Forthcoming Seminars

Thu, 28/05/2009
16:00 		Werner Bley (Kassel) Number Theory Seminar Add to calendar L3
Numerical evidence for the equivariant Birch and Swinnerton-Dyer conjecture
In the first part of the talk we briefly describe an algorithm which computes a relative algebraic K-group as an abstract abelian group. We also show how this representation can be used to do computations in these groups. This is joint work with Steve Wilson. Our motivation for this project originates from the study of the Equivariant Tamagawa Number Conjecture which is formulated as an equality of an analytic and an algebraic element in a relative algebraic K-group. As a first application we give some numerical evidence for ETNC in the case of the base change of an elliptic curve defined over the rational numbers. In this special case ETNC is an equivariant version of the Birch and Swinnerton-Dyer conjecture
Thu, 28/05/2009
16:30 		Xanthippi Markenscoff (California) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
Radiated Fields, Energy-Release Rate and Evolution Equation for a Half-Space Eshelby Inclusion
In the context of the linear theory of elasticity with eigenstrains, the radiated fields, including inertia effects, and the energy-release rates (“driving forces”) of a spherically expanding and a plane inclusion with constant dilatational eigenstrains are calculated. The fields of a plane boundary with dilatational eigenstrain moving from rest in general motion are calculated by a limiting process from the spherical ones, as the radius tends to infinity, which yield the time-dependent tractions that need to be applied on the lateral boundaries for the global problem to be well-posed. The energy-release rate required to move the plane inclusion boundary (and to create a new volume of eigenstrain) in general motion is obtained here for a superposed loading of a homogeneous uniaxial tensile stress. This provides the relation of the applied stress to the boundary velocity through the energy-rate balance equation, yielding the “equation of motion” (or “kinetic relation”) of the plane boundary under external tensile axial loading. This energy-rate balance expression is the counterpart to the Peach-Koehler force on a dislocation plus the “self-force” of the moving dislocation.
Thu, 28/05/2009
17:00 		Tim Gendron (Mexico) Logic Seminar Add to calendar L3
Arithmetic and Geometric Irrationality via Substructures of Nonstandard Models
This purpose of this talk will be to introduce the idea that the spectrum of nonstandard models of a “standard” algebraic object can be used much like a microscope with which one may perceive and codify irrationality invisible within the standard model. This will be done by examining the following three themes:
  • Algebraic topology of foliated spaces We define the fundamental germ, a generalization of fundamental group for foliations, and show that the fundamental germ of a foliation that covers a manifold $ M $ is detected (as a substructure) by a nonstandard model of the fundamental group of $ M $.
  • Real algebraic number theory. We introduce the group $ (r) $ of diophantine approximations of a real number $ r $, a subgroup of a nonstandard model of the integers, and show how $ (r) $ gives rise to a notion of principal ideal generated by $ r $. The general linear group $ GL(2, \mathbb{Z}) $ plays here the role of a Galois group, permuting the real ideals of equivalent real numbers.
    • \item Modular invariants of a Noncommutative Torus. We use the fundamental germ of the associated Kronecker foliation as a lattice and define the notion of Eisenstein series, Weierstrass function, Weierstrass equation and j-invariant.
    Fri, 29/05/2009
    10:00     		Myles Allen, David Frame and Chris Farmer (Physics, Smith School and Maths, Oxford (respectively)) Industrial and Interdisciplinary Workshops Add to calendar DH 1st floor SR
    Bayesian and non-bayesian approaches to climate modelling
    Fri, 29/05/2009
    14:00     		Dr Francesca Shearer (Queen's University Belfast) Mathematical Biology and Ecology Seminar Add to calendar L3
    Mathematical modelling of cancer and radiotherapy
    Fri, 29/05/2009
    14:15     		Martin Schweizer (ETH) Nomura Seminar Add to calendar Oxford-Man Institute
    BSDEs from utility indifference valuation: Some new results and techniques
    One of the popular approaches to valuing options in incomplete financial markets is exponential utility indifference valuation. The value process for the corresponding stochastic control problem can often be described by a backward stochastic differential equation (BSDE). This is very useful for proving theoretical properties, but actually solving these equations is difficult. With the goal of obtaining more information, we therefore study BSDE transformations that allow us to derive upper and/or lower bounds, in terms of solutions of other BSDEs, that can be computed more explicitly. These ideas and techniques also are of independent interest for BSDE theory. This is joint work with Christoph Frei and Semyon Malamud.
    Fri, 29/05/2009
    16:30     		Professor Dave Benson Colloquia Add to calendar L2
    Classifying spaces and cohomology of finite groups
    I shall give a gentle introduction to the cohomology of finite groups from the point of view of algebra, topology, group actions and number theory
    Mon, 01/06/2009
    12:00     		David Tong (Cambridge) String Theory Seminar Add to calendar L3
    Berry Phase and Supersymmetry
    Abstract: I will give an introduction to the phenomenon of non-Abelian Berry phase. This process, which describes the holonomy of degenerate quantum states as parameters are varied, is governed by a non-Abelian gauge connection. I will explain why this set of ideas is particularly natural in supersymmetric quantum mechanics and will show that the connection is governed by well known equations of mathematical physics such as the Hitchin equation, the Bogomolnyi equation and generalizations.
    Mon, 01/06/2009
    14:15     		Oscar Randal-Williams (Oxford) Geometry and Analysis Seminar Add to calendar L3
    Monoids of moduli spaces of manifolds
    Joint work with Soren Galatius. We study categories C of d-dimensional cobordisms, from the perspective of Galatius, Madsen, Tillmann and Weiss. Their main result is the determination of the homotopy type of the classifying-space of such cobordism categories, as the infinite loop space of a certain Thom spectrum. One can investigate subcategories D of C having the property that the classifying-space BD is equivalent to BC, the smaller such D one can find the better. We prove that in may cases of interest, D can be taken to be a homotopy commutative monoid. As a consequence, the stable cohomology of many moduli spaces of surfaces can be identified with that of the infinite loop space of certain Thom spectra.
    Mon, 01/06/2009
    14:15     		Anastasia Papavasiliou (Warwick) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
    Parameter estimation for Rough Differential Equations
    My goal is to estimate unknown parameters in the vector field of a rough differential equation, when the expected signature for the driving force is known and we estimate the expected signature of the response by Monte Carlo averages. I will introduce the "expected signature matching estimator" which extends the moment matching estimator and I will prove its consistency and asymptomatic normality, under the assumption that the vector field is polynomial.  Finally, I will describe the polynomial system one needs to solve in order to compute this estimatior.
    Mon, 01/06/2009
    15:45     		TBA Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
    To Be Announced
    Mon, 01/06/2009
    15:45     		Dr Cornelia Drutu (Oxford) Topology Seminar Add to calendar L3
    The asymptotic geometry of mapping class groups and application
    I shall describe the asymptotic geometry of the mapping class group, in particular its tree-graded structure and its equivariant embedding in a product of trees. This can be applied to study homomorphisms into mapping class groups defined on groups with property (T) and on lattices in semisimple groups. The talk is based upon two joint works with J. Behrstock, Sh. Mozes and M. Sapir.
    Mon, 01/06/2009
    16:00     		George Walker (Mathematical Insitute, Oxford) Junior Number Theory Seminar Add to calendar SR1
    Introduction to the Birch–Swinnerton-Dyer Conjecture. III: Average ranks, the Artin–Tate conjecture and function fields.
    In the previous talks we have seen the formulation of the Birch–Swinnerton-Dyer conjecture. This talk will focus on a fundamental question in diophantine geometry. Namely, given an algebraic curve C defined over $ \mathbb{Q} $ possessing at least one rational point, what is the probability that C has infinitely many rational points? For curves of genus 0, the answer has been known ever since the ancient Greeks roamed the earth, and for genus > 1 the answer is also known (albeit for a much shorter time). The remaining case is genus 1, and this question has a history filled with tension and conflict between data and conjecture. I shall describe the heuristics behind the conjectures, taking into account the Birch–Swinnerton-Dyer Conjecture and the Parity Conjecture. I shall go on to outline the contrary numeric data, both in families of elliptic curves and for all elliptic curves of increasing conductor. If one instead considers elliptic curves over function fields $ \mathbb{F}_{q} (t) $, then, via a conjecture of Artin and Tate, one can compute the rank (and more) of elliptic curves of extremely large discriminant degree. I shall briefly describe the interplay between Artin–Tate and Birch–Swinnerton-Dyer, and give new evidence finally supporting the conjecture.
    Tue, 02/06/2009
    12:00     		Spyridon Alexakis (MIT) Relativity Seminar Add to calendar L3
    A black hole uniqueness theorem.
    I will discuss recent joint work with A. Ionescu and S. Klainerman on the black hole uniqueness problem. A classical result of Hawking (building on earlier work of Carter and Robinson) asserts that any vacuum, stationary black hole exterior region must be isometric to the Kerr exterior, under the restrictive assumption that the space-time metric should be analytic in the entire exterior region. We prove that Hawking's theorem remains valid without the assumption of analyticity, for black hole exteriors which are apriori assumed to be "close" to the Kerr exterior solution in a very precise sense. Our method of proof relies on certain geometric Carleman-type estimates for the wave operator.
    Tue, 02/06/2009
    14:30     		Ben Green (Cambridge) Combinatorial Theory Seminar Add to calendar L3
    Approximate groups
    Let $ A $ be a finite set in some ambient group. We say that $ A $ is a $ K $-approximate group if $ A $ is symmetric and if the set $ A.A $ (the set of all $ xy $, where $ x $, $ y $ lie in $ A $) is covered by $ K $ translates of $ A $. I will illustrate this notion by example, and will go on to discuss progress on the "rough classification" of approximate groups in various settings: abelian groups, nilpotent groups and matrix groups of fixed dimension. Joint work with E. Breuillard.
    Tue, 02/06/2009
    16:30     		Dr Beth A. Wingate (Los Alamos National Laboratories) Geophysical and Nonlinear Fluid Dynamics Seminar Add to calendar Dobson Room, AOPP
    The alpha model - an energy conserving turbulence closure
    Tue, 02/06/2009
    17:00     		Michael Aschbacher (Caltech) Algebra Seminar Add to calendar L2
    Local group theory and fusion systems
    Tue, 02/06/2009
    17:00     		Antonio Fernandez Lopez (Malaga) Functional Analysis Seminar Add to calendar L3
    Banach-Lie algebras with extremal elements

    For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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