Forthcoming Seminars
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Mon, 16/01/2012 11:00 |
Gua Thiang, Robert Laugwitz, Jan Vonk |
Topology Advanced Classes  |
L3 |
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Three short talks by the authors of essays on topics related to c3 Algebraic topology: Whitehead's theorem, Cohomology of fibre bundles, Division algebras |
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Mon, 16/01/2012 12:00 |
Nadav Drukker (King's College London) |
String Theory Seminar |
L3 |
| I will present a two-parameter family of Wilson loop operators in N = 4 supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines. These observables capture a natural generalization of the quark-antiquark potential. These loops are calculated on the gauge theory side to second order in perturbation theory and in a semiclassical expansion in string theory to one-loop order. The resulting determinants are given in integral form and can be evaluated numerically for general values of the parameters or analytically in a systematic expansion around the 1/2 BPS configuration. I will comment about the feasibility of deriving all-loop results for these Wilson loops. | |||
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Mon, 16/01/2012 14:15 |
Sergey Grigorian (Simons Center Stony Brook) |
Geometry and Analysis Seminar |
L3 |
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Mon, 16/01/2012 15:45 |
Richard Hepworth (Aberdeen) |
Topology Seminar |
L3 |
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Chataur and Menichi showed that the homology of the free loop space of the classifying space of a compact Lie group admits a rich algebraic structure: It is part of a homological field theory, and so admits operations parametrised by the homology of mapping class groups. I will present a new construction of this field theory that improves on the original in several ways: It enlarges the family of admissible Lie groups. It extends the field theory to an open-closed one. And most importantly, it allows for the construction of co-units in the theory. This is joint work with Anssi Lahtinen. |
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Mon, 16/01/2012 17:00 |
Bernd Kirchheim (OxPDE, University of Oxford) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
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Tue, 17/01/2012 11:00 |
Dr Andrew Dawson ((AOPP (Oxford University))) |
Applied Dynamical Systems and Inverse Problems Seminar |
DH 3rd floor SR |
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Tue, 17/01/2012 12:00 |
Prof Graeme Segal (Oxford) |
Relativity Seminar |
L3 |
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The WZW functional for a map from a surface to a Lie group has a role in the theory of harmonic maps, and it also arises as the determinant of a d-bar operator on the surface, as the action functional for a 2-dimensional quantum field theory, as the partition function of 3-dimensional Chern-Simons theory on a manifold with boundary, and as the norm-squared of a state-vector. It is intimately related to the quantization of the symplectic manifold of flat bundles on the surface, a fascinating test-case for different approaches to geometric quantization. It is also interesting as an example of interpolation between commutative and noncommutative geometry. I shall try to give an overview of the area, focussing on the aspects which are still not well understood. |
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Tue, 17/01/2012 14:00 |
Helge Ruddat (Universität Mainz) |
Algebraic and Symplectic Geometry Seminar |
SR1 |
| Assuming the natural compactification X of a hypersurface in (C^*)^n is smooth, it can exhibit any Kodaira dimension depending on the size and shape of the Newton polyhedron of X. In a joint work with Mark Gross and Ludmil Katzarkov, we give a construction for the expected mirror symmetry partner of a complete intersection X in a toric variety which works for any Kodaira dimension of X. The mirror dual might be a reducible and is equipped with a sheaf of vanishing cycles. We give evidence for the duality by proving the symmetry of the Hodge numbers when X is a hypersurface. The leading example will be the mirror of a genus two curve. If time permits, I will explain relations to homological mirror symmetry and the Gross-Siebert construction. | |||
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Tue, 17/01/2012 14:15 |
Prof. Steve Tobias (University of Leeds) |
Geophysical and Nonlinear Fluid Dynamics Seminar |
Dobson Room, AOPP |
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Tue, 17/01/2012 15:45 |
Helge Ruddat (Universität Mainz) |
Algebraic and Symplectic Geometry Seminar |
L3 |
| Assuming the natural compactification X of a hypersurface in (C^*)^n is smooth, it can exhibit any Kodaira dimension depending on the size and shape of the Newton polyhedron of X. In a joint work with Mark Gross and Ludmil Katzarkov, we give a construction for the expected mirror symmetry partner of a complete intersection X in a toric variety which works for any Kodaira dimension of X. The mirror dual might be a reducible and is equipped with a sheaf of vanishing cycles. We give evidence for the duality by proving the symmetry of the Hodge numbers when X is a hypersurface. The leading example will be the mirror of a genus two curve. If time permits, I will explain relations to homological mirror symmetry and the Gross-Siebert construction. | |||
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Tue, 17/01/2012 17:00 |
Simon Chandler-Wilde (Reading) |
Functional Analysis Seminar |
L3 |
| In this talk I will describe recent work by myself and others (E.B. Davies (KCL), M. Lindner (Chemnitz), S. Roch (Darmstadt)) on the spectrum and essential spectrum of bi-infinite and semi-infinite (not necessarily self-adjoin) tri-diagonal random operators, and the implications of these results for the spectra of associated random matrices, and for the finite section method for infinite tri-diagonal systems. A main tool will be limit operator methods, as described in Chandler-Wilde and Lindner, Memoirs AMS, 2011), supplemented by certain symmetry arguments including a Coburn lemma for random matrices. | |||
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Tue, 17/01/2012 17:00 |
Professor S Gurevich (Wisconsin) |
Algebra Seminar |
L2 |
| In the digital radar problem we design a function (waveform) S(t) in the Hilbert space H=C(Z/p) of complex valued functions on Z/p={0,...,p-1}, the integers modulo a prime number p>>0. We transmit the function S(t) using the radar to the object that we want to detect. The wave S(t) hits the object, and is reflected back via the echo wave R(t) in H, which has the form R(t) = exp{2πiωt/p}⋅S(t+τ) + W(t), where W(t) in H is a white noise, and τ,ω in ℤ/p, encode the distance from, and velocity of, the object. Problem (digital radar problem) Extract τ,ω from R and S. I first introduce the classical matched filter (MF) algorithm that suggests the 'traditional' way (using fast Fourier transform) to solve the digital radar problem in order of p^2⋅log(p) operations. I will then explain how to use techniques from group representation theory to design (construct) waveforms S(t) which enable us to introduce a fast matched filter (FMF) algorithm, that we call the "flag algorithm", which solves the digital radar problem in a much faster way of order of p⋅log(p) operations. I will demonstrate additional applications to mobile communication, and global positioning system (GPS). This is a joint work with A. Fish (Math, Madison), R. Hadani (Math, Austin), A. Sayeed (Electrical Engineering, Madison), and O. Schwartz (Electrical Engineering and Computer Science, Berkeley). | |||
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Wed, 18/01/2012 11:30 |
Peter Pappas (Oxford) |
Algebra Kinderseminar |
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| I will present a history of the problem, relate it to other conjectures, and, with time permitting, indicate recent developments. The focus will primarily be group-theoretic and intended for the non-specialist. | |||
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Wed, 18/01/2012 15:45 |
Owen Cotton-Barratt |
Junior Geometric Group Theory Seminar |
SR2 |
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Thu, 19/01/2012 12:00 |
Vittoria Bussi |
Junior Geometry and Topology Seminar |
L3 |
| This is the first of two talks about Derived Algebraic Geometry. Due to the vastity of the theory, the talks are conceived more as a kind of advertisement on this theory and some of its interesting new features one should contemplate and try to understand, as it might reveal interesting new insights also on classical objects, rather than a detailed and precise exposition. We will start with an introduction on the very basic idea of this theory, and we will expose some motivations for introducing it. After a brief review on the existing literature and a speculation about homotopy theories and higher categorical structures, we will review the theory of dg-categories, model categories, S-categories and Segal categories. This is the technical part of the seminar and it will give us the tools to understand the basic setting of Topos theory and Homotopical Algebraic Geometry, whose applications will be exploited in the next talk. | |||
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Thu, 19/01/2012 12:30 |
Paolo Antonelli (DAMPT, University of Cambridge) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
| In this seminar I will expose some results obtained jointly with P. Marcati, concerning the global existence of weak solutions for the Quantum Hydrodynamics System in the space of energy. We don not require any additional regularity and/or smallness assumptions on the initial data. Our approach replaces the WKB formalism with a polar decomposition theory which is not limited by the presence of vacuum regions. In this way we set up a self consistent theory, based only on particle density and current density, which does not need to define velocity fields in the nodal regions. The mathematical techniques we use in this paper are based on uniform (with respect to the approximating parameter) Strichartz estimates and the local smoothing property. I will then discuss some possible future extensions of the theory. | |||
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Thu, 19/01/2012 13:00 |
Martin Gould |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| In recent years, limit order books have been adopted as the pricing mechanism in more than half of the world's financial markets. Thanks to recent technological advances, traders around the globe also now have real-time access to limit order book trading platforms and can develop trading strategies that make use of this "ultimate microscopic level of description". In this talk I will briefly describe the limit order book trade-matching mechanism, and explain how the extra flexibility it provides has vastly impacted the problem of how a market participant should optimally behave in a given set of circumstances. I will then discuss the findings from my recent statistical analysis of real limit order book data for spot trades of 3 highly liquid currency pairs (namely, EUR/USD, GBP/USD, and EUR/GBP) on a large electronic trading platform during May and June 2010, and discuss how a number of my findings highlight weaknesses in current models of limit order books. | |||
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Thu, 19/01/2012 14:00 |
Dr Jennifer Scott (STFC, Rutherford Appleton Laboratory) |
Computational Mathematics and Applications |
Rutherford Appleton Laboratory, nr Didcot |
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Thu, 19/01/2012 14:00 |
Shamgar Gurevich (Madison) |
Representation Theory Seminar |
L3 |
| This is a sequel to Lecture I (given in the algebra seminar, Tuesday). It will be slightly more specialized. The finite Weil representation is the algebra object that governs the symmetries of the Hilbert space H =C(Z/p): The main objective of this talk is to introduce the geometric Weil representation which is an algebra-geometric (l-adic perverse Weil sheaf) counterpart of the finite Weil representation. Then, I will explain how the geometric Weil representation is used to prove the main technical results stated in Lecture I. In the course, I will explain the Grothendieck geometrization procedure by which sets are replaced by algebraic varieties and functions by sheaf theoretic objects. This is a joint work with R. Hadani (Austin). | |||
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Thu, 19/01/2012 16:00 |
Russell Davies (Cardiff) |
Industrial and Applied Mathematics Seminar |
DH 1st floor SR |
| It is an inherent premise in Boltzmann's formulation of linear viscoelasticity, that for shear deformations at constant pressure and constant temperature, every material has a unique continuous relaxation spectrum. This spectrum defines the memory kernel of the material. Only a few models for representing the continuous spectrum have been proposed, and these are entirely empirical in nature. Extensive laboratory time is spent worldwide in collecting dynamic data from which the relaxation spectra of different materials may be inferred. In general the process involves the solution of one or more exponentially ill-posed inverse problems. In this talk I shall present rigorous models for the continuous relaxation spectrum. These arise naturally from the theory of continuous wavelet transforms. In solving the inverse problem I shall discuss the role of sparsity as one means of regularization, but there is also a secondary regularization parameter which is linked, as always, to resolution. The topic of model-induced super-resolution is discussed, and I shall give numerical results for both synthetic and real experimental data. The talk is based on joint work with Neil Goulding (Cardiff University). | |||
