Thu, 28 Jan 2016

16:00 - 17:00
L5

Iwasawa theory for the symmetric square of a modular form

David Loeffler
(University of Warwick)
Abstract

Iwasawa theory is a powerful technique for relating the behaviour of arithmetic objects to the special values of L-functions. Iwasawa originally developed this theory in order to study the class groups of number fields, but it has since been generalised to many other settings. In this talk, I will discuss some new results in the Iwasawa theory of the symmetric square of a modular form. This is a joint project with Sarah Zerbes, and the main tool in this work is the Euler system of Beilinson-Flach elements, constructed in our earlier works with Kings and Lei.

Thu, 21 Jan 2016

16:00 - 17:00
L5

Height of rational points on elliptic curves in families

Pierre Le Boudec
(EPFL (Ecole Polytechnique Federale de Lausanne))
Abstract

Given a family $F$ of elliptic curves defined over $Q$, we are interested in the set $H(Y)$ of curves $E$ in $F$, of positive rank, and for which the minimum of the canonical heights of non-torsion rational points on $E$ is bounded by some parameter $Y$. When one can show that this set is finite, it is natural to investigate statistical properties of arithmetic objects attached to elliptic curves in the set $H(Y)$. We will describe some problems related to this, and will state some results in the case of families of quadratic twists of a fixed elliptic curve.

Wed, 02 Dec 2015

11:30 - 12:30
S2.37

Representation Dimension and Quasihereditary algebras

Teresa Conde
(Oxford)
Abstract


The representation dimension of an algebra was introduced in the early 70's by M. Auslander, with the goal of measuring how far an algebra is from having finite number of finitely generated indecomposable modules (up to isomorphism). This invariant is not well understood. For instance, it was not until 2002 that O. Iyama proved that every algebra has finite representation dimension. This was done by constructing special quasihereditary algebras. In this talk I will give an introduction to this topic and I shall briefly explain Iyama's construction.

Tue, 01 Dec 2015
15:00
L1

Data Assimilation for Weather Forecasting: Reducing the Curse of Dimensionality

Professor Philippe Toint
(University of Namur)
Abstract
Weather prediction and, more generally, data assimilation in earth sciences, set a significant computing challenge 
because the size of the problem involved is very large.  The talk discusses algorithmic aspects related to the numerical 
solution of such problems and, in particular, focusses on how the lower dimensionality of the (dual) observation space 
may be used to advantage for computing a primal solution.  This is achieved both by adapting the preconditioned 
conjugate gradient and trust-region algorithms to dual space and by reducing the dimensionality of the latter as much 
as possible using observation hierarchies.
 
 
Mon, 30 Nov 2015

17:00 - 18:00
L1

Slightly Rubbish Modular Ax-Lindemann

Haden Spence
(Oxford University)
Abstract

In quite an elementary, hands-on talk, I will discuss some Ax-Lindemann type results in the setting of modular functions.  There are some very powerful results in this area due to Pila, but in nonclassical variants we have only quite weak results, for a rather silly reason to be discussed in the talk.

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