Forthcoming Seminars
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Tue, 22/02/2011 12:00 |
Dr Fernando Alday (Oxford) |
Relativity Seminar  |
L3 |
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Tue, 22/02/2011 13:15 |
Yi Ming Lai (OCCAM) |
Junior Applied Mathematics Seminar |
Gibson Grd floor SR |
| We examine several aspects of introducing stochasticity into dynamical systems, with specific applications to modellingpopulations of neurons. In particular, we use the example of a interactingpopulations of excitatory and inhibitory neurons (E-I networks). As eachnetwork consists of a large but finite number of neurons that firestochastically, we can study the effect of this intrinsic noise using a masterequation formulation. In the parameter regime where each E-I network acts as alimit cycle oscillator, we combine phase reduction and averaging to study thestationary distribution of phase differences in an ensemble of uncoupled E-Ioscillators, and explore how the intrinsic noise disrupts synchronization dueto a common external noise source. | |||
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Tue, 22/02/2011 14:00 |
Tony Pantev (Univesity of Pennsylvania) |
Algebraic and Symplectic Geometry Seminar |
SR1 |
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I will explain how essential information about the structure of symplectic manifolds is captured by algebraic data, and specifically by the non-commutative mixed Hodge structure on the cohomology of the Fukaya category. I will discuss computable Hodge theoretic invariants arising from twist functors, and from geometric extensions. I will also explain how the instanton-corrected Chern-Simons theory fits in the framework of normal functions in non-commutative Hodge theory and will give applications to explicit descriptions of quantum Lagrangian branes. This is a joint work with L. Katzarkov and M. Kontsevich. |
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Tue, 22/02/2011 14:30 |
James King (Oxford) |
Combinatorial Theory Seminar |
L3 |
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Tue, 22/02/2011 15:45 |
Tony Pantev (University of Pennsylvania) |
Algebraic and Symplectic Geometry Seminar |
L3 |
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Tue, 22/02/2011 17:00 |
Lars Louder (Oxford) |
Algebra Seminar |
L2 |
| I will prove that generating sets of surface groups are either reducible or Nielsen equivalent to standard generating sets, improving upon a theorem of Zieschang. Equivalently, Aut(F_n) acts transitively on Epi(F_n,S) when S is a surface group. | |||
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Wed, 23/02/2011 11:30 |
David Craven (University of Oxford) |
Algebra Kinderseminar |
ChCh, Tom Gate, Room 2 |
| The representation theory of the symmetric groups is far more advanced than that of arbitrary finite groups. The blocks of symmetric groups with defect group of order pn are classified, in the sense that there is a finite list of possible Morita equivalence types of blocks, and it is relatively straightforward to write down a representative from each class.In this talk we will look at the case where n=2. Here the theory is fairly well understood. After introducing combinatorial wizardry such as cores, the abacus, and Scopes moves, we will see a new result, namely that the simple modules for any p-block of weight 2 "come from" (technically, have isomorphic sources to) simple modules for S2p or the wreath product of Sp and C2. | |||
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Wed, 23/02/2011 16:00 |
Hemanth Saratchandran (Oxford University) |
Junior Geometric Group Theory Seminar |
SR2 |
| I will give a brief introduction to the Steenrod squares and move on to show some applications of them in Topology and Geometry. | |||
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Thu, 24/02/2011 12:30 |
Kenneth H. Karlsen (Univ. of Oslo) |
OxPDE Lunchtime Seminar |
Gibson 1st Floor SR |
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We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes. |
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Thu, 24/02/2011 13:00 |
Dirk Schlueter (University of Oxford) |
Junior Geometry and Topology Seminar |
SR1 |
| The topology of the moduli space of stable bundles (of coprime rank and degree) on a smooth curve can be understood from different points of view. Atiyah and Bott calculated the Betti numbers by gauge-theoretic methods (using equivariant Morse theory for the Yang-Mills functional), arriving at the same inductive formula which had been obtained previously by Harder and Narasimhan using arithmetic techniques. An intermediate interpretation (algebro-geometric in nature but dealing with infinite-dimensional parameter spaces as in the gauge theory picture) comes from thinking about vector bundles in terms of matrix divisors, generalising the Abel-Jacobi map to higher rank bundles. I'll sketch these different approaches, emphasising their parallels, and in the end I'll speculate about how (some of) these methods could be made to work when the underlying curve acquires nodal singularities. | |||
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Thu, 24/02/2011 13:00 |
Michael Monoyios |
Mathematical Finance Internal Seminar |
DH 1st floor SR |
| We consider an optimal stopping problem arising in connection with the exercise of an executive stock option by an agent with inside information. The agent is assumed to have noisy information on the terminal value of the stock, does not trade the stock or outside securities, and maximises the expected discounted payoff over all stopping times with regard to an enlarged filtration which includes the inside information. This leads to a stopping problem governed by a time-inhomogeneous diffusion and a call-type reward. Using stochastic flow ideas we establish properties of the value function (monotonicity, convexity in the log-stock price), conditions under which the option value exhibits time decay, and derive the smooth fit condition for the solution to the free boundary problem governing the maximum expected reward. From this we derive the early exercise decomposition of the value function. The resulting integral equation for the unknown exercise boundary is solved numerically and this shows that the insider may exercise the option before maturity, in situations when an agent without the privileged information may not. | |||
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Thu, 24/02/2011 14:00 |
Dr Juan Vera (Tilburg University) |
Computational Mathematics and Applications |
Gibson Grd floor SR |
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Polynomial Programs are ussually solved by using hierarchies of convex relaxations. This scheme rapidly becomes computationally expensive and is often tractable only for problems of small sizes. We propose an iterative scheme that improves an initial relaxation without incurring exponential growth in size. The key ingredient is a dynamic scheme for generating valid polynomial inequalities for general polynomial programs. These valid inequalities are then used to construct better approximations of the original problem. As a result, the proposed scheme is in principle scalable to large general combinatorial optimization problems. Joint work with Bissan Ghaddar and Miguel Anjos |
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Thu, 24/02/2011 16:00 |
Eddie Wilson (Southampton) |
Differential Equations and Applications Seminar |
DH 1st floor SR |
| "Most drivers will recognize the scenario: you are making steady progress along the motorway when suddenly you come to a sudden halt at the tail end of a lengthy queue of traffic. When you move off again you look for the cause of the jam, but there isn't one. No accident damaged cars, no breakdown, no dead animal, and no debris strewn on the road. So what caused everyone to stop?" RAC news release (2005) The (by now well-known) answer is that such "phantom traffic jams" exist as waves that propagate upstream (opposite to the driving direction) - so that the vast majority of individuals do not observe the instant at which the jam was created - yet what exactly goes on at that instant is still a matter of debate. In this talk I'll give an overview of empirical data and models to describe such spatiotemporal patterns. The key property we need is instability: and using the framework of car-following (CF) models, I'll show how different sorts of linear (convective and absolute) and nonlinear instability can be used to explain empirical patterns. | |||
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Thu, 24/02/2011 17:00 |
Jean-Philippe Rolin (Dijon) |
Logic Seminar |
L3 |
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It is known that the expansion of the real field by some quasianalytic algebras of functions are o-minimal and polynomially bounded. We prove that, for these structures, the preparation theorem for definable functions proved by L. van den Dries and P. Speissegger has an explicit form, from which it is easy to deduce a quantifier elimination result. |
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Fri, 25/02/2011 00:00 |
Mathematical Biology and Ecology Seminar |
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Fri, 25/02/2011 10:00 |
Paul Davies, Edward Stansfield and Ian Ellis (Thales UK) |
Industrial and Interdisciplinary Workshops |
DH 1st floor SR |
| This will be on the topic of the CASE project Thales will be sponsoring from Oct '11. | |||
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Fri, 25/02/2011 14:15 |
Prof Damiano Brigo (King's College London) |
Nomura Seminar |
Oxford-Man Institute |
| We present three examples of credit products whose valuation poses challenging modeling problems related to armageddon scenarios and extreme losses, analyzing their behaviour pre- and in-crisis. The products are Credit Index Options (CIOs), Collateralized Debt Obligations (CDOs), and Credit Valuation Adjustment (CVA) related products. We show that poor mathematical treatment of possibly vanishing numeraires in CIOs and lack of modes in the tail of the loss distribution in CDOs may lead to inaccurate valuation, both pre- and especially in crisis. We also consider the limits of copula models in trying to represent systemic risk in credit intensity models. We finally enlarge the picture and comment on a number of common biases in the public perception of modeling in relationship with the crisis. | |||
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Fri, 25/02/2011 14:30 |
Anthony Anderson (DAMTP) |
Mathematical Geoscience Seminar |
DH 3rd floor SR |
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Mon, 28/02/2011 11:00 |
Ulrike Tillmann (Oxford) |
Topology Advanced Classes |
SR2 |
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Persistent homology is a relatively new tool to analyse the topology of data sets. We will give a brief introduction and tutorial as preparation for the third talk in the afternoon. |
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Mon, 28/02/2011 12:00 |
String Theory Seminar |
L3 | |
