Forthcoming Seminars
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Mon, 21/04/2008 12:00 |
Mohab Abou Zeid (Institute for Mathematical Sciences) |
String Theory Seminar  |
L3 |
| I will present a modification of twistor string theory which gives the spectrum of super Yang-Mills theory coupled to Einstein supergravity instead of the higher derivative conformal supergravity arising in the original twistor strings of Witten and of Berkovits. After reviewing the world-sheet formulation of the Berkovits model, I will describe the symmetries of the so-called beta-gamma systems and their gauging. I will then explain how the analysis can be applied to the construction of a family of new gauged Berkovits twistor strings which are free from world-sheet anomalies. The new theories include one with the spectrum of N=8 supergravity, two theories with the spectrum of N=4 supergravity coupled to N=4 Yang-Mills, a family of N>0 models with the spectra of self-dual supergravity coupled to self-dual super-Yang-Mills, and a non-supersymmetric string with the spectrum of self-dual gravity coupled to self-dual Yang-Mills and a scalar. Time permitting, I will discuss what is known about the interactions in the new theories. | |||
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Mon, 21/04/2008 14:15 |
Dr Charles Bordenave (Université de Toulouse) |
Stochastic Analysis Seminar |
Oxford-Man Institute |
| We will analyze the convergence of the spectrum of large random graphs to the spectrum of a limit infinite graph. These results will be applied to graphs converging locally to trees and derive a new formula for the Stieljes transform of the spectral measure of such graphs. We illustrate our results on the uniform regular graphs, Erdos-Renyi graphs and graphs with prescribed degree distribution. We will sketch examples of application for weighted graphs, bipartite graphs and the uniform spanning tree of n vertices. If time allows, we will discuss related open problems. This is a joint work with Marc Lelarge (INRIA & Ecole Normale Supérieure). | |||
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Mon, 21/04/2008 14:15 |
Alexey Bolsinov (Loughborough) |
Geometry and Analysis Seminar |
L3 |
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Mon, 21/04/2008 15:45 |
Mr. Dan Osborne (Oxford) |
Stochastic Analysis Seminar |
Oxford-Man Institute |
| Let u be a vector field on a bounded domain in R^3. The absolute boundary condition states that both the normal part of u and the tangential part of curl(u) vanish on the boundary. After motivating the use of this condition in the context of the Navier Stokes equation, we prove local (in time) existence with this boundary behaviour. This work is together with Dr. Z. Qian and Prof. G. Q. Chen, Northwestern University. | |||
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Mon, 21/04/2008 17:00 |
V.P. Smyshlyaev (University of Bath) |
Partial Differential Equations Seminar |
L3 |
| Multi-well relaxation problem emerges e.g. in characterising effective properties of composites and in phase transformations. This is a nonlinear problem and one approach uses its reformulation in Fourier space, known in the theory of composites as Hashin-Shtrikman approach, adapted to nonlinear composites by Talbot and Willis. Characterisation of admissible mixtures, subjected to appropriate differential constraints, leads to a quasiconvexification problem. The latter is equivalently reformulated in the Fourier space as minimisation with respect to (extremal points of) H-measures of characteristic functions (Kohn), which in a sense separates the microgeometry of mixing from the differential constraints. For three-phase mixtures in 3D we obtain a full characterisation of certain extremal H-measures. This employs Muller's Haar wavelet expansion estimates in terms of Riesz transform to establish via the tools of harmonic analysis weak lower semicontinuity of certain functionals with rank-2 convex integrands. As a by-product, this allows to fully solve the problem of characterisation of quasiconvex hulls for three arbitrary divergence-free wells. We discuss the applicability of the results to problems with other kinematic constraints, and other generalisations. Joint work with Mariapia Palombaro, Leipzig. | |||
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Tue, 22/04/2008 12:00 |
David Hoyle (Manchester) |
Quantum Field Theory Seminar |
L3 |
| Modern molecular biology research produces data on a massive scale. This data is predominantly high-dimensional, consisting of genome-wide measurements of the transcriptome, proteome and metabalome. Analysis of these data sets often face the additional problem of having small sample sizes, as experimental data points may be difficult and expensive to come by. Many analysis algorithms are based upon estimating the covariance structure from this high-dimensional small sample size data, with the consequence that the eigenvalues and eigenvectors of the estimated covariance matrix are markedly different from the true values. Techniques from statistical physics and Random Matrix Theory allow us to understand how these discrepancies in the eigenstructure arise, and in particular locate the phase transition points where the eigenvalues and eigenvectors of the estimated covariance matrix begin to genuinely reflect the underlying biological signals present in the data. In this talk I will give a brief non-specialist introduction to the biological background motivating the work and highlight some recent results obtained within the statistical physics approach. | |||
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Tue, 22/04/2008 15:45 |
Miles Reid (Warwick) |
Algebraic and Symplectic Geometry Seminar |
L3 |
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Tue, 22/04/2008 16:30 |
Dr. Paul Dellar (Oxford) |
Geophysical and Nonlinear Fluid Dynamics Seminar |
Dobson Room, AOPP |
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Tue, 22/04/2008 17:00 |
Udo Baumgartner (Newcastle) |
Algebra Seminar |
L1 |
| As a small step towards an understanding of the relationship of the two fields in the title, I will present a uniformness result for embeddings of finitely generated, virtually free groups as cocompact, discrete subgroups in totally disconnected, locally compact groups. | |||
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Thu, 24/04/2008 13:00 |
I. Gallagher (Paris VII) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
| It is well known that the three dimensional, incompressible Navier-Stokes equations have a unique, global solution provided the initial data is small enough in a scale invariant space (say L3 for instance). We are interested in finding examples for which no smallness condition is imposed, but nevertheless the associate solution is global and unique. The examples we will present are due to collaborations with Jean-Yves Chemin, and with Marius Paicu. | |||
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Thu, 24/04/2008 13:00 |
Christopher Reisinger |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| (based on joint work with Helen Haworth, William Shaw, and Ben Hambly) The simulation of multi-name credit derivatives raises significant challenges, among others from the perspective of dependence modelling, calibration, and computational complexity. Structural models are based on the evolution of firm values, often modelled by market and idiosyncratic factors, to create a rich correlation structure. In addition to this, we will allow for contagious effects, to account for the important scenarios where the default of a number of companies has a time-decaying impact on the credit quality of others. If any further evidence for the importance of this was needed, the recent developments in the credit markets have furnished it. We will give illustrations for small n-th-to-default baskets, and propose extensions to large basket credit derivatives by exploring the limit for an increasing number of firms | |||
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Thu, 24/04/2008 14:00 |
Prof Toby Driscoll (University of Delaware) |
Computational Mathematics and Applications |
Comlab |
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Thu, 24/04/2008 14:30 |
Kevin McGerty (Imperial College, London) |
Representation Theory Seminar |
L3 |
| Lusztig discover an integral lift of the Frobenius morphism for algebraic groups in positive characteristic to quantum groups at a root of unity. We will describe how this map may be constructed via the Hall algebra realization of a quantum group. | |||
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Thu, 24/04/2008 16:00 |
Ronald van Luijk (Warwick) |
Number Theory Seminar |
L3 |
| It is a wide open question whether the set of rational points on a smooth quartic surface in projective three-space can be nonempty, yet finite. In this talk I will treat the case of diagonal quartics V, which are given by: a x^4 + b y^4 + c z^4 + d w^4 = 0 for some nonzero rational a,b,c,d. I will assume that the product abcd is a square and that V contains at least one rational point P. I will prove that if none of the coordinates of P is zero, and P is not contained in one of the 48 lines on V, then the set of rational points on V is dense. This is based on joint work with Adam Logan and David McKinnon. | |||
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Thu, 24/04/2008 16:30 |
Margaret Beck (University of Surrey) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| "Time-periodic shocks in systems of viscous conservation laws are shown to be nonlinearly stable. The result is obtained by representing the evolution associated to the linearized, time-periodic operator using a contour integral, similar to that of strongly continuous semigroups. This yields detailed pointwise estimates on the Green's function for the time-periodic operator. The evolution associated to the embedded zero eigenvalues is then extracted. Stability follows from a Gronwall-type estimate, proving algebraic decay of perturbations." | |||
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Fri, 25/04/2008 10:00 |
Industrial and Interdisciplinary Workshops |
DH 3rd floor SR | |
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Fri, 25/04/2008 12:00 |
Dr Maciej Dunajski (Cambridge) |
Geometry and Integrability |
L3 |
| Cover a plane with curves, one curve through each point in each direction. How can you tell whether these curves are the geodesics of some metric? This problem gives rise to a certain closed system of partial differential equations and hence to obstructions to finding such a metric. It has been an open problem for at least 80 years. Surprisingly it is harder in two dimensions than in higher dimensions. I shall present a solution obtained jointly with Robert Bryant and Mike Eastwood. | |||
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Fri, 25/04/2008 13:30 |
Gui-Qiang Chen (USA) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
| In this talk we will start with various shock reflection-diffraction phenomena, their fundamental scientific issues, and their theoretical roles in the mathematical theory of multidimensional hyperbolic systems of conservation laws. Then we will describe how the global shock reflection-diffraction problems can be formulated as free boundary problems for nonlinear conservation laws of mixed-composite hyperbolic-elliptic type.Finally we will discuss some recent developments in attacking the shock reflection-diffraction problems, including the existence, stability, and regularity of global regular configurations of shock reflection-diffraction by wedges. The approach includes techniques to handle free boundary problems, degenerate elliptic equations, and corner singularities, which is highly motivated by experimental, computational, and asymptotic results. Further trends and open problems in this direction will be also addressed. This talk will be mainly based on joint work with M. Feldman. | |||
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Fri, 25/04/2008 14:00 |
Professor Michael Mackey (McGill University) |
Mathematical Biology and Ecology Seminar |
L3 |
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Fri, 25/04/2008 14:15 |
Karl Kunisch (University of Graz) |
Mathematical Finance Seminar |
DH 1st floor SR |
| Efficient numerical solutions of several important partial-differential equation based models in mathematical finance are impeded by the fact that they contain operators which are Lipschitz continuous but not continuously differentiable. As a consequence, Newton methods are not directly applicable and, more importantly, do not provide their typical fast convergence properties. In this talk semi-smooth Newton methods are presented as a remedy to the the above-mentioned difficulties. We also discuss algorithmic issues including the primal-dual active set strategy and path following techniques. | |||
