Forthcoming Seminars

Thu, 31/05/2012 16:00	Jochen Koenigsmann (Oxford)	Logic Seminar Number Theory Seminar	L3
	Fields with the absolute Galois group of $\mathbb{Q}$ .

Fri, 01/06/2012 00:00		Mathematical Biology and Ecology Seminar
	No Seminar

Fri, 01/06/2012
10:00

Andy Stove (Thales UK)

Industrial and Interdisciplinary Workshops

DH 1st floor SR

Sensor Resource Management

The issue of resource management arises with any sensor which is capable either of sensing only a part of its total field of view at any one time, or which is capable of having a number of operating modes, or both.

A very simple example is a camera with a telephoto lens. The photographer has to decide what he is going to photograph, and whether to zoom in to get high resolution on a part of the scene, or zoom out to see more of the scene. Very similar issues apply, of course, to electro-optical sensors (visible light or infra-red 'TV' cameras) and to radars.

The subject has, perhaps, been most extensively studied in relation to multi mode/multi function radars, where approaches such as neural networks, genetic algorithms and auction mechanisms have been proposed as well as more deterministic mangement schemes, but the methods which have actually been implemented have been much more primitive.

The use of multiple, disparate, sensors on multiple mobile, especially airborne, platforms adds further degrees of freedom to the problem - an extension is of growing interest.

The presentation will briefly review the problem for both the single-sensor and the multi-platform cases, and some of the approaches which have been proposed, and will highlight the remaining current problems.

Fri, 01/06/2012 14:15	Prof Scott Robertosn (Pittsburgh)	Nomura Seminar	DH 1st floor SR
	Utility-Based Pricing in the Large Position, Nearly Complete Limit
	In this talk, approximations to utility indifference prices for a contingent claim in the large position size limit are provided. Results are valid for general utility functions and semi-martingale models. It is shown that as the position size approaches infinity, all utility functions with the same rate of decay for large negative wealths yield the same price. Practically, this means an investor should price like an exponential investor. In a sizeable class of diffusion models, the large position limit is seen to arise naturally in conjunction with the limit of a complete model and hence approximations are most appropriate in this setting.

Fri, 01/06/2012 14:30	Dr Jari Fowkes (University of Edinburgh)	Mathematical Geoscience Seminar	DH 3rd floor SR
	Global Optimization of Lipschitz Continuous Function with Applications to Reservoir Simulation
	This talk will consist of two parts. In the first part we will present a motivating application from oil reservoir simulation, namely finding the location and trajectory of an oil producing well which maximises oil production. We will show how such a problem can be tackled through the use of radial basis function (RBF) approximation (also known as Kriging or Gaussian process regression) and a branch and bound global optimization algorithm. In the second part of the talk we will show how one can improve the branch and bound algorithm through the use of Lipschitz continuity of the RBF approximation. This leads to an entirely new global optimization algorithm for twice differentiable functions with Lipschitz continuous Hessian. The algorithm makes use of recent cubic regularisation techniques from local optimization to obtain the necessary bounds within the branch and bound algorithm.

Mon, 04/06/2012 14:15	Luis Fernando Alday (Oxford)	Geometry and Analysis Seminar	L3
	On the AGT conjecture

Mon, 04/06/2012 16:00	Alastair Irving	Junior Number Theory Seminar	SR1
	Diophantine Approximation with Primes

Mon, 04/06/2012 17:00	Hoai-Minh Nguyen (University of Minnesota)	Partial Differential Equations Seminar	Gibson 1st Floor SR
	Approximate cloaking using transformation optics and negative index materials
	Cloaking recently attracts a lot of attention from the scientific community due to the progress of advanced technology. There are several ways to do cloaking. Two of them are based on transformation optics and negative index materials. Cloaking based on transformation optics was suggested by Pendry and Leonhardt using transformations which blow up a point into the cloaked regions. The same transformations had previously used by Greenleaf et al. to establish the non-uniqueness for Calderon's inverse problem. These transformations are singular and hence create a lot of difficulty in analysis and practical applications. The second method of cloaking is based on the peculiar properties of negative index materials. It was proposed by Lai et al. and inspired from the concept of complementary media due to Pendry and Ramakrishna. In this talk, I will discuss approximate cloaking using these two methods. Concerning the first one, I will consider the situation, first proposed in the work of Kohn et al., where one uses transformations which blow up a small ball (instead of a point) into cloaked regions. Many interesting issues such as finite energy and resonance will be mentioned. Concerning the second method, I provide the (first) rigorous analysis for cloaking using negative index materials by investigating the situation where the loss (damping) parameter goes to 0. I will also explain how the arguments can be used not only to establish the rigor for other interesting related phenomena using negative index materials such as superlenses and illusion optics but also to enlighten the mechanism of these phenomena.

Tue, 05/06/2012 12:30	Dominic Breit (Universität München)	OxPDE Special Seminar	Gibson 1st Floor SR
	Solenoidal Lipschitz truncation for parabolic PDEs
	We consider functions $u\in L^\infty(0,T;L^2({B}))\cap L^p(0,T;W^{1,p}({B}))$ where $p\in(1,\infty)$ , $T$ is positive and ${B}\subset\mathbb R^d$ bounded. Solutions to non-linear evolutionary PDE's typically belong to these spaces. Many applications require an approximation $u_\lambda$ of $u$ which is Lipschitz-continous and coincides with $u$ on a large set. For problems arising in fluid mechanics one needs to work with functions which are divergence-free thus we construct a function $u_\lambda\in L^\infty(0,T;W^{1,\mathrm{BMO}}({B}))$ which is in addition to the properties from the known truncation methods solenoidal. As an application we revisit the existence proof for non-stationary generalized Newtonian fluids. Since $\mathrm{div}\,u_\lambda=0$ we can completely avoid the appearance of the pressure term and the proof can be heavily simplified.

Tue, 05/06/2012 15:45	Frank Gounelas (Oxford)	Algebraic and Symplectic Geometry Seminar	L3
	Free curves on varieties
	This talk will be about various ways in which a variety can be "connected by higher genus curves", mimicking the notion of rational connectedness. At least in characteristic zero, the existence of a curve with a large deformation space of morphisms to a variety implies that the variety is in fact rationally connected. Time permitting I will discuss attempts to show this result in positive characteristic.

Tue, 05/06/2012 17:00	Professor S. Rees (Newcastle)	Algebra Seminar	L2
	Artin groups of large type: from geodesics to Baum-Connes
	I’ll report on my recent work (with co-authors Holt and Ciobanu) on Artin groups of large type, that is groups with presentations of the form G = hx1, . . . , xn \| xixjxi · · · = xjxixj · · · , 8i < ji for which both sides of the ‘braid relation’ on xi and xj have length mij 2 N [1 with mij 3. (In fact, our results still hold when some, but not all possible, relations with mij = 2 are allowed.) Recently, Holt and I characterised the geodesic words in these groups, and described an effective method to reduce any word to geodesic form. That proves the groups shortlex automatic and gives an effective (at worst quadratic) solution to the word problem. Using this characterisation of geodesics, Holt, Ciobanu and I can derive the rapid decay property for most large type groups, and hence deduce for most of these that the Baum-Connes conjec- ture holds; this has various consequence, in particular that the Kadison- Kaplansky conjecture holds for these groups, i.e. that the group ring CG contains no non-trivial idempotents. 1

Wed, 06/06/2012 10:15	Garegin Papoian (University of Maryland)	OCCAM Wednesday Morning Event	OCCAM Common Room (RI2.28)
	Mechano-chemical feedbacks govern stochastic dynamics of actin networks in eukaryotic cells
	Actin polymerization in vivo is regulated spatially and temporally by a web of signalling proteins. We developed detailed physico-chemical, stochastic models of lamellipodia and filopodia, which are projected by eukaryotic cells during cell migration, and contain dynamically remodelling actin meshes and bundles. In a recent work we studied how molecular motors regulate growth dynamics of elongated organelles of living cells. We determined spatial distributions of motors in such organelles, corresponding to a basic scenario when motors only walk along the substrate, bind, unbind, and diffuse. We developed a mean field model, which quantitatively reproduces elaborate stochastic simulation results as well as provides a physical interpretation of experimentally observed distributions of Myosin IIIa in stereocilia and filopodia. The mean field model showed that the jamming of the walking motors is conspicuous, and therefore damps the active motor flux. However, when the motor distributions are coupled to the delivery of actin monomers towards the tip, even the concentration bump of G-actin that they create before they jam is enough to speed up the diffusion to allow for severalfold longer filopodia. We found that the concentration profile of G-actin along the filopodium is rather non-trivial, containing a narrow minimum near the base followed by a broad maximum. For efficient enough actin transport, this non-monotonous shape is expected to occur under a broad set of conditions. We also find that the stationary motor distribution is universal for the given set of model parameters regardless of the organelle length, which follows from the form of the kinetic equations and the boundary conditions.

Wed, 06/06/2012 16:00	Chris Good (University of Birmingham)	Analytic Topology in Mathematics and Computer Science	L3
	A space that admits all possible orbit spectra of homeomorphisms of uncountable compact metric spaces
	Joint work with: Sina Greenwood, Brian Raines and Casey Sherman Abstract: We say a space $X$ with property $\C P$ is universal for orbit spectra of homeomorphisms with property $\C P$ provided that if $Y$ is any space with property $\C P$ and the same cardinality as $X$ and $h:Y\to Y$ is any (auto)homeomorphism then there is a homeomorphism $g:X\to X$ such that the orbit equivalence classes for $h$ and $g$ are isomorphic. We construct a compact metric space $X$ that is universal for homeomorphisms of compact metric spaces of cardinality the continuum. There is no universal space for countable compact metric spaces. In the presence of some set theoretic assumptions we also give a separable metric space of size continuum that is universal for homeomorphisms on separable metric spaces.

Thu, 07/06/2012 12:00	Tom Hawes	Junior Geometry and Topology Seminar
	An Introduction to Reductive GIT
	The aim of this talk is to give an introduction to Geometric Invariant Theory (GIT) for reductive groups over the complex numbers. Roughly speaking, GIT is concerned with constructing quotients of group actions in the category of algebraic varieties. We begin by discussing what properties we should like quotient varieties to possess, highlighting so-called `good' and `geometric' quotients, and then turn to search for these quotients in the case of affine and projective varieties. Here we shall see that the construction runs most smoothly when we assume our group to be reductive (meaning it can be described as the complexification of a maximal compact subgroup). Finally, we hope to say something about the Hilbert-Mumford criterion regarding semi-stability and stability of points, illustrating it by constructing the rough moduli space of elliptic curves.

Thu, 07/06/2012
12:30

Leonid V. Berlyand (Penn State University)

OxPDE Lunchtime Seminar

Gibson 1st Floor SR

Minimizers with Vortices of the Ginzburg-Landau functional with Semi-Stiff Boundary conditions.

We study minimizers of the Ginzburg-Landau (GL) functional

$E_\epsilon(u):=\frac{1}{2}\int_A |\nabla u|^2 + \frac{1}{4\epsilon^2} \int_A(1-|u|^2)^2$

for a complex-valued order parameter $u$ (with no magnetic ﬁeld). This functional is of fundamental importance in the theory of superconductivity and superuidity; the development of these theories led to three Nobel prizes. For a $2D$ domain $A$ with holes we consider “semistiff” boundary conditions: a Dirichlet condition for the modulus $|u|$ , and a homogeneous Neumann condition for the phase $\phi = \mathrm{arg}(u)$ . The principal result of this work (with V. Rybalko) is a proof of the existence of stable local minimizers with vortices (global minimizers do not exist). These vortices are novel in that they approach the boundary and have bounded energy as $\epsilon\to0$ . In contrast, in the well-studied Dirichlet (“stiff”) problem for the GL PDE, the vortices remain distant from the boundary and their energy blows up as $\epsilon\to 0$ . Also, there are no stable minimizers to the homogeneous Neumann (“soft”) problem with vortices.
Next, we discuss more recent results (with V. Rybalko and O. Misiats) on global minimizers of the full GL functional (with magnetic ﬁeld) subject to semi-stiff boundary conditions. Here, we show the existence of global minimizers with vortices for both simply and doubly connected domains and describe the location of their vortices.

Thu, 07/06/2012 13:00	Radek Erban	Mathematical Finance Internal Seminar	DH 1st floor SR
	Hybrid Modelling of Reaction, Diffusion and Taxis Processes in Biology
	I will discuss methods for spatio-temporal modelling in cellular and molecular biology. Three classes of models will be considered: (i) microscopic (molecular-based, individual-based) models which are based on the simulation of trajectories of individual molecules and their localized interactions (for example, reactions); (ii) mesoscopic (lattice-based) models which divide the computational domain into a finite number of compartments and simulate the time evolution of the numbers of molecules in each compartment; and (iii) macroscopic (deterministic) models which are written in terms of reaction-diffusion-advection PDEs for spatially varying concentrations. In the first part of my talk, I will discuss connections between the modelling frameworks (i)-(iii). I will consider chemical reactions both at a surface and in the bulk. In the second part of my talk, I will present hybrid (multiscale) algorithms which use models with a different level of detail in different parts of the computational domain. The main goal of this multiscale methodology is to use a detailed modelling approach in localized regions of particular interest (in which accuracy and microscopic detail is important) and a less detailed model in other regions in which accuracy may be traded for simulation efficiency. I will also discuss hybrid modelling of chemotaxis where an individual-based model of cells is coupled with PDEs for extracellular chemical signals.

Thu, 07/06/2012 14:00	Dr Chris Farmer (University of Oxford)	Computational Mathematics and Applications	Rutherford Appleton Laboratory, nr Didcot
	From Numerical Rocks to Spatial Data Assimilation
	Uncertainty quantification can begin by specifying the initial state of a system as a probability measure. Part of the state (the 'parameters') might not evolve, and might not be directly observable. Many inverse problems are generalisations of uncertainty quantification such that one modifies the probability measure to be consistent with measurements, a forward model and the initial measure. The inverse problem, interpreted as computing the posterior probability measure of the states, including the parameters and the variables, from a sequence of noise-corrupted observations, is reviewed in the talk. Bayesian statistics provides a natural framework for a solution but leads to very challenging computational problems, particularly when the dimension of the state space is very large, as when arising from the discretisation of a partial differential equation theory. In this talk we show how the Bayesian framework leads to a new algorithm - the 'Variational Smoothing Filter' - that unifies the leading techniques in use today. In particular the framework provides an interpretation and generalisation of Tikhonov regularisation, a method of forecast verification and a way of quantifying and managing uncertainty. To deal with the problem that a good initial prior may not be Gaussian, as with a general prior intended to describe, for example a geological structure, a Gaussian mixture prior is used. This has many desirable properties, including ease of sampling to make 'numerical rocks' or 'numerical weather' for visualisation purposes and statistical summaries, and in principle can approximate any probability density. Robustness is sought by combining a variational update with this full mixture representation of the conditional posterior density.

Thu, 07/06/2012 16:00	Luciano da F. Costa (Brazil University of São Paulo)	Industrial and Applied Mathematics Seminar	DH 1st floor SR
	STRUCTURE AND DYNAMICS IN COMPLEX NETWORKS
	Complex networks have been used to model almost any real-world complex systems. An especially important issue regards how to related their structure and dynamics, which contributes not only for the better understanding of such systems, but also to the prediction of important dynamical properties from specific topological features. In this talk I revise related research developed recently in my group. Particularly attention is given to the concept of accessibility, a new measurement integrating topology and dynamics, and the relationship between frequency of visits and node degree in directed modular complex networks. Analytical results are provided that allow accurate prediction of correlations between structure and dynamics in systems underlain by directed diffusion. The methodology is illustrated with respect to the macaque cortical network.

Thu, 07/06/2012 16:00	Jakob Stix (Heidelberg) (Heidelberg)	Logic Seminar Number Theory Seminar	L3
	On the section conjecture in anabelian geometry
	The section conjecture of Grothendieck's anabelian geometry speculates about a description of the set of rational points of a hyperbolic curve over a number field entirely in terms of profinite groups and Galois theory. In the talk we will discuss local to global aspects of the conjecture, and what can be achieved when sections with additional group theoretic properties are considered.

Fri, 08/06/2012 11:30	Various	OCCAM Special Seminar	OCCAM Common Room (RI2.28)
	OCCAM Group Meeting
	Savina Joseph - Current generation in solar cells Shengxin Zhu - Spectral distribution, smoothing effects and smoothness matching for radial basis functions Ingrid von Glehn - Solving surface PDEs with the closest point method