Forthcoming Seminars

Tue, 30/11/2010
17:00 		Tatiana Bandman (Bar-Ilan) Algebra Seminar Add to calendar L2
Geometry and dynamics of some word maps on SL(2, Fq)
I will speak about a geometric method, based on the classical trace map, for investigating word maps on groups PSL(2, q) and SL(2, q). In two different papers (with F. Grunewald, B. Kunyavskii, and Sh. Garion, F. Grunewald, respectively) this approach was applied to the following problems. 1. Description of Engel-like sequences of words in two variables which characterize finite solvable groups. The original problem was reformulated in the language of verbal dynamical systems on SL(2). This allowed us to explain the mechanism of the proofs for known sequences and to obtain a method for producing more sequences of the same nature. 2. Investigation of the surjectivity of the word map defined by the n-th Engel word [[[X, Y ], Y ], . . . , Y ] on the groups PSL(2, q) and SL(2, q). Proven was that for SL(2, q), this map is surjective onto the subset SL(2, q) $ \setminus $ {−id} $ \subset $ SL(2, q) provided that q $ \ge q_0(n) $ is sufficiently large. If $ n\le 4 $ then the map was proven to be surjective for all PSL(2, q).
Tue, 30/11/2010
17:00 		Matthew Tarbard (Oxford) Functional Analysis Seminar Add to calendar L3
Banach spaces with few operators
Wed, 01/12/2010
11:30 		Jason Semeraro (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
Reformulating the Weight Conjecture
Given a block, b, of a finite group, Alperin's weight conjecture predicts a miraculous equality between the number of isomorphism classes of simple b-modules and the number of G-orbits of b-weights. Radha Kessar showed that the latter can be written in terms of the fusion system of the block and Markus Linckelmann has computed it as an Euler characteristic of a certain space (provided certain conditions hold). We discuss these reformulations and give some examples.
Thu, 02/12/2010
11:00 		Prof Boris Zilber Advanced Class Logic Add to calendar SR2
"On a problem by Bogomolov-Korotaev-Tschinkel"
Thu, 02/12/2010
13:00 		Gechun Liang Mathematical Finance Internal Seminar Add to calendar L3
A Functional Approach to FBSDEs and Its Application in Optimal Portfolios
In [Liang, Lyons and Qian(2009): Backward Stochastic Dynamics on a Filtered Probability Space, to appear in the Annals of Probability], the authors demonstrated that BSDEs can be reformulated as functional differential equations, and as an application, they solved BSDEs on general filtered probability spaces. In this paper the authors continue the study of functional differential equations and demonstrate how such approach can be used to solve FBSDEs. By this approach the equations can be solved in one direction altogether rather than in a forward and backward way. The solutions of FBSDEs are then employed to construct the weak solutions to a class of BSDE systems (not necessarily scalar) with quadratic growth, by a nonlinear version of Girsanov's transformation. As the solving procedure is constructive, the authors not only obtain the existence and uniqueness theorem, but also really work out the solutions to such class of BSDE systems with quadratic growth. Finally an optimal portfolio problem in incomplete markets is solved based on the functional differential equation approach and the nonlinear Girsanov's transformation. The talk is based on the joint work with Lyons and Qian: http://arxiv4.library.cornell.edu/abs/1011.4499
Thu, 02/12/2010
13:00 		Arman Taghavi-Chabert (University of Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
A Lie-theoretic approach to prolongations of differential systems
I will sketch a method to prolong certain classes of differential equations on manifolds using Lie algebra cohomology. The talk will be based on articles by Branson, Cap, Eastwood and Gover (arXiv:math/0402100 and ESI preprint 1483).
Thu, 02/12/2010
14:00 		Dr Julian Hall (University of Edinburgh) Computational Mathematics and Applications Add to calendar Rutherford Appleton Laboratory, nr Didcot
A high performance dual revised simplex solver
Implementations of the revised simplex method for solving large scale sparse linear programming (LP) problems are highly efficient for single-core architectures. This talk will discuss the limitations of the underlying techniques in the context of modern multi-core architectures, in particular with respect to memory access. Novel techniques for implementing the dual revised simplex method will be introduced, and their use in developing a dual revised simplex solver for multi-core architectures will be described.
Thu, 02/12/2010
16:00 		Simon Cotter (Oxford) Differential Equations and Applications Seminar Add to calendar Gibson Grd floor SR
Multiscale stochastic modelling of biochemical reactions
When modeling biochemical reactions within cells, it is vitally important to take into account the effect of intrinsic noise in the system, due to the small copy numbers of some of the chemical species. Deterministic systems can give vastly different types of behaviour for the same parameter sets of reaction rates as their stochastic analogues, giving us an incorrect view of the bifurcation diagram. Stochastic Simulation Algorithms (SSAs) exist which draw exact trajectories from the Chemical Master Equation (CME). However, these methods can be very computationally expensive, particularly where there is a separation of time scales of the evolution of some of the chemical species. Some of the species may react many times on a time scale for which others are highly unlikely to react at all. Simulating all of these reactions of the fast species is a waste of computational effort, and many different methods exist for reducing the system to one which only contains the slow variables. In this talk we will introduce the conditional Gillespie algorithm, a method for sampling directly from the conditional distribution on the fast variables, given a static value for the slow variables. Using this, we will go on to describe the constrained Gillespie approach, which uses simulations of the CG algorithm to estimate the drift and diffusion terms of the effective dynamics of the slow variables. If there is time at the end, I will briefly describe my work on another project, which involves full sampling of the posterior distributions in various problems in data assimilation using Monte Carlo Markov Chain (MCMC) methods.
Thu, 02/12/2010
17:00 		Salma Kuhlmann (Konstanz) Logic Seminar Add to calendar L3
Valued di fferential fields of exponential logarithmic series.
Consider the valued field $ \mathbb{R}((\Gamma)) $ of generalised series, with real coefficients and monomials in a totally ordered multiplicative group $ \Gamma $ . In a series of papers, we investigated how to endow this formal algebraic object with the analogous of classical analytic structures, such as exponential and logarithmic maps, derivation, integration and di fference operators. In this talk, we shall discuss series derivations and series logarithms on $ \mathbb{R}((\Gamma)) $ (that is, derivations that commute with in finite sums and satisfy an in finite version of Leibniz rule, and logarithms that commute with infi nite products of monomials), and investigate compatibility conditions between the logarithm and the derivation, i.e. when the logarithmic derivative is the derivative of the logarithm.
Fri, 03/12/2010
10:00 		Valerie Livina (University of East Anglia) Industrial and Interdisciplinary Workshops Add to calendar DH 3rd floor SR
Potential analysis of geophysical time series
We apply the novel method of potential analysis to study climatic records. The method comprises (i) derivation of the number of climate states from time series, (ii) derivation of the potential coefficients. Dynamically monitoring patterns of potential analysis yields indications of possible bifurcations and transitions of the system. The method is tested on artificial data and then applied to various climatic records [1,2]. It can be applied to a wide range of stochastic systems where time series of sufficient length and temporal resolution are available and transitions or bifurcations are surmised. A recent application of the method in a model of globally coupled bistable systems [3] confirms its general applicability for studying time series in statistical physics. [1] Livina et al, Climate of the Past, 2010. [2] Livina et al, Climate Dynamics (submitted) [3] Vaz Martins et al, Phys. Rev. E, 2010
Fri, 03/12/2010
14:15 		Kees Oosterlee (Delft University of Technology) Nomura Seminar Add to calendar L3
The Heston model with stochastic interest rates and pricing options with Fourier-cosine expansions.
In this presentation we discuss the Heston model with stochastic interest rates driven by Hull-White or Cox-Ingersoll-Ross processes. We present approximations in the Heston-Hull-White hybrid model, so that a characteristic function can be derived and derivative pricing can be efficiently done using the Fourier Cosine expansion technique. This pricing method, called the COS method, is explained in some detail. We furthermore discuss the effect of the approximations in the hybrid model on the instantaneous correlations, and check the influence of the correlation between stock and interest rate on the implied volatilities.
Fri, 03/12/2010
14:30 		Liora Malki-Epshtein (UCL) Mathematical Geoscience Seminar Add to calendar DH 3rd floor SR
Internal waves generated by double diffusion
Fri, 03/12/2010
14:30 		Liora Malki (UCL) Mathematical Geoscience Seminar Add to calendar DH 3rd floor SR
To Be Announced

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

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