Forthcoming Seminars
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Thu, 27/10/2011 16:00 |
Peter Clarkson (University of Kent) |
Differential Equations and Applications Seminar  |
DH 1st floor SR |
| In this talk I shall discuss special polynomials associated with rational solutions of the Painlevé equations and of the soliton equations which are solvable by the inverse scattering method, including the Korteweg-de Vries, Boussinesq and nonlinear Schrodinger equations. Further I shall illustrate applications of these polynomials to vortex dynamics and rogue waves. The Painlevé equations are six nonlinear ordinary differential equations that have been the subject of much interest in the past thirty years, and have arisen in a variety of physical applications. Further the Painlevé equations may be thought of as nonlinear special functions. Rational solutions of the Painlevé equations are expressible in terms of the logarithmic derivative of certain special polynomials. For the fourth Painlevé equation these polynomials are known as the generalized Hermite polynomials and generalized Okamoto polynomials. The locations of the roots of these polynomials have a highly symmetric (and intriguing) structure in the complex plane. It is well known that soliton equations have symmetry reductions which reduce them to the Painlevé equations, e.g. scaling reductions of the Boussinesq and nonlinear Schrödinger equations are expressible in terms of the fourth Painlevé equation. Hence rational solutions of these equations can be expressed in terms of the generalized Hermite and generalized Okamoto polynomials. I will also discuss the relationship between vortex dynamics and properties of polynomials with roots at the vortex positions. Classical polynomials such as the Hermite and Laguerre polynomials have roots which describe vortex equilibria. Stationary vortex configurations with vortices of the same strength and positive or negative configurations are located at the roots of the Adler-Moser polynomials, which are associated with rational solutions of the Kortweg-de Vries equation. Further, I shall also describe some additional rational solutions of the Boussinesq equation and rational-oscillatory solutions of the focusing nonlinear Schrödinger equation which have applications to rogue waves. | |||
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Thu, 27/10/2011 16:00 |
Paul-James White (Oxford) |
Number Theory Seminar |
L3 |
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Thu, 27/10/2011 17:00 |
Anand Pillay (Leeds) |
Logic Seminar |
L3 |
| (Joint with Ronnie Nagloo.) I investigate algebraic relations between sets of solutions (and their derivatives) of the "generic" Painlevé equations I-VI, proving a somewhat weaker version of “there are NO algebraic relations". | |||
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Fri, 28/10/2011 10:00 |
Mark Thompson (Department of Engineering Science) |
Industrial and Interdisciplinary Workshops |
DH 1st floor SR |
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Fri, 28/10/2011 14:00 |
Prof Tim Newman (University of Dundee) |
Mathematical Biology and Ecology Seminar |
L1 |
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Fri, 28/10/2011 14:15 |
Vladmir Vovk (Royal Holloway University of London) |
Nomura Seminar |
DH 1st floor SR |
| The standard approach to continuous-time finance starts from postulating a statistical model for the prices of securities (such as the Black-Scholes model). Since such models are often difficult to justify, it is interesting to explore what can be done without any stochastic assumptions. There are quite a few results of this kind (starting from Cover 1991 and Hobson 1998), but in this talk I will discuss probability-type properties emerging without a statistical model. I will only consider the simplest case of one security, and instead of stochastic assumptions will make some analytic assumptions. If the price path is known to be cadlag without huge jumps, its quadratic variation exists unless a predefined trading strategy earns infinite capital without risking more than one monetary unit. This makes it possible to apply the known results of Ito calculus without probability (Follmer 1981, Norvaisa) in the context of idealized financial markets. If, moreover, the price path is known to be continuous, it becomes Brownian motion when physical time is replaced by quadratic variation; this is a probability-free version of the Dubins-Schwarz theorem. | |||
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Mon, 31/10/2011 12:00 |
Nikolay Gromov (King's College London) |
String Theory Seminar |
L3 |
| We compute three-point functions of single trace operators in planar N = 4 SYM. We consider the limit where one of the operators is much smaller than the other two. We find a precise match between weak and strong coupling in the Frolov-Tseytlin classical limit for a very general class of classical solutions. To achieve this match we clarify the issue of back-reaction and identify precisely which three-point functions are captured by a classical computation. | |||
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Mon, 31/10/2011 14:15 |
(University of Oxford) |
Stochastic Analysis Seminar |
Oxford-Man Institute |
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In the recent series of papers Kleban, Simmons, and Ziff gave a non-rigorous
computation (base on Conformal Field Theory) of probabilities of several
connectivity events for critical percolation. In particular they showed that
the probability that there is a percolation cluster connecting two points on
the boundary and a point inside the domain can be
factorized in therms of pairwise connection probabilities. We are going to use
SLE techniques to rigorously compute probabilities of several connectivity
events and prove the factorization formula. |
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Mon, 31/10/2011 14:15 |
Frances Kirwan |
Geometry and Analysis Seminar |
L3 |
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Symplectic implosion is a construction in symplectic geometry due to Guillemin, Jeffrey and Sjamaar, which is related to geometric invariant theory for non-reductive group actions in algebraic geometry. This talk (based on joint work in progress with Andrew Dancer and Andrew Swann) is concerned with an analogous construction in hyperkahler geometry. |
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Mon, 31/10/2011 15:45 |
Ilya Kazachkov (Oxford) |
Topology Seminar |
L3 |
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We introduce the notion of a real cubing. Roughly speaking, real cubings are to CAT(0) cube complexes what real trees are to simplicial trees. We develop an analogue of the Rips’ machine and establish the structure of groups acting nicely on real cubings. |
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Mon, 31/10/2011 15:45 |
Irina Ignatiouk (Universite Cergy) |
Stochastic Analysis Seminar |
Oxford-Man Institute |
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To identify the Martin boundary for a transient Markov chain with Green's function G(x,y), one has to identify all possible limits Lim G(x,y_n)/G(0,y_n) with y_n "tending to infinity". For homogeneous random walks, these limits are usually obtained from the exact asymptotics of Green's function G(x,y_n). For non-homogeneous random walks, the exact asymptotics af Green's function is an extremely difficult problem. We discuss several examples where Martin boundary can beidentified by using large deviation technique. The minimal Martin boundary is in general not homeomorphic to the "radial" compactification obtained by Ney and Spitzer for homogeneous random walks in Z^d : convergence of a sequence of points y_n toa point on the Martin boundary does not imply convergence of the sequence y_n/|y_n| on the unit sphere. Such a phenomenon is a consequence of non-linear optimal large deviation trajectories. |
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Mon, 31/10/2011 16:00 |
Alastair Irving |
Junior Number Theory Seminar |
SR1 |
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Mon, 31/10/2011 17:00 |
Yaroslav Kurylev (University College, London) |
Partial Differential Equations Seminar |
Gibson 1st Floor SR |
| We consider the mathematical theory of invisibility. We start with singular transformation which provide exact (both active and passive) invisibility. We then show how to approximate this highly anisotropic, singular material parameters with homogeneous non-singular ones. We then apply this construction to produce some unusual phenomena in quantum physics, acoustics, etc. (like invisible sensor and Schrodinger Hat potential) | |||
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Tue, 01/11/2011 12:00 |
Dr Paul Heslop (Durham University) |
Relativity Seminar |
L3 |
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Tue, 01/11/2011 13:15 |
Laura Gallimore (Oxford Centre for Collaborative Applied Mathematics) |
Junior Applied Mathematics Seminar |
DH 1st floor SR |
| Cell motility is a crucial part of many biological processes including wound healing, immunity and embryonic development. The interplay between mechanical forces and biochemical control mechanisms make understanding cell motility a rich and exciting challenge for mathematical modelling. We consider the two-phase, poroviscous, reactive flow framework used in the literature to describe crawling cells and present a stripped down version. Linear stability analysis and numerical simulations provide insight into the onset of polarization of a stationary cell and reveal qualitatively distinct families of travelling wave solutions. The numerical solutions also capture the experimentally observed behaviour that cells crawl fastest when the surface they crawl over is neither too sticky nor too slippy. | |||
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Tue, 01/11/2011 15:15 |
Tamas Szekely |
Stochastic Numerics Seminar |
Oxford-Man Institute |
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Tue, 01/11/2011 15:30 |
Professor. J. Michel (Paris VII) |
Algebra Seminar |
SR2 |
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Tue, 01/11/2011 15:45 |
Heinrich Hartmann (Oxford) |
Algebraic and Symplectic Geometry Seminar |
L3 |
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Tue, 01/11/2011 17:00 |
Dr. N. Nikolov (Imperial) |
Algebra Seminar |
L2 |
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Tue, 01/11/2011 17:00 |
David Applebaum (Sheffield) |
Functional Analysis Seminar |
L3 |
