Forthcoming Seminars

Thu, 14/06/2012 13:00	Ian Angus	Mathematical Finance Internal Seminar	DH 1st floor SR
	Marginal utility-based pricing of a stochastic income

Thu, 14/06/2012
14:00

Dr Christoph Reisinger (University of Oxford)

Computational Mathematics and Applications

Gibson Grd floor SR

Piecewise constant control approximation to multi-dimensional HJB equations

While a general framework of approximating the solution to Hamilton-Jacobi-Bellman (HJB) equations by difference methods is well established, and efficient numerical algorithms are available for one-dimensional problems, much less is known in the multi-dimensional case. One difficulty is the monotone approximation of cross-derivatives, which guarantees convergence to the viscosity solution. We propose a scheme combining piecewise freezing of the policies in time with a suitable spatial discretisation to establish convergence for a wide class of equations, and give numerical illustrations for a diffusion equation with uncertain parameters. These equations arise, for instance, in the valuation of financial derivatives under model uncertainty.

This is joint work with Peter Forsyth.

Thu, 14/06/2012 15:30	Dr M Movshev (Stonybrook)	Twistor Workshop	Gibson Grd floor SR
	Twistors in 11 dimensions

Thu, 14/06/2012 16:00	Michele Piana (Universita' di Verona Italy)	Industrial and Applied Mathematics Seminar	DH 1st floor SR
	From science to data to images to science with applications to astrophysics, neuroscience and physiology
	The computational analysis of a mathematical model describing a complex system is often based on the following roadmap: first, an experiment is conceived, in which the measured data are (either directly or indirectly) related to the input data of the model equations; second, such equations are computationally solved to provide iconographic reconstructions of the unknown physical or physiological parameters of the system; third, the reconstructed images are utilized to validate the model or to inspire appropriate improvements. This talk will adopt such framework to investigate three applied problems, respectively in solar physics, neuroscience and physiology. The solar physics problem is concerned with the exploitation of hard X-ray data for the comprehension of energy transport mechanisms in solar flares. The neuroscientific problem is the one to model visual recognition in humans with the help of a magnetocencephalography experiment. Finally, the physiological problem investigates the kinetics of the kidney-bladder system by means of nuclear data.

Thu, 14/06/2012 16:00	Roger Heath-Brown (Oxford)	Number Theory Seminar	L3
	Burgess's estimates for character sums

Thu, 14/06/2012 17:00	Özlem Beyarslan (Bogazici)	Logic Seminar	L3
	Algebraic closure in pseudofinite fields
	A pseudofinite field is a perfect pseudo-algebraically closed (PAC) field which has $\hat{\mathbb{Z}}$ as absolute Galois group. Pseudofinite fields exists and they can be realised as ultraproducts of finite fields. A group $G$ is geometrically represented in a theory $T$ if there are modles $M_0\prec M$ of $T$ , substructures $A,B$ of $M$ , $B\subset acl(A)$ , such that $M_0\le A\le B\le M$ and $Aut(B/A)$ is isomorphic to $G$ . Let $T$ be a complete theory of pseudofinite fields. We show that, geometric representation of a group whose order is divisibly by $p$ in $T$ heavily depends on the presence of $p^n$ 'th roots of unity in models of $T$ . As a consequence of this, we show that, for almost all completions of the theory of pseudofinite fields, over a substructure $A$ , algebraic closure agrees with definable closure, if $A$ contains the relative algebraic closure of the prime field. This is joint work with Ehud Hrushovski.

Fri, 15/06/2012 00:00		Mathematical Biology and Ecology Seminar
	No Seminar

Fri, 15/06/2012 14:15	Dr Antoine Jacquier (Imperial College London)	Nomura Seminar	DH 1st floor SR
	Asymptotic expansions for diffusions
	Given a diffusion in R^n, we prove a small-noise expansion for its density. Our proof relies on the Laplace method on Wiener space and stochastic Taylor expansions in the spirit of Benarous-Bismut. Our result applies (i) to small-time asymptotics and (ii) to the tails of the distribution and (iii) to small volatility of volatility. We shall study applications of this result to stochastic volatility models, recovering the Berestycki- Busca-Florent formula (using (i)), the Gulisashvili-Stein expansion (from (ii)) and Lewis' expansions (using (iii)). This is a joint work with J.D. Deuschel (TU Berlin), P. Friz (TU Berlin) and S. Violante (Imperial College London).

Fri, 15/06/2012 14:30	Dr Henry Winstanley (University of Limerick)	Mathematical Geoscience Seminar	DH 3rd floor SR
	Modelling rate limitations in dissimilatory iron reduction
	Respiration is a redox reaction in which oxidation of a substrate (often organic) is coupled to the reduction of a terminal electron acceptor (TEA) such as oxygen. Iron oxides in various mineral forms are abundant in sediments and sedimentary rocks, and many subsurface microbes have the ability to respire using Fe(III) as the TEA in anoxic conditions. This process is environmentally important in the degradation of organic substrates and in the redox-cycling of iron. But low mineral solubility limits the bioavailability of Fe(III), which microbes access primarily through reductive dissolution. For aqueous nutrients, expressions for microbial growth and nutrient uptake rates are standardly based on Monod kinetics. We address the question of what equivalent description is appropriate when solid phase Fe(III) is the electron acceptor.