Past Seminars
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Tue, 19/02 10:15 |
Thomas Hillen (University of Alberta) |
OCCAM Wednesday Morning Event  |
OCCAM Common Room (RI2.28) |
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***** PLEASE NOTE THIS SEMINAR WILL TAKE PLACE ON TUESDAY 19TH FEBRUARY ***** With "fully anisotropic" I describe diffusion models of the form u_t=\nabla \nabla (D(x) u), where the diffusion tensor appears inside both derivatives. This model arises naturally in the modeling of brain tumor spread and wolf movement and other applications. Since this model does not satisfy a maximum principle, it can lead to interesting spatial pattern formation, even in the linear case. I will present a detailed derivation of this model and discuss its application to brain tumors and wolf movement. Furthermore, I will present an example where, in the linear case, the solution blows-up in infinite time; a quite surprising result for a linear parabolic equation (joint work with K.J. Painter and M. Winkler). |
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Mon, 18/02 17:00 |
Raphaël Danchin (Université Paris Est) |
Partial Differential Equations Seminar |
Gibson Grd floor SR |
| In this talk we focus on the incompressible Navier–Stokes equations with variable density. The aim is to prove existence and uniqueness results in the case of a discontinuous initial density (typically we are interested in discontinuity along an interface). In the first part of the talk, by making use of Fourier analysis techniques, we establish the existence of global-in-time unique solutions in a critical functional framework, under some smallness condition over the initial data, In the second part, we use another approach to avoid the smallness condition over the nonhomogeneity : as a matter of fact, one may consider any density bounded and bounded away from zero and still get a unique solution. The velocity is required to have subcritical regularity, though. In all the talk, the Lagrangian formulation for describing the flow plays a key role in the analysis. | |||
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Mon, 18/02 16:00 |
Ben Green (Oxford) |
Junior Number Theory Seminar |
SR1 |
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Mon, 18/02 15:45 |
GIDI AMIR (Bar-Ilan University) |
Stochastic Analysis Seminar |
Oxford-Man Institute |
| Abstract: A central question in the theory of random walks on groups is how symmetries of the underlying space gives rise to structure and rigidity of the random walks. For example, for nilpotent groups, it is known that random walks have diffusive behavior, namely that the rate of escape, defined as the expected distance of the walk from the identity satisfies E|Xn|~=n^{1/2}. On nonamenable groups, on the other hand we have E|Xn| ~= n. (~= meaning upto (multiplicative) constants ) In this work, for every 3/4 <= \beta< 1 we construct a finitely generated group so that the expected distance of the simple random walk from its starting point after n steps is n^\beta (up to constants). This answers a question of Vershik, Naor and Peres. In other examples, the speed exponent can fluctuate between any two values in this interval. Previous examples were only of exponents of the form 1-1/2^k or 1 , and were based on lamplighter (wreath product) constructions.(Other than the standard beta=1/2 and beta=1 known for a wide variety of groups) In this lecture we will describe how a variation of the lamplighter construction, namely the permutational wreath product, can be used to get precise bounds on the rate of escape in terms of return probabilities of the random walk on some Schreier graphs. We will then show how groups of automorphisms of rooted trees, related to automata groups , can be constructed and analyzed to get the desired rate of escape. This is joint work with Balint Virag of the University of Toronto. (Paper available at http://arxiv.org/abs/1203.6226) No previous knowledge of random walks,automaton groups or wreath products is assumed. | |||
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Mon, 18/02 15:45 |
Nathalie Wahl (Copenhagen) |
Topology Seminar |
L3 |
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Mon, 18/02 14:15 |
Thomas Mohaupt (Liverpool) |
Geometry and Analysis Seminar |
L3 |
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Mon, 18/02 14:15 |
NICOLAS PERKOWSKI (Humboldt University, Berlin) |
Stochastic Analysis Seminar |
Oxford-Man Institute |
| Abstract: Hairer recently had the remarkable insight that Lyons' theory of rough paths can be used to make sense of nonlinear SPDEs that were previously ill-defined due to spatial irregularities. Since rough path theory deals with the integration of functions defined on the real line, the SPDEs studied by Hairer have a one-dimensional spatial index variable. I will show how to combine paraproducts, a notion from functional analysis, with ideas from the theory of controlled rough paths, in order to develop a formulation of rough path theory that works in any index dimension. As an application, I will present existence and uniqueness results for an SPDE with multidimensional spatial index set, for which previously it was not known how to describe solutions. No prior knowledge of rough paths or paraproducts is required for understanding the talk. This is joint work with Massimiliano Gubinelli and Peter Imkeller. | |||
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Mon, 18/02 12:00 |
Mike Duff (Imperial College) |
String Theory Seminar |
L3 |
| I will give a division algebra R,C,H,O description of D = 3 Yang-Mills with N = 1,2,4,8 and hence, by tensoring left and right multiplets, a magic square RR, CR, CC, HR, HC, HH, OR, OC, OH, OO description of D = 3 supergravity with N = 2, 3, 4, 5, 6, 8, 9, 10, 12, 16. | |||
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Fri, 15/02 16:00 |
Alvaro Cartea (University College London) |
Nomura Seminar |
DH 1st floor SR |
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Fri, 15/02 14:00 |
Prof Michael Stumpf (London) |
Mathematical Biology and Ecology Seminar |
L1 |
| In this talk I will discuss recent developments in information theoretical approaches to fundamental molecular processes that affect the cellular decision making processes. One of the challenges of applying concepts from information theory to biological systems is that information is considered independently from meaning. This means that a noisy signal carries quantifiably more information than a unperturbed signal. This has, however, led us to consider and develop new approaches that allow us to quantify the level of noise contributed by any molecular reactions in a reaction network. Surprisingly this analysis reveals an important and hitherto often overlooked role of degradation reactions on the noisiness of biological systems. Following on from this I will outline how such ideas can be used in order to understand some aspects of cell-fate decision making, which I will discuss with reference to the haematopoietic system in health and disease. | |||
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Fri, 15/02 10:00 |
Victoria Nockles (Department of Earth Sciences, University of Oxford) |
Industrial and Interdisciplinary Workshops |
DH 1st floor SR |
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InSAR (Interferometric Synthetic Aperture Radar) is an important space geodetic technique (i.e. a technique that uses satellite data to obtain measurements of the Earth) of great interest to geophysicists monitoring slip along fault lines and other changes to shape of the Earth. InSAR works by using the difference in radar phase returns acquired at two different times to measure displacements of the Earth’s surface. Unfortunately, atmospheric noise and other problems mean that it can be difficult to use the InSAR data to obtain clear measurements of displacement. Persistent Scatterer (PS) InSAR is a later adaptation of InSAR that uses statistical techniques to identify pixels within an InSAR image that are dominated by a single back scatterer, producing high amplitude and stable phase returns (Feretti et al. 2001, Hooper et al. 2004). PS InSAR has the advantage that it (hopefully) chooses the ‘better’ datapoints, but it has the disadvantage that it throws away a lot of the data that might have been available in the original InSAR signal. InSAR and PS InSAR have typically been used in isolation to obtain slip-rates across faults, to understand the roles that faults play in regional tectonics, and to test models of continental deformation. But could they perhaps be combined? Or could PS InSAR be refined so that it doesn’t throw away as much of the original data? Or, perhaps, could the criteria used to determine what data are signal and what are noise be improved? The key aim of this workshop is to describe and discuss the techniques and challenges associated with InSAR and PS InSAR (particularly the problem of atmospheric noise), and to look at possible methods for improvement, by combining InSAR and PS InSAR or by methods for making the choice of thresholds. |
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Thu, 14/02 17:00 |
Jonathan Kirby (UEA) |
Logic Seminar |
L3 |
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Thu, 14/02 16:00 |
John Coates (Cambridge) |
Number Theory Seminar |
L3 |
| I will explain the beautiful generalization recently discovered by Y. Tian of Heegner's original proof of the existence of infinitely many primes of the form 8n+5, which are congruent numbers. At the end, I hope to mention some possible generalizations of his work to other elliptic curves defined over the field of rational numbers. | |||
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Thu, 14/02 16:00 |
David Abrahams (Manchester) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
| Motivated by industrial and biological applications, the Waves Group at Manchester has in recent years been interested in developing methods for obtaining the effective properties of complex composite materials. As time allows we shall discuss a number of issues, such as differences between composites with periodic and aperiodic distributions of inclusions, and modelling of nonlinear composites. | |||
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Thu, 14/02 15:00 |
Antonio De Capua |
Junior Geometry and Topology Seminar |
SR1 |
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Thu, 14/02 14:00 |
Professor Simon Chandler-Wilde (University of Reading) |
Computational Mathematics and Applications |
Gibson Grd floor SR |
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We address, in the study of acoustic scattering by 2D and 3D planar screens, three inter-related and challenging questions. Each of these questions focuses particularly on the formulation of these problems as boundary integral equations. The first question is, roughly, does it make sense to consider scattering by screens which occupy arbitrary open sets in the plane, and do different screens cause the same scattering if the open sets they occupy have the same closure? This question is intimately related to rather deep properties of fractional Sobolev spaces on general open sets, and the capacity and Haussdorf dimension of their boundary. The second question is, roughly, that, in answering the first question, can we understand explicitly and quantitatively the influence of the frequency of the incident time harmonic wave? It turns out that we can, that the problems have variational formations with sesquilinear forms which are bounded and coercive on fractional Sobolev spaces, and that we can determine explicitly how continuity and coercivity constants depend on the frequency. The third question is: can we design computational methods, adapted to the highly oscillatory solution behaviour at high frequency, which have computational cost essentially independent of the frequency? The answer here is that in 2D we can provably achieve solutions to any desired accuracy using a number of degrees of freedom which provably grows only logarithmically with the frequency, and that it looks promising that some extension to 3D is possible.
This is joint work with Dave Hewett, Steve Langdon, and Ashley Twigger, all at Reading. |
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Thu, 14/02 14:00 |
Stephane Guillermou (Grenoble) |
Algebraic and Symplectic Geometry Seminar |
L3 |
Several recent works by D. Tamarkin, D. Nadler, E. Zaslow make use of the microlocal theory of sheaves of M. Kashiwara and P. Schapira to obtain results in symplectic geometry. The link between sheaves on a manifold  and the symplectic geometry of the cotangent bundle of is given by the microsupport of a sheaf, which is a conic co-isotropic subset of the cotangent bundle. In the above mentioned works properties of a given Lagrangian submanifold  are deduced from the existence of a sheaf with microsupport , which we call a quantization of .
In the third talk we will see that admits a canonical quantization if it is a "conification" of a compact exact Lagrangian submanifold of a
cotangent bundle. We will see how to use this quantization to recover results of Fukaya-Seidel-Smith and Abouzaid on the topology of . |
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Thu, 14/02 14:00 |
Stephane Guillermou (Grenoble) |
Representation Theory Seminar |
L3 |
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Several recent works by D. Tamarkin, D. Nadler, E. Zaslow make use of the microlocal theory of sheaves of M. Kashiwara and P. Schapira to obtain results in symplectic geometry. The link between sheaves on a manifold $M$ and the symplectic geometry of the cotangent bundle of $M$ is given by the microsupport of a sheaf, which is a conic co-isotropic subset of the cotangent bundle. In the above mentioned works properties of a given Lagrangian submanifold $\Lambda$ are deduced from the existence of a sheaf with microsupport $\Lambda$, which we call a quantization of $\Lambda$. In the third talk we will see that $\Lambda$ admits a canonical quantization if it is a "conification" of a compact exact Lagrangian submanifold of a cotangent bundle. We will see how to use this quantization to recover results of Fukaya-Seidel-Smith and Abouzaid on the topology of $\Lambda$. |
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Thu, 14/02 13:00 |
Marek Musiela (Mathematics (Oxford)) |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| The second order sensitivity of a trading position, the so called gamma, has a very real and intuitive meaning to the traders. People think that convex payoffs must generate convex prices. Being long or short of gamma is a strategy used to balance risks in options books. While the simples models, like Black Scholes, are consistent with this intuition other popular models used in the industry are not. I will give examples of simple and popular models which do not always convert a convex payoff into a convex price. I will also give the necessary and sufficient conditions under which the convexity is propagated. | |||
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Thu, 14/02 12:15 |
Paul Tod (OxPDE) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
| The new schedule will follow shortly | |||
