Forthcoming Seminars

Fri, 22/05/2009
14:30 		Dr. Andy Ellis (OCCAM (Oxford)) Mathematical Geoscience Seminar Add to calendar DH 3rd floor SR
Mathematical modelling of sand dune formation.
Fri, 22/05/2009
16:30 		Paul Moore (University of Oxford) Junior Applied Mathematics Seminar Add to calendar DH 3rd floor SR
Modelling bipolar disorder
Mon, 25/05/2009
00:00 		Topology Seminar Add to calendar
NO SEMINAR
Mon, 25/05/2009
12:00 		John Dixon String Theory Seminar Add to calendar L3
Cybersusy–a new mechanism for supersymmetry breaking in the standard supersymmetric mode
Abstract: Cybersusy is a new approach to supersymmetry breaking, based on the BRS cohomology of composite operators in the supersymmetric standard model (analyzed using spectral sequences). The cohomology generates a new kind of supersymmetry algebra and a new effective action.  When the gauge symmetry is broken (from the vacuum expectation value of a scalar field), supersymmetry breaking is also induced. Applied to the leptons, the result is consistent with experiment, and the vacuum energy remains zero, and no annoying mass sum rules are present.
Mon, 25/05/2009
14:15 		Greg Pavliotis Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Long time/weak friction asymptotics for the Langevin equation in a periodic potential.
In this talk we will review some recent results on the long-time/large-scale, weak-friction asymptotics for the one dimensional Langevin equation with a periodic potential. First we show that the Freidlin-Wentzell and central limit theorem (homogenization) limits commute. We also show that, in the combined small friction, long-time/large-scale limit the particle position converges weakly to a Brownian motion with a singular diffusion coefficient which we compute explicitly. Furthermore we prove that the same result is valid for a whole one parameter family of space/time rescalings. We also present a new numerical method for calculating the diffusion coefficient and we use it to study the multidimensional problem and the problem of Brownian motion in a tilted periodic potential.
Mon, 25/05/2009
15:45 		Philippe Marchal Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
To Be Announced
Mon, 25/05/2009
16:00 		Frank Gounelas (Mathematical Institute, Oxford) Junior Number Theory Seminar Add to calendar SR1
An Introduction to the Birch–Swinnerton-Dyer Conjecture II
This is the second (of two) talks concerning the Birch–Swinnerton-Dyer Conjecture.
Tue, 26/05/2009
12:00 		Nick Manton (DAMTP, Cambridge) Quantum Field Theory Seminar Add to calendar L3
Vortex Geometry
Tue, 26/05/2009
14:30 		Mark Walters (QMUL) Combinatorial Theory Seminar Add to calendar L3
Hamilton cycles in random geometric graphs
The Gilbert model of a random geometric graph is the following: place points at random in a (two-dimensional) square box and join two if they are within distance $ r $ of each other. For any standard graph property (e.g.  connectedness) we can ask whether the graph is likely to have this property.  If the property is monotone we can view the model as a process where we place our points and then increase $ r $ until the property appears.  In this talk we consider the property that the graph has a Hamilton cycle.  It is obvious that a necessary condition for the existence of a Hamilton cycle is that the graph be 2-connected. We prove that, for asymptotically almost all collections of points, this is a sufficient condition: that is, the smallest $ r $ for which the graph has a Hamilton cycle is exactly the smallest $ r $ for which the graph is 2-connected.  This work is joint work with Jozsef Balogh and Béla Bollobás
Tue, 26/05/2009
15:45 		Nicos Kapouleas (US) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Gluing constructions of special Lagrangian cones
I will survey the recent work of Haskins and myself constructing new special Lagrangian cones in $ {\mathbb C}^n $ for all $ n\ge3 $ by gluing methods. The link (intersection with the unit sphere $ {\cal S}^{2n-1} $) of a special Lagrangian cone is a special Legendrian $ (n-1) $-submanifold. I will start by reviewing the geometry of the building blocks used. They are rotationally invariant under the action of $ SO(p)\times SO(q) $ ($ p+q=n $) special Legendrian $ (n-1) $-submanifolds of $ {\cal S}^{2n-1} $. These we fuse (when $ p=1 $, $ p=q $) to obtain more complicated topologies. The submanifolds obtained are perturbed to satisfy the special Legendrian condition (and their cones therefore the special Lagrangian condition) by solving the relevant PDE. This involves understanding the linearized operator and its small eigenvalues, and also ensuring appropriate decay for the solutions.
Tue, 26/05/2009
16:30 		Prof. Robb McDonald (University College) Geophysical and Nonlinear Fluid Dynamics Seminar Add to calendar Dobson Room, AOPP
Some related problems in ocean and industrial flows
Tue, 26/05/2009
17:00 		Pham Tiep (University of Florida) Algebra Seminar Add to calendar L2
Divisibility properties of character degrees and p-local structure of finite groups
Many classical results and conjectures in representation theory of finite groups (such as theorems of Thompson, Ito, Michler, the McKay conjecture, ...) address the influence of global properties of representations of a finite group G on its p-local structure. It turns out that several of them also admit real, resp. rational, versions, where one replaces the set of all complex representations of G by the much smaller subset of real, resp. rational, representations. In this talk we will discuss some of these results, recently obtained by the speaker and his collaborators. We will also discuss recent progress on the Brauer height zero conjecture for 2-blocks of maximal defect.
Wed, 27/05/2009
11:30 		Algebra Kinderseminar Add to calendar
NO SEMINAR
Thu, 28/05/2009
09:30 		Michael Harris (Univ. Paris 7) Special Lecture Add to calendar Taught Course Center
Automorphic Forms, Galois Representations and Geometry
Thu, 28/05/2009
12:15 		Dawid Kielak (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
Helly's Theorem through dimension theory
Thu, 28/05/2009
12:30 		Xanthippi Markenscoff (University of California, San Diego) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
The Cosserat Spectrum Theory of Elasticity
The Cosserat brothers’ ingenuous and powerful idea (presented in several papers in the Comptes Rendus at the turn of the 20th century) of solving elasticity problems by considering the homogeneous Navier equations as an eigenvalue problem is presented. The theory was taken up by Mikhlin in the 1970’s who rigorously studied it in the context of spectral analysis of pde’s, and who also presented a representation theorem for the solution of the boundary-value problems of displacement and traction in elasticity as a convergent series of the ( orthogonal and complete in the Sobolev space H1) Cosserat eigenfunctions. The feature of this representation is that the dependence of the solution on geometry, material constants and loading is provided explicitly. Recent work by the author and co-workers obtains the set of eigenfunctions for the spherical shell and compares them with the Cosserat expressions, and further explores applications and a new variational principle. In cases that the loading is orthogonal to some of the eigenfunctions, the form of the solution can be greatly simplified. Applications, in addition to elasticity theory, include thermoelasticity, poroelesticity, thermo-viscoelasticity, and incompressible Stokes flow; several examples are presented, with comparisons to known solutions, or new solutions.
Thu, 28/05/2009
13:00 		Lei Jin Mathematical Finance Internal Seminar Add to calendar DH 1st floor SR
Particle System and Stochastic PDE in Credit Portfolio Modelling (Theoretical Part)
In this talk, we try to construct a dynamical model for the basket credit products in the credit market under the structural-model framework. We use the particle representation for the firms' asset value and investigate the evolution of the empirical measure of the particle system. By proving the convergence of the empirical measure we can achieve a stochastic PDE which is satisfied by the density of the limit empirical measure and also give an explicit formula for the default proportion at any time t. Furthermore, the dynamics of the underlying firms' asset values can be assumed to be either driven by Brownian motions or more general Levy processes, or even have some interactive effects among the particles. This is a joint work with Dr. Ben Hambly.
Thu, 28/05/2009
14:00 		Prof. Bengt Fornberg (University of Colorado) Computational Mathematics and Applications Add to calendar Comlab
Radial Basis Functions for Solving Partial Differential Equations
For the task of solving PDEs, finite difference (FD) methods are particularly easy to implement. Finite element (FE) methods are more flexible geometrically, but tend to be difficult to make very accurate. Pseudospectral (PS) methods can be seen as a limit of FD methods if one keeps on increasing their order of accuracy. They are extremely effective in many situations, but this strength comes at the price of very severe geometric restrictions. A more standard introduction to PS methods (rather than via FD methods of increasing orders of accuracy) is in terms of expansions in orthogonal functions (such as Fourier, Chebyshev, etc.). Radial basis functions (RBFs) were first proposed around 1970 as a tool for interpolating scattered data. Since then, both our knowledge about them and their range of applications have grown tremendously. In the context of solving PDEs, we can see the RBF approach as a major generalization of PS methods, abandoning the orthogonality of the basis functions and in return obtaining much improved simplicity and flexibility. Spectral accuracy becomes now easily available also when using completely unstructured meshes, permitting local node refinements in critical areas. A very counterintuitive parameter range (making all the RBFs very flat) turns out to be of special interest. Computational cost and numerical stability were initially seen as serious difficulties, but major progress have recently been made also in these areas.

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

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