Forthcoming Seminars

Fri, 30/10/2009
14:00 		Professor Martin Howard (John Innes Centre) Mathematical Biology and Ecology Seminar Add to calendar L3
Optimising noisy concentration gradients in developmental biology
Fri, 30/10/2009
14:15 		Mark Davis (Imperial) Nomura Seminar Add to calendar DH 1st floor SR
Jump-Diffusion Risk-Sensitive Asset Management Mark H.A. Davis, Sebastien Lleo
This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion 'factor' process. The criterion, following earlier work by Bielecki, Pliska, Nagai and others, is risk-sensitive optimization (equivalent to maximizing the expected growth rate subject to a constraint on variance.) By using a change of measure technique introduced by Kuroda and Nagai we show that the problem reduces to solving a certain stochastic control problem in the factor process, which has no jumps. The main result of the paper is that the Hamilton-Jacobi-Bellman equation for this problem has a classical solution. The proof uses Bellman's "policy improvement" method together with results on linear parabolic PDEs due to Ladyzhenskaya et al. This is joint work with Sebastien Lleo.
Mon, 02/11/2009
12:00 		Jock McOrist (Cambridge) String Theory Seminar Add to calendar L3
Dynamical Vacuum Selection and Supersymmetry Breaking in String Theory
Intersecting brane models in string theory have proven a useful tool for studying the dynamics of quantum field theories. I will describe how certain brane models may be used to shed light on the phenomenon of supersymmetry breaking and vacuum selection in a cosmological context.
Mon, 02/11/2009
14:15 		Mireille Capitaine (Université de Toulouse) Stochastic Analysis Seminar Add to calendar Eagle House
The Largest Eigenvalues of Finite Rank Deformation of Large Wigner Matrices: Convergence and Fluctuations
Joint work with C. Donati-Martin and D. Feral
Mon, 02/11/2009
15:45 		Karen Vogtmann (Cornell and MPI Bonn) Topology Seminar Add to calendar L3
Embeddings of Out(Fn)
Mon, 02/11/2009
16:00 		Hung Manh Bui (Mathematical Institute, Oxford) Junior Number Theory Seminar Add to calendar SR1
Extreme values of $ S(T) $
Mon, 02/11/2009
17:00 		Thomas Schmidt (Universität Erlangen-Nürnberg) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
A uniqueness result for graphs of least gradient
We investigate the minimization problem for the variational integral
$$\int_\Omega\sqrt{1+|Dw|^2}\,dx$$
in Dirichlet classes of vector-valued functions $ w $. It is well known that the existence of minimizers can be established if the problem is formulated in a generalized way in the space of functions of bounded variation. In this talk we will discuss a uniqueness theorem for these generalized minimizers. Actually, the theorem holds for a larger class of variational integrals with linear growth and was obtained in collaboration with Lisa Beck (SNS Pisa).
Tue, 03/11/2009
12:00 		Piotr Bizon (Jagiellonian University) Relativity Seminar Add to calendar L3
Late-time tails of self-gravitating waves
I will present recent joint work with Tadek Chmaj and Andrzej Rostworowski concerning late-time behavior of self-gravitating massless fields.  We show that the asymptotic convergence to a static equilibrium (Minkowski or Schwarzschild) is an essentially nonlinear phenomenon which cannot, despite many assertions to the contrary in the literature, be properly described by the theory of linearized perturbations on a fixed static asymptotically flat background (so called Price's tails). To substantiate this claim in the case of small initial data we compute the late-time tails (both the decay rate and the amplitude) in four and higher even spacetime dimensions using nonlinear perturbation theory and we verify the results numerically. The reason for considering this problem in higher dimensions was motivated by the desire to demonstrate an accidental and misleading character of equality of decay rates of linear and nonlinear tails in four dimensions. 
Tue, 03/11/2009
14:00 		Gabriel Koch (University of Oxford) OxPDE Lunchtime Seminar Add to calendar Gibson 1st Floor SR
An alternative approach to regularity for the Navier-Stokes equations in critical spaces
We present an alternative viewpoint on recent studies of regularity of solutions to the Navier-Stokes equations in critical spaces. In particular, we prove that mild solutions which remain bounded in the space $ \dot H^{1/2} $ do not become singular in finite time, a result which was proved in a more general setting by L. Escauriaza, G. Seregin and V. Sverak using a different approach. We use the method of "concentration-compactness" + "rigidity theorem" which was recently developed by C. Kenig and F. Merle to treat critical dispersive equations. To the authors' knowledge, this is the first instance in which this method has been applied to a parabolic equation. This is joint work with Carlos Kenig.
Tue, 03/11/2009
14:30 		Oliver Riordan (Oxford) Combinatorial Theory Seminar Add to calendar L3
A general class of self-dual percolation models
One of the main aims in the theory of percolation is to find the `critical probability' above which long range connections emerge from random local connections with a given pattern and certain individual probabilities. The quintessential example is Kesten's result from 1980 that if the edges of the square lattice are selected independently with probability $ p $, then long range connections appear if and only if $ p>1/2 $.  The starting point is a certain self-duality property, observed already in the early 60s; the difficulty is not in this observation, but in proving that self-duality does imply criticality in this setting. Since Kesten's result, more complicated duality properties have been used to determine a variety of other critical probabilities. Recently, Scullard and Ziff have described a very general class of self-dual percolation models; we show that for the entire class (in fact, a larger class), self-duality does imply criticality.
Tue, 03/11/2009
16:00 		Benno Kuckuck Junior Geometric Group Theory Seminar Add to calendar DH 1st floor SR
Finiteness properties of groups
Tue, 03/11/2009
17:00 		Graham Vincent-Smith (Oxford) Functional Analysis Seminar Add to calendar L3
Intrinsic Gaussian fields
Wed, 04/11/2009
11:30 		Tobias Barthel (University of Oxford) Algebra Kinderseminar Add to calendar ChCh, Tom Gate, Room 2
The Quest for $ \mathbb{F}_\mathrm{un} $
We will present different ideas leading to and evolving around geometry over the field with one element. After a brief summary of the so-called numbers-functions correspondence we will discuss some aspects of Weil's proof of the Riemann hypothesis for function fields. We will see then how lambda geometry can be thought of as a model for geometry over $ \mathbb{F}_\mathrm{un} $ and what some familiar objects should look like there. If time permits, we will explain a link with stable homotopy theory.

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

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