Forthcoming Seminars
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Wed, 16/11/2011 10:10 |
Min Chen |
OCCAM Wednesday Morning Event  |
OCCAM Common Room (RI2.28) |
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Wed, 16/11/2011 11:30 |
Peter Neumann |
Algebra Kinderseminar |
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Wed, 16/11/2011 16:00 |
Ric Wade |
Junior Geometric Group Theory Seminar |
DH 3rd floor SR |
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Wed, 16/11/2011 16:00 |
István Juhász (Renyi Institute, Budapest) |
Analytic Topology in Mathematics and Computer Science |
L3 |
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Wed, 16/11/2011 17:00 |
Professor Vladimir Zakharov (University of Arizona) |
Brooke Benjamin Lecture |
L1 |
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The self-consistent analytic theory of the wind-driven sea can be developed due to the presence of small parameter, ratio of atmospheric and water densities. Because of low value of this parameter the sea is "weakly nonlinear" and the average steepness of sea surface is also relatively small. Nevertheless, the weakly nonlinear four-wave resonant interaction is the dominating process in the energy balance. The wind-driven sea can be described statistically in terms of the Hasselmann kinetic equation. This equation has a rich family of Kolmogorov-type solutions perfectly describing "rear faces" of wave spectra right behind the spectral peak. More short waves are described by steeper Phillips spectrum formed by ensemble of microbreakings. From the practical view-point the most important question is the spatial and temporal evolution of spectral peaks governed by self-similar solutions of the Hasselmann equation. This analytic theory is supported by numerous experimental data and computer simulations. |
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Thu, 17/11/2011 11:00 |
Adam Harris (Oxford) |
Advanced Class Logic |
SR2 |
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Thu, 17/11/2011 12:00 |
Michael Gröchenig |
Junior Geometry and Topology Seminar |
SR2 |
This is the first in a series of  talks about Stable Homotopy Theory. We will motivate the definition of spectra by the Brown Representability Theorem, which allows us to interpret a spectrum as a generalized cohomology theory. Along the way we recall basic notions from homotopy theory, such as suspension, loop spaces and smash products. |
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Thu, 17/11/2011 12:30 |
Elizabeth Leicht |
Networks Journal Club |
T14 |
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Thu, 17/11/2011 12:30 |
Parth Soneji (Oxford Centre for Nonlinear PDE) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
| An overview is given of some key issues and definitions in the Calculus of Variations, with a focus on lower semicontinuity and quasiconvexity. Some well known results and instructive counterexamples are also discussed. We then move to consider variational problems in the BV setting, and present a new lower semicontinuity result for quasiconvex integrals of subquadratic growth. The proof of this requires some interesting techniques, such as obtaining boundedness properties for an extension operator, and exploiting fine properties of Sobolev maps. | |||
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Thu, 17/11/2011 13:00 |
Vladimir Cherny |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| We consider a portfolio optimisation problem on infinite horizon when the investment policy satisfies the drawdown constraint, which is the wealth process of an investor is always above a threshold given as a function of the past maximum of the wealth process. The preferences are given by a utility function and investor aims to maximise an asymptotic growth rate of her expected utility of wealth. This problem was firstly considered by Grossman and Zhou [3] and solved for a Black-Scholes market and linear drawdown constraint. The main contribution of the paper is an equivalence result: the constrained problem with utility U and drawdown function w has the same value function as the unconstrained problem with utility UoF, where function F is given explicitly in terms of w. This work was inspired by ideas from [2], whose results are a special case of our work. We show that the connection between constrained and unconstrained problems holds for a much more general setup than their paper, i.e. a general semimartingale market, larger class of utility functions and drawdown function which is not necessarily linear. The paper greatly simplifies previous approaches using the tools of Azema-Yor processes developed in [1]. In fact we show that the optimal wealth process for constrained problem can be found as an explicit Azema-Yor transformation of the optimal wealth process for the unconstrained problem. We further provide examples with explicit solution for complete and incomplete markets. [1] Carraro, L., Karoui, N. E., and Obloj, J. On Azema-Yor processes, their optimal properties and the Bachelier-Drawdown equation, to appear in Annals of Probability, 2011. [2] Cvitanic, J., and Karatzas, I. On portfolio optimization under drawdown constraints. IMA Volumes in Mathematics and Its Applications 65(3), 1994, 35-45 [3] Grossman, S. J., and Zhou, Z. Optimal investment strategies for controlling drawdowns. Mathematical Finance 3(3), 1993, 241-276 | |||
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Thu, 17/11/2011 14:00 |
Prof Nancy Nichols (University of Reading) |
Computational Mathematics and Applications |
Rutherford Appleton Laboratory, nr Didcot |
| Variational data assimilation techniques for optimal state estimation in very large environmental systems currently use approximate Gauss-Newton (GN) methods. The GN method solves a sequence of linear least squares problems subject to linearized system constraints. For very large systems, low resolution linear approximations to the model dynamics are used to improve the efficiency of the algorithm. We propose a new approach for deriving low order system approximations based on model reduction techniques from control theory which can be applied to unstable stochastic systems. We show how this technique can be combined with the GN method to retain the response of the dynamical system more accurately and improve the performance of the approximate GN method. | |||
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Thu, 17/11/2011 15:00 |
Professor Charles A Stuart |
OxPDE Special Seminar |
Gibson 1st Floor SR |
| • Review of the basic notions concerning bifurcation and asymptotic linearity. • Review of differentiability in the sense of Gˆateaux, Fréchet, Hadamard. • Examples which are Hadamard but not Fréchet differentiable. The Dirichlet problem for a degenerate elliptic equation on a bounded domain. The stationary nonlinear Schrödinger equation on RN | |||
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Thu, 17/11/2011 16:00 |
Dominic Vella (OCCAM) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
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Thu, 17/11/2011 16:15 |
Mike Giles |
Stochastic Numerics Seminar |
Oxford-Man Institute |
| In these two talks we will look at a recent paper by David Anderson and Des Higham: http://arxiv.org/pdf/1107.2181 This paper takes the Multilevel Monte Carlo method which I developed in 2006 for Brownian SDEs, and comes up with an elegant way of applying it to stochastic biochemical reaction networks. | |||
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Thu, 17/11/2011 17:00 |
David Evans (UEA) |
Logic Seminar |
L3 |
| We give an exposition of some results from matroid theory which characterise the finite pregeometries arising from Hrushovski's predimension construction as the strict gammoids: a class of matroids studied in the early 1970's which arise from directed graphs. As a corollary, we observe that a finite pregeometry which satisfies Hrushovski's flatness condition arises from a predimension. We also discuss the isomorphism types of the pregeometries of countable, saturated strongly minimal structures in Hrushovski's 1993 paper and answer some open questions from there. This last part is joint work with Marco Ferreira, and extends results in his UEA PhD thesis. | |||
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Fri, 18/11/2011 00:00 |
Mathematical Biology and Ecology Seminar |
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Fri, 18/11/2011 10:00 |
Glen Davidson (Thales UK) |
Industrial and Interdisciplinary Workshops |
DH 1st floor SR |
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Fri, 18/11/2011 14:30 |
Dr Simon Holgate (National Oceanography Centre) |
Mathematical Geoscience Seminar |
DH 3rd floor SR |
| Rising sea levels are frequently cited as one of the most pressing societal consequences of climate change. In order to understand the present day change in sea level we need to place it in the context of historical changes. The primary source of information on sea level change over the past 100-150 years is tide gauges. However, these tide gauges are a globally sparse set of point measurements located largely at the coast. "Global mean sea level" calculated from these tide gauges is therefore biased and is also more variable than than global mean sea level calculated from the past 19 years of satellite altimtery measurements. The work presented here explores the use of simple statistical approaches which make use of reanalysis wind stress datasets and heat content reconstructions to model the sea level records. It is shown that these simple models have skill in reproducing variability at decadal time-scales. The results suggest that there are active regions of wind stress and heat content in the ocean which affect regional variability in sea level records that point to the atmospheric and oceanic processes which drive the variability. Acceleration seen in the longest continous sea level record at Brest is shown to be partially attributable to changes in wind stress over the past 140 years. | |||
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Fri, 18/11/2011 15:30 |
Mohit Dalwadi (Oxford Centre for Industrial and Applied Mathematics) |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
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A common way to replace body tissue is via donors, but as the world population is ageing at an unprecedented rate there will be an even smaller supply to demand ratio for replacement parts than currently exists. Tissue engineering is a process in which damaged body tissue is repaired or replaced via the engineering of artificial tissues. We consider one type of this; a two-phase flow through a rotating high-aspect ratio vessel (HARV) bioreactor that contains a porous tissue construct. We extend the work of Cummings and Waters [2007], who considered a solid tissue construct, by considering flow through the porous construct described by a rotating form of Darcy's equations. By simplifying the equations and changing to bipolar variables, we can produce analytic results for the fluid flow through the system for a given construct trajectory. It is possible to calculate the trajectory numerically and couple this with the fluid flow to produce a full description of the flow behaviour. Finally, coupling with the numerical result for the tissue trajectory, we can also analytically calculate the particle paths for the flow which will lead to being able to calculate the spatial and temporal nutrient density. |
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Mon, 21/11/2011 12:00 |
James Sparks (Oxford) |
String Theory Seminar |
L3 |
| In just the last year it has been realized that one can define supersymmetric gauge theories on non-trivial compact curved manifolds, coupled to a background R-symmetry gauge field, and moreover that expectation values of certain BPS operators reduce to finite matrix integrals via a form of localization. I will argue that a general approach to this topic is provided by the gauge/gravity correspondence. In particular, I will present several examples of supersymmetric gauge theories on different 1-parameter deformations of the three-sphere, which have a large N limit, together with their gravity duals (which are solutions to Einstein-Maxwell theory). The Euclidean gravitational partition function precisely matches a large N matrix model evaluation of the field theory partition function, as an exact function of the deformation parameter. | |||
