Forthcoming Seminars

Mon, 08/10/2007
12:00 		Amihay Hanany (Imperial College) String Theory Seminar Add to calendar L3
Baryonic Moduli Spaces and Counting Chiral Operators in SCFT's
Abstract: Supersymmetric gauge theories have a spectrum of chiral operators which are preserved under at least 2 supercharges. These operators are sometimes called BPS operators in the chiral ring. The problem of counting operators in the chiral ring is reasonably simple and reveals information about the moduli space of vacua for the supersymmetric gauge theory. In this talk I will review the counting problem and present exact results on the moduli space of both mesonic and baryonic operators for a large class of gauge theories
Mon, 08/10/2007
14:15 		Nigel Hitchin (University of Oxford) Geometry and Analysis Seminar Add to calendar L3
Hyperbolic monopoles and Einstein metrics
Mon, 08/10/2007
15:45 		Martin Bridson (Oxford) Topology Seminar Add to calendar L3
Quasiregular maps, hyperbolic groups, and rigidity of manifolds
Roughly speaking, a quasiregular map is a possibly-branched covering map with bounded distortion. The theory of such maps was developed in the 1970s to carry over to higher dimensions the more geometric aspects of the theory of complex analytic functions of the plane. In this talk I shall outline the proof of rigidity theorems describing the quasiregular self-maps of hyperbolic manifolds. These results rely on an extension of Sela's work concerning the stability of self-maps of hyperbolic groups, and on older topological ideas concerning discrete-open and light-open maps, particularly their effect on fundamental groups. I shall explain how these two sets of ideas also lead to topological rigidity theorems. This talk is based on a paper with a similar title by Bridson, Hinkkanen and Martin (to appear in Compositio shortly). http://www2.maths.ox.ac.uk/~bridson/papers/QRhyp/
Mon, 08/10/2007
16:30 		Daniel Isaacson Seminar Add to calendar Ryle Room (10 Merton Street)
"Mathematical structures and the reality of mathematics"
Mon, 08/10/2007
17:00 		Yves Capdeboscq (Oxford) Applied Analysis and Mechanics Seminar Add to calendar L3
A zero-Laplacian approach to impedance imaging
Electrical impedance tomography (EIT) technique has been an active research topic since the early 1980s. In EIT, one measures the boundary voltages due to multiple injection currents to reconstruct images of the conductivity distribution. However, these boundary voltages are insensitive to a local change of the conductivity distribution and the relation between them is highly nonlinear. Medical imaging has been one of the important application areas of EIT. Indeed, biological tissues have different electrical properties that change with cell concentration, cellular structure, and molecular composition. Such changes of electrical properties are the manifestations of structural, functional, metabolic, and pathological conditions of tissues, and thus provide valuable diagnostic information. Since all the present EIT technologies are only practically applicable in feature extraction of anomalies, improving EIT calls for innovative measurement techniques that incorporate structural information. The core idea of the approach presented in this talk is to extract more information about the conductivity from data that has been enriched by coupling the electric measurements to localized elastic perturbations. More precisely, we propose to perturb the medium during the electric measurements, by focusing ultrasonic waves on regions of small diameter inside the body. Using a simple model for the mechanical effects of the ultrasound waves, we show that the difference between the measurements in the unperturbed and perturbed configurations is asymptotically equal to the pointwise value of the energy density at the center of the perturbed zone. In practice, the ultrasounds impact a spherical or ellipsoidal zone, of a few millimeters in diameter. The perturbation should thus be sensitive to conductivity variations at the millimeter scale, which is the precision required for breast cancer diagnostic. The material presented in this talk concerning the imaging by perturbation approach, is based on a joint work with Habib Ammari, Eric Bonnetier, Michael Tanter & Mathias Fink and on an ongoing collaboration with Frédéric de Gournay, Otared Kavian and Jérôme Fehrenbach. I will also discuss recent results concerning perturbation of asymptotically small volume fraction which are based on joint works with Michael Vogelius.
Tue, 09/10/2007
12:00 		Stefan Hollands Relativity Seminar Add to calendar L3
The classification of higher-dimensional black holes
It has been known for some time that in more than 4 spacetime dimensions, there is a considerably larger variety of black "hole" solutions, having e.g. different horizon topology. In particular, they are no longer fully characterized by their asymptotic charges (mass, angular momenta) alone. We give a partial classification theorem for higher dimensions, for solutions with sufficiently many axial Killing fields. We show that higher dimensional black holes may be fully characterized by their asymptotic charges, together with certain "moduli" and "winding numbers" that are analogous to those of Seiffert fibrations. In particular, we find constraints on the possible horizon topologies. In 5 dimensions, they may be either a black "hole" (sphere), black "ring", or a black "lens".
Tue, 09/10/2007
14:30 		Bruce Reed (McGill/INRIA/CNRS)) Combinatorial Theory Seminar Add to calendar L3
Tying down the diameter of G(n,p).
We show that the diameter of G(n,p) is concentrated on one of three values provided the average degree p(n-1) goes to infity with n. This is joint work with N. Fountoulakis even though he refuses to admit it.
Tue, 09/10/2007
17:00 		Andrew Wynn (Oxford) Functional Analysis Seminar Add to calendar L3
Weighted admissibility
Tue, 09/10/2007
17:00 		Prof. M. Bridson (Oxford) Algebra Seminar Add to calendar L1
The Andrews-Curtis conjecture
Wed, 10/10/2007
11:30 		Eliana Hechter (Oxford) Algebra Kinderseminar Add to calendar Queen's College
Genomes, Groups and Geometry
Wed, 10/10/2007
16:00 		Dr. Robin Knight (Oxford) Logic Seminar Add to calendar L3
Categories of Scott Spaces
Thu, 11/10/2007
12:00 		Carlos Mora-Corral (Oxford University Mathematical Institute) OxMOS Workshop/Meeting/Lecture Add to calendar DH 3rd floor SR
OxMOS Lecture - Bifurcation Theory I
Local Bifurcation Theory (I): Theorem of Crandall and Rabinowitz
Thu, 11/10/2007
12:00 		Oscar Randal-Williams (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
The Poincaré - Hopf index theorem
We will prove an extended Poincaré - Hopf theorem, identifying several invariants of a manifold $ M $. These are its Euler characteristic $ \chi(M) $, the sum $ \sum_{x_i} ind_V(x_i) $ of indices at zeroes of a vector field $ V $ on $ M $, the self-intersection number $ \Delta \cap \Delta $ of the diagonal $ \Delta \subset M \times M $ and finally the integral $ \int_M e(TM) $ of the Euler class of the tangent bundle.
Thu, 11/10/2007
14:00 		Dr Omar Lakkis (University of Sussex) Computational Mathematics and Applications Add to calendar Comlab
Explicit A Posteriori Error Analysis for Evolution Equation's Finite Element Approximation

I will address the usage of the elliptic reconstruction technique (ERT) in a posteriori error analysis for fully discrete schemes for parabolic partial differential equations. A posteriori error estimates are effective tools in error control and adaptivity and a mathematical rigorous derivation justifies and improves their use in practical implementations.

The flexibility of the ERT allows a virtually indiscriminate use of various parabolic PDE techniques such as energy methods, duality methods and heat-kernel estimates, as opposed to direct approaches which leave less maneuver room. Thanks to ERT parabolic stability techniques can be combined with different elliptic a posteriori error analysis techniques, such as residual or recovery estimators, to derive a posteriori error bounds. The method has the merit of unifying previously known approaches, as well as providing new ones and providing us with novel error bounds (e.g., pointwise norm error bounds for the heat equation). [These results are based on joint work with Ch. Makridakis and A. Demlow.]

Another feature, which I would like to highlight, of the ERT is its simplifying power. It allows us to derive estimates where the analysis would be very complicated otherwise. As an example, I will illustrate its use in the context of non-conforming methods, with a special eye on discontinuous Galerkin methods. [These are recent results obtained jointly with E. Georgoulis.]

Thu, 11/10/2007
16:00 		Michael Rubinstein (Waterloo) Number Theory Seminar Add to calendar L3
Probability models for elliptic curves
Thu, 11/10/2007
16:15 		Dimitri Kazakov (JINR & Moscow) String Theory Seminar Add to calendar Fisher Room
Renormalize 1/N Expansion for Field Theories in Extra Dimensions

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

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