Forthcoming Seminars

Tue, 17/05/2011 15:45	Arend Bayer (University of Connecticut)	Algebraic and Symplectic Geometry Seminar	L3
	Towards Bridgeland stability conditions on threefolds
	I will discuss a conjectural Bogomolov-Gieseker type inequality for "tilt-stable" objects in the derived category of coherent sheaves on smooth projective threefolds. The conjecture implies the existence of Bridgeland stability conditions on threefolds, and also has implications to birational geometry: it implies a slightly weaker version of Fujita's conjecture on very ampleness of adjoint line bundles.

Tue, 17/05/2011
17:00

Dr Khalid Bou-Rabee (Michigan)

Algebra Seminar

'Detecting a group through it's pronilpotent completion'

In 1939, Wilhelm Magnus gave a characterization of free groups in terms of their rank and nilpotent quotients. Our goal in this talk is to present results giving both positive and negative answers to the following question: does a similar characterization hold within the class of finite-extensions of finitely generated free groups? This talk covers joint work with Brandon Seward.

Tue, 17/05/2011 17:00	Michael Levitin (Reading)	Functional Analysis Seminar	L3
	Fourier transform, null variety, and Laplacian's eigenvalues

Wed, 18/05/2011 11:30		Algebra Kinderseminar
	NO SEMINAR

Wed, 18/05/2011 12:45	Robert Elliott (University of Adelaide and University of Calgary)	Nomura Seminar	Oxford-Man Institute
	A BSDE Approach to a Risk-Based Optimal Investment of an Insurer
	We discuss a backward stochastic differential equation, (BSDE), approach to a risk-based, optimal investment problem of an insurer. A simplified continuous-time economy with two investment vehicles, namely, a fixed interest security and a share, is considered. The insurer's risk process is modeled by a diffusion approximation to a compound Poisson risk process. The goal of the insurer is to select an optimal portfolio so as to minimize the risk described by a convex risk measure of his/her terminal wealth. The optimal investment problem is then formulated as a zero-sum stochastic differential game between the insurer and the market. The BSDE approach is used to solve the game problem. This leads to a simple and natural approach for the existence and uniqueness of an optimal strategy of the game problem without Markov assumptions. Closed-form solutions to the optimal strategies of the insurer and the market are obtained in some particular cases.

Wed, 18/05/2011 16:00	David Hume (University of Oxford)	Junior Geometric Group Theory Seminar	SR1
	Optimal embeddings of groups into Hilbert spaces
	We begin by showing the underlying ideas Bourgain used to prove that the Cayley graph of the free group of finite rank can be embedded into a Hilbert space with logarithmic distortion. Equipped with these ideas we then tackle the same problem for other metric spaces. Time permitting these will be: amalgamated products and HNN extensions over finite groups, uniformly discrete hyperbolic spaces with bounded geometry and Cayley graphs of cyclic extensions of small cancellation groups.

Thu, 19/05/2011
12:30

Dominic Breit (University of Saarbrucken)

OxPDE Lunchtime Seminar

Gibson 1st Floor SR

On stationary motions of Prandtl-Eyring fluids in 2D

We prove the existence of weak solutions to steady Navier Stokes equations

$\text{div}\, \sigma+f=\nabla\pi+(\nabla u)u.$

Here $u:\mathbb{R}^2\supset \Omega\rightarrow \mathbb{R}^2$ denotes the velocity field satisfying $\text{div}\, u=0$ , $f:\Omega\rightarrow\mathbb{R}^2$ and $\pi:\Omega\rightarrow\mathbb{R}$ are external volume force and pressure, respectively. In order to model the behavior of Prandtl-Eyring fluids we assume

$\sigma= DW(\varepsilon (u)),\quad W(\varepsilon)=|\varepsilon|\log (1+|\varepsilon|).$

A crucial tool in our approach is a modified Lipschitz truncation preserving the divergence of a given function.

Thu, 19/05/2011 13:00	Lukasz Szpruch	Mathematical Finance Internal Seminar	DH 1st floor SR
	To Be Announced

Thu, 19/05/2011
14:00

Dr Maciek Korzec (Technical University of Berlin)

Computational Mathematics and Applications

Gibson Grd floor SR

Modelling and simulation of the self-assembly of thin solid films

Many continuum models have been derived in recent years which describe the self-assembly of industrially utilisable crystalline films to a level of detail that allows qualitative comparisons with experiments. For thin-film problems, where the characteristic length scales in vertical and horizontal directions differ significantly, the governing surface diffusion equations can be reduced to simpler PDEs by making use of asymptotic expansions. Many mathematical problems and solutions emerge from such new evolution equations and many of them remind of Cahn-Hilliard type equations. The surface diffusion models are of high, of fourth or even sixth, order.

We present the modeling, model reduction and simulation results for heteroepitaxial growth as for Ge/Si quantum dot self-assembly. The numerical methods we are using are based on trigonometric interpolation. These kind of pseudospectral methods seem very well suited for simulating the coarsening of large quantum dot arrays. When the anisotropy of the growing crystalline film is strong, it might become necessary to add a corner regularisation to the model. Then the transition region between neighboring facets is still smooth, but its scale is rather small. In this case it might be useful to think about an adaptive extension of the existing method.

Figure 1: Ostwald ripening process of quantum dots depicted at consecutive time points. One fourth of the whole, periodic, simulated domain is shown.

Joint work with Peter Evans and Barbara Wagner

Thu, 19/05/2011 14:30	Roozbeh Hazrat (Belfast)	Representation Theory Seminar	L3
	Leavitt Path Algebras

Thu, 19/05/2011 16:00	Lauder (Oxford)	Number Theory Seminar	L3
	Computations with classical and p-adic modular forms

Thu, 19/05/2011 16:00	Ralph Kenna (University of Coventry)	Differential Equations and Applications Seminar	DH 1st floor SR
	Mass and the dependency of research quality on group size
	The notion of critical mass in research is one that has been around for a long time without proper definition. It has been described as some kind of threshold group size above which research standards significantly improve. However no evidence for such a threshold has been found and critical mass has never been measured – until now. We present a new, simple, sociophysical model which explains how research quality depends on research-group structure and in particular on size. Our model predicts that there are, in fact, two critical masses in research, the values of which are discipline dependent. Research quality tends to be linearly dependent on group size, but only up to a limit termed the 'upper critical mass'. The upper critical mass is interpreted as the average maximum number of colleagues with whom a given individual in a research group can meaningfully interact. Once the group exceeds this size, it tends to fragment into sub-groups and research quality no longer improves significantly with increasing size. There is also a lower critical mass, which small research groups should strive to achieve for stability. Our theory is tested using empirical data from RAE 2008 on the quantity and quality of research groups, for which critical masses are determined. For pure and applied mathematics, the lower critical mass is about 2 and 6, respectively, while for statistics and physics it is 9 and 13. The upper critical mass, beyond which research quality does not significantly improve with increasing group size, is about twice the lower value.

Thu, 19/05/2011 17:00		Logic Seminar	L3
	To Be Announced

Fri, 20/05/2011 10:00	Gero Miesenboeck and Shamik DasGupta (Physiology, Anatomy and Genetics)	Industrial and Interdisciplinary Workshops	DH 1st floor SR
	Decision making on the fly

Fri, 20/05/2011 12:00	Laura Schaposnik (University of Oxford)	Junior Geometry and Topology Seminar	SR1
	Spectral data for principal Higgs bundles
	In this talk I shall present some ongoing work on principal G-Higgs bundles, for G a simple Lie group. In particular, we will consider two non-compact real forms of GL(p+q,C) and SL(p+q,C), namely U(p,q) and SU(p,q). By means of the spectral data that principal Higgs bundles carry for these non-compact real forms, we shall give a new description of the moduli space of principal U(p,q) and SU(p,q)-Higgs bundles. As an application of our method, we will count the connected components of these moduli spaces.

Fri, 20/05/2011 14:00	Prof C Bangham (London))	Mathematical Biology and Ecology Seminar	L2
	Dynamics of persistent infection with the human leukaemia virus, HTLV-1.

Fri, 20/05/2011 14:15	Prof Tom Hurd (McMaster University)	Nomura Seminar	DH 1st floor SR
	Two Factor Models of a Firm's Capital Structure
	We argue that a natural extension of the well known structural credit risk framework of Black and Cox is to model both the firm's assets and liabilities as correlated geometric Brownian motions. This financially reasonable assumption leads to a unification of equity derivatives (written on the stock price), and credit securities like bonds and credit default swaps (CDS), nesting the Black-Cox credit model with a particular stochastic volatility model for the stock. As we will see, it yields reasonable pricing performance with acceptable computational efficiency. However, it has been well understood how to extend a credit framework like this quite dramatically by the trick of time- changing the Brownian motions. We will find that the resulting two factor time-changed Brownian motion framework can encompass well known equity models such as the variance gamma model, and at the same time reproduce the stylized facts about default stemming from structural models of credit. We will end with some encouraging calibration results for a dataset of equity and credit derivative prices written on Ford Motor Company.

Mon, 23/05/2011 12:00	Amihay Hanany (Imperial College)	String Theory Seminar	L3
	Trivertices and SU(2)'s
	Given a graph with lines and 3-valent vertices, one can construct, using a simple dictionary, a Lagrangian that has N=2 supersymmetry in 3+1 dimensions. This is a construction which generalizes the notion of a quiver. The vacuum moduli space of such a theory is well known to give moment map equations for a HyperKahler manifold. We will discuss the class of hyperkahler manifolds which arise due to such a construction and present their special properties. The Hilbert Series of these spaces can be computed and turns out to be a function of the number of external legs and loops in the graph but not on its detailed structure. The corresponding SCFT consequence of this property indicates a crucial universality of many Lagrangians, all of which have the same dynamics. The talk is based on http://arXiv.org/pdf/1012.2119.

Mon, 23/05/2011 14:15	Vassili Kolokoltsov (ETH Zurich)	Stochastic Analysis Seminar	Oxford-Man Institute
	'Nonlilnear Lévy Processes and Interacting Particles'.
	I will introduce the notion of a nonlinear Levy process, discuss basic well-posednes, SDE links and the connection with interacting particles. The talk is aimed to be an introduction to the topic of my recent CUP monograph 'Nonllinear Markov processes and kinetic equations'.

Mon, 23/05/2011 14:15	Olivier Biquard (Ecole Normale)	Geometry and Analysis Seminar	L3
	Desingularization of Einstein orbifolds