Forthcoming Seminars
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Mon, 25/10/2010 14:15 |
Udo Hertrich-Jeromin (Bath) |
Geometry and Analysis Seminar  |
L3 |
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Mon, 25/10/2010 14:15 |
Annie Millet |
Stochastic Analysis Seminar |
Eagle House |
| We consider a non linear Schrödinger equation on a compact manifold of dimension d subject to some multiplicative random perturbation. Using some stochastic Strichartz inequality, we prove the existence and uniqueness of a maximal solution in H^1 under some general conditions on the diffusion coefficient. Under stronger conditions on the noise, the nonlinearity and the diffusion coefficient, we deduce the existence of a global solution when d=2. This is a joint work with Z. Brzezniak. | |||
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Mon, 25/10/2010 15:45 |
Istvan Berkes (Graz University of Technology) |
Stochastic Analysis Seminar |
Eagle House |
| The sequence {nα}, where α is an irrational number and {.} denotes fractional part, plays a fundamental role in probability theory, analysis and number theory. For suitable α, this sequence provides an example for "most uniform" infinite sequences, i.e. sequences whose discrepancy has thesmallest possible order of magnitude. Such 'low discrepancy' sequences have important applications in Monte Carlo integration and other problems of numerical mathematics. For rapidly increasing nk the behaviour of {nkα} is similar to that of independent random variables, but its asymptotic properties depend strongly also on the number theoretic properties of nk, providing a simple example for pseudorandom behaviour. Finally, for periodic f the sequence f(nα) provides a generalization of the trig-onometric system with many interesting properties. In this lecture, we give a survey of the field (going back more than 100 years) and formulate new results. | |||
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Mon, 25/10/2010 15:45 |
Udo Hertrich-Jeromin (Bath) |
Geometry and Analysis Seminar |
L3 |
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Mon, 25/10/2010 17:00 |
Luigi Berselli (Universita di Pisa) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
| I will make a short review of some continous approximations to the Navier-Stokes equations, especially with the aim of introducing alpha models for the Large Eddy Simulation of turbulent flows. Next, I will present some recent results about approximate deconvolution models, derived with ideas similar to image processing. Finally, I will show the rigorous convergence of solutions towards those of the averaged fluid equations. | |||
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Tue, 26/10/2010 10:00 |
Dr L.F. Alday (Oxford) |
Twistor Workshop |
Gibson 1st Floor SR |
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Tue, 26/10/2010 12:00 |
Prof ET Newman (University of Pittsburgh) |
Relativity Seminar |
L3 |
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Tue, 26/10/2010 14:30 |
Raphael Clifford (Bristol) |
Combinatorial Theory Seminar |
L3 |
| Combinatorial pattern matching is a subject which has given us fast and elegant algorithms for a number of practical real world problems as well as being of great theoretical interest. However, when single character wildcards or so-called "don't know" symbols are introduced into the input, classic methods break down and it becomes much more challenging to find provably fast solutions. This talk will give a brief overview of recent results in the area of pattern matching with don't knows and show how techniques from fields as disperse FFTs, group testing and algebraic coding theory have been required to make any progress. We will, if time permits, also discuss the main open problems in the area. | |||
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Tue, 26/10/2010 15:45 |
Alexander Ritter (Cambridge) |
Algebraic and Symplectic Geometry Seminar |
L3 |
| Symplectic cohomology is an invariant of symplectic manifolds with contact type boundary. For example, for disc cotangent bundles it recovers the homology of the free loop space. The aim of this talk is to describe algebraic operations on symplectic cohomology and to deduce applications in symplectic topology. Applications range from describing the topology of exact Lagrangian submanifolds, to proving existence theorems about closed Hamiltonian orbits and Reeb chords. | |||
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Tue, 26/10/2010 16:00 |
Jessica Banks (Oxford University) |
Junior Geometric Group Theory Seminar |
DH 3rd floor SR |
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Tue, 26/10/2010 17:00 |
Algebra Seminar |
L2 | |
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Tue, 26/10/2010 17:00 |
Maria Martinez (Zaragoza) |
Functional Analysis Seminar |
L3 |
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Wed, 27/10/2010 11:30 |
Richard Williamson (University of Oxford) |
Algebra Kinderseminar |
ChCh, Tom Gate, Room 2 |
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From a categorical point of view, the standard Zermelo-Frankel set theoretic approach to the foundations of mathematics is fundamentally deficient: it is based on the notion of equality of objects in a set. Equalities between objects are not preserved by equivalences of categories, and thus the notion of equality is 'incorrect' in category theory. It should be replaced by the notion of 'isomorphism'. Moving higher up the categorical ladder, the notion of isomorphism between objects is 'incorrect' from the point of view of 2-category, and should be replaced by the notion of 'equivalence'... Recently, people have started to take seriously the idea that one should be less dogmatic about working with set-theoretic axiomatisiations of mathematics, and adopt the more fluid point of view that different foundations of mathematics might be better suited to different areas of mathematics. In particular, there are currently serious attempts to develop foundations for mathematics built on homotopy types, or, in another language, ∞-groupoids. An (∞,1)-topos should admit an internal 'homotopical logic', just as an ordinary (1-)topos admits an internal logic modelling set theory. It turns out that formalising such a logic is rather closely related to the problem of finding good foundations for 'intensional dependent type theory' in theoretical computer science/logic. This is sometimes referred to as the attempt to construct a 'homotopy lambda calculus'. It is expected that a homotopy theoretic formalisation of the foundations of mathematics would be of genuine practical significance to the average mathematician! In this talk we will give an introduction to these ideas, and to the recent work of Vladimir Voevodsky and others in this area. |
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Thu, 28/10/2010 11:00 |
Dr Dick Dee (ECMWF) |
Applied Dynamical Systems and Inverse Problems Seminar |
DH 3rd floor SR |
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Thu, 28/10/2010 12:30 |
Lisa Harris (University of Warwick) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
| It has long been known that many materials are crystalline when in their energy-minimizing states. Two of the most common crystalline structures are the face-centred cubic (fcc) and hexagonal close-packed (hcp) crystal lattices. Here we introduce the problem of crystallization from a mathematical viewpoint and present an outline of a proof that the ground state of a large system of identical particles, interacting under a suitable potential, behaves asymptotically like fcc or hcp, as the number of particles tends to infinity. An interesting feature of this result is that it holds under no initial assumption on the particle positions. The talk is based upon a joint work in progress with Florian Theil. | |||
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Thu, 28/10/2010 13:00 |
Sergey Nadtochiy |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| We solve the problem of static hedging of (upper) barrier options (we concentrate on up-and-out put, but show how the other cases follow from this one) in models where the underlying is given by a time-homogeneous diffusion process with, possibly, independent stochastic time-change. The main result of the paper includes analytic expression for the payoff of a (single) European-type contingent claim (which pays a certain function of the underlying value at maturity, without any pathdependence), such that it has the same price as the barrier option up until hitting the barrier. We then consider some examples, including the Black-Scholes, CEV and zero-correlation SABR models, and investigate an approximation of the exact static hedge with two vanilla (call and put) options. | |||
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Thu, 28/10/2010 13:00 |
Maria Buzano (University of Oxford) |
Junior Geometry and Topology Seminar |
SR1 |
| We will recall basic definitions and facts about homogeneous Riemannian manifolds and we will discuss the Einstein condition on this kind of spaces. In particular, we will talk about non existence results of invariant Einstein metrics. Finally, we will talk briefly about the Ricci flow equation in the homogeneous setting. | |||
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Thu, 28/10/2010 14:00 |
Prof. Yvan Notay (Universite Libre de Bruxelles) |
Computational Mathematics and Applications |
Gibson Grd floor SR |
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Algebraic multigrid methods are nowadays popular to solve linear systems arising from the discretization of elliptic PDEs. They try to combine the efficiency of well tuned specific schemes like classical (geometric-based) multigrid methods, with the ease of use of general purpose preconditioning techniques. This requires to define automatic coarsening procedures, which set up an hierarchy of coarse representations of the problem at hand using only information from the system matrix. In this talk, we focus on aggregation-based algebraic multigrid methods. With these, the coarse unknowns are simply formed by grouping variables in disjoint subset called aggregates. In the first part of the talk, we consider symmetric M-matrices with nonnegative row-sum. We show how aggregates can then be formed in such a way that the resulting method satisfies a prescribed bound on its convergence rate. That is, instead of the classical paradigm that applies an algorithm and then performs its analysis, the analysis is integrated in the set up phase so as to enforce minimal quality requirements. As a result, we obtain one of the first algebraic multigrid method with full convergence proof. The efficiency of the method is further illustrated by numerical results performed on finite difference or linear finite element discretizations of second order elliptic PDEs; the set of problems includes problems with jumps, anisotropy, reentering corners and/or unstructured meshes, sometimes with local refinement. In the second part of the talk, we discuss nonsymmetric problems. We show how the previous approach can be extended to M-matrices with row- and column-sum both nonnegative, which includes some stable discretizations of convection-diffusion equations with divergence free convective flow. Some (preliminary) numerical results are also presented. This is joint work with Artem Napov. |
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Thu, 28/10/2010 14:30 |
David Stewart (Oxford) |
Representation Theory Seminar |
L3 |
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Thu, 28/10/2010 16:00 |
Dr M. Belolipetsky (University of Durham) |
Number Theory Seminar |
L3 |
| While studying growth of lattices in semisimple Lie groups we encounter many interesting number theoretic problems. In some cases we can show an equivalence between the two classes of problems, while in the other the true relation between them is unclear. On the talk I will give a brief overview of the subject and will then try to focus on some particularly interesting examples. | |||
