. For example, certain Salem numbers can be associated with Salem graphs, but other algebraic integers (and other combinatorial objects) will be considered too. This talk will be a survey of some results in this area, with an emphasis on number theory rather than combinatorics, describing recent research and discussing several interesting problems that remain open.
 28 May 2012 — Lynne Walling (Bristol)
Title: Siegel modular forms, Hecke operators, and Eisenstein series.
Abstract: To study the number of times a quadratic form represents other quadratic forms, Siegel introduced generalised theta series. These were the first examples of what are now known as Siegel modular forms. As with elliptic modular forms, we have Hecke operators acting on the forms; however, in the case of Siegel modular forms, the action of Hecke operators on Fourier coefficients is much more complicated. We also have Eisenstein series that are Siegel modular forms; their Fourier coefficients are much more complicated than those of Eisenstein series that are elliptic modular forms. In fact, given a basis for the subspace of Siegel Eisenstein series of level greater than 1, formulas for the Fourier coefficients for most of these Eisenstein series are currently unknown.
In this talk, I will introduce Siegel modular forms, Hecke operators, and Eisenstein series, with particular focus on the case of "Siegel degree" 2. I will describe how to determine the action of the Hecke operators on Eisenstein series of squarefree level. This gives us Hecke relations among these Eisenstein series; in the case of trivial character, these relations can be used to generate the Fourier coefficients of a basis for the subspace of Eisenstein series. As well, this subspace has a basis of simultaneous eigenforms (this holds for arbitrary character), and the above work allows us to compute their eigenvalues.This talk is designed for a general audience in pure mathematics.
Organiser: William Hart
201112 Term 2
 16 January 2012 Michael Mourao (Warwick)
The set of rational points of an algebraic curve.
 23 January 2012 Ambrus Pal (Imperial)
The BrauerManin obstruction to the localglobal principle for the embedding problem.
 30 January 2012 Luke Stanbra (Durham)
Modular forms, theta functions and a theta lift in the setting of SU(1,1).
 6 February 2012 Johan Bosman (Warwick)
Ranks of elliptic curves with prescribed torsion over number fields.
 13 February 2012 Alex Bartel (Postech)
Units of number fields and MordellWeil groups as Galois modules.
 20 February 2012 Tim Dokchitser (Bristol)
Lfunctions of hyperelliptic curves.
 27 February 2012 Arsen Elkin (Warwick)
De Rham cohomology of hyperelliptic jacobians in characteristic two.
 5 March 2012 Teruyoshi Yoshida (Cambridge)
On nonabelian LubinTate theory for the Iwahori level of GL(n).
 12March 2012 Marco Streng (Warwick)
Smaller class invariants for quartic CMfields.
 2 April 2012 Gaetan Bisson (Macquarie)
Abelian varieties, isogenies and endomorphism rings.
Organiser: David Loeffler
201112 Term 1

3 Oct Ivan Fesenko (Nottingham)
From explicit 2d class field theory via zeta integrals to the rank part of the BSD conjecture 
10 Oct Thanasis Bouganis (Heidelberg)
Nonabelian padic Lfunctions and Eisenstein series of unitary groups 
17 Oct Steve Donnelly (Sydney)
Computing Hilbert modular forms and modular elliptic curves 
24 Oct Sarah Zerbes (Exeter)
Iwasawa theory and padic Lfunctions over Zp^{2}extensions 
31 Oct Kimi Tsukazaki (Warwick)
Explicit isogenies of lower degree 
7 Nov Chris Hughes (York)
Linear combinations of Lfunctions 
14 Nov Simon Wadsley (Cambridge)
Dimensions of Iwasawa modules 
21 Nov Richard Hill (UCL)
Metaplectic eigenvarieties 
28 Nov Hendrik Lenstra (Leiden)
Prime degree wild extensions of local fields 
5 Dec Toby Gee (Imperial)
Recent progress on the automorphy of Galois representations