Forthcoming Seminars

Thu, 03/05/2012 16:00	Minhyong Kim (Oxford)	Number Theory Seminar	L3
	Homotopy theory and Diophantine geometry, an upduate

Thu, 03/05/2012 16:00	Linda Cummings (New Jersey Institute of Technology Newark)	Industrial and Applied Mathematics Seminar	DH 1st floor SR
	Free surface flow of nematic liquid crystal: spreading and instability
	Nematic liquid crystals (NLCs) are materials that flow like liquids, but have some crystalline features. Their molecules are typically long and thin, and tend to align locally, which imparts some elastic character to the NLC. Moreover at interfaces between the NLC and some other material (such as a rigid silicon substrate, or air) the molecules tend to have a preferred direction (so-called "surface anchoring"). This preferred behaviour at interfaces, coupled with the internal "elasticity", can give rise to complex instabilities in spreading free surface films. This talk will discuss modelling approaches to describe such flows. The models presented are capable of capturing many of the key features observed experimentally, including arrested spreading (with or without instability). Both 2D and 3D spreading scenarios will be considered, and simple ways to model nontrivial surface anchoring patterns, and "defects" within the flows will also be discussed.

Fri, 04/05/2012 00:00		Mathematical Biology and Ecology Seminar
	No Seminar

Fri, 04/05/2012
10:00

Gary Barnes (Arkex)

Industrial and Interdisciplinary Workshops

DH 1st floor SR

Noise reduction for airborne gravity gradiometer instrumentation

ARKeX is a geophysical exploration company that conducts airborne gravity gradiometer surveys for the oil industry. By measuring the variations in the gravity field it is possible to infer valuable information about the sub-surface geology and help find prospective areas.

A new type of gravity gradiometer instrument is being developed to have higher resolution than the current technology. The basic operating principles are fairly simple - essentially measuring the relative displacement of two proof masses in response to a change in the gravity field. The challenge is to be able to see typical signals from geological features in the presence of large amounts of motional noise due to the aircraft. Fortunately, by making a gradient measurement, a lot of this noise is cancelled by the instrument itself. However, due to engineering tolerances, the instrument is not perfect and residual interference remains in the measurement.

Accelerometers and gyroscopes record the motional disturbances and can be used to mathematically model how the noise appears in the instrument and remove it during a software processing stage. To achieve this, we have employed methods taken from the field of system identification to produce models having typically 12 inputs and a single output. Generally, the models contain linear transfer functions that are optimised during a training stage where controlled accelerations are applied to the instrument in the absence of any anomalous gravity signal. After training, the models can be used to predict and remove the noise from data sets that contain signals of interest.

High levels of accuracy are required in the noise correction schemes to achieve the levels of data quality required for airborne exploration. We are therefore investigating ways to improve on our existing methods, or find alternative techniques. In particular, we believe non-linear and non-stationary models show benefits for this situation.

Fri, 04/05/2012 14:00	Prof Kostas Kardars (Boston University)	Nomura Seminar	DH 1st floor SR
	A guide through market viability for frictionless markets
	In this talk, we elaborate on the notions of no-free-lunch that have proved essential in the theory of financial mathematics—most notably, arbitrage of the first kind. Focus will be given in most recent developments. The precise connections with existence of deflators, numeraires and pricing measures are explained, as well as the consequences that these notions have in the existence of bubbles and the valuation of illiquid assets in the market.

Fri, 04/05/2012 14:30	Prof. Peter Jan van Leeuwen (University of Reading)	Mathematical Geoscience Seminar	DH 3rd floor SR
	Nonlinear data assimilation in highly nonlinear large-dimensional systems
	Data assimilation in highly nonlinear and high dimensional systems is a hard problem. We do have efficient data-assimilation methods for high-dimensional weakly nonlinear systems, exploited in e.g. numerical weather forecasting. And we have good methods for low-dimensional (<5) nonlinear systems. The combination is more difficult, however. Recently our data-assimilation group managed to generate efficient particle filters that seem to scale almost perfectly with the dimension of the system, that is the number of particles (model runs) needed is independent of the system dimension. This will be demonstrated on the barotropic vorticity equations in the chaotic regime, exploring different observation strategies. The main question now is why these methods are so efficient. The performance seems to be independent of traditional measures of stability, such as the number of positive Lyaponov exponents or decorrelation times of the dynamics. Our latest progress in this area will be discussed, bringing in elements of extreme value statistics and the stability of the combined model/observation system.

Fri, 04/05/2012 16:30	Professor Steven Strogatz (Cornell University)	Colloquia	L2
	Social networks that balance themselves
	Consider a fully-connected social network of people, companies,or countries, modeled as an undirected complete graph with real numbers onits edges. Positive edges link friends; negative edges link enemies.I'll discuss two simple models of how the edge weights of such networksmight evolve over time, as they seek a balanced state in which "the enemy ofmy enemy is my friend." The mathematical techniques involve elementaryideas from linear algebra, random graphs, statistical physics, anddifferential equations. Some motivating examples from internationalrelations and social psychology will also be discussed. This is joint workwith Seth Marvel, Jon Kleinberg, and Bobby Kleinberg.

Mon, 07/05/2012 12:00	Noppadol Mekareeya (Max Planck Institut fuer Physik)	String Theory Seminar	L3
	Integer Partitions, Mirror Symmetry and 3d Gauge Theories
	In this talk, I will focus on an infinite class of 3d N=4 gauge theories which can be constructed from a certain set of ordered pairs of integer partitions. These theories can be elegantly realised on brane intervals in string theory. I will give an elementary review on such brane constructions and introduce to the audience a symmetry, known as mirror symmetry, which exchanges two different phases (namely the Higgs and Coulomb phases) of such theories. Using mirror symmetry as a tool, I will discuss a certain geometrical aspect of the vacuum moduli spaces of such theories in the Coulomb phase. It turns out that there are certain infinite subclasses of such spaces which are special and rather simple to study; they are complete intersections. I will mention some details and many interesting features of these spaces.

Mon, 07/05/2012 16:00	Netan Dogra	Junior Number Theory Seminar	SR1
	p-adic zeta functions, p-adic polylogarithms and fundamental groups
	This talk will attempt to say something about the p-adic zeta function, a p-adic analytic object which encodes information about Galois cohomology of Tate twists in its special values. We first explain the construction of the p-adic zeta function, via p-adic Fourier theory. Then, after saying something about Coleman integration, we will explain the interpretation of special values of the p-adic zeta function as limiting values of p-adic polylogarithms, in analogy with the Archimedean case. Finally, we will explore the consequences for the de Rham and etale fundamental groupoids of the projective line minus three points.

Mon, 07/05/2012 17:00	Dehua Wang (University of Pittsburgh)	Partial Differential Equations Seminar	Gibson 1st Floor SR
	Some mixed type problems in gas dynamics and geometry

Tue, 08/05/2012
10:15

Nicolas Triantafyllidis (Ecole Polytechnique)

OCCAM Special Seminar

OCCAM Common Room (RI2.28)

Stability of periodic structures: from composites to crystal lattices

Stability plays an important role in engineering, for it limits the load carrying capacity of all kinds of structures. Many failure mechanisms in advanced engineering materials are stability-related, such as localized deformation zones occurring in fiber-reinforced composites and cellular materials, used in aerospace and packaging applications. Moreover, modern biomedical applications, such as vascular stents, orthodontic wire etc., are based on shape memory alloys (SMA’s) that exploit the displacive phase transformations in these solids, which are macroscopic manifestations of lattice-level instabilities.

The presentation starts with the introduction of the concepts of stability and bifurcation for conservative elastic systems with a particular emphasis on solids with periodic microstructures. The concept of Bloch wave analysis is introduced, which allows one to find the lowest load instability mode of an infinite, perfect structure, based solely on unit cell considerations. The relation between instability at the microscopic level and macroscopic properties of the solid is studied for several types of applications involving different scales: composites (fiber-reinforced), cellular solids (hexagonal honeycomb) and finally SMA's, where temperature- or stress-induced instabilities at the atomic level have macroscopic manifestations visible to the naked eye.

Tue, 08/05/2012 11:00	Shilan Mistry (OCIAM, Oxford)	Applied Dynamical Systems and Inverse Problems Seminar	DH 3rd floor SR
	Evaluating Probabilistic Forecasts

Tue, 08/05/2012 12:00	Lionel Mason	Quantum Field Theory Seminar	L3
	Einstein gravity amplitudes from twistor-string theory

Tue, 08/05/2012 14:30	Hao Huang (UCLA)	Combinatorial Theory Seminar	L3
	Extremal Problems in Eulerian Digraphs
	Graphs and digraphs behave quite differently, and many classical results for graphs are often trivially false when extended to general digraphs. Therefore it is usually necessary to restrict to a smaller family of digraphs to obtain meaningful results. One such very natural family is Eulerian digraphs, in which the in-degree equals out-degree at every vertex. In this talk, we discuss several natural parameters for Eulerian digraphs and study their connections. In particular, we show that for any Eulerian digraph G with n vertices and m arcs, the minimum feedback arc set (the smallest set of arcs whose removal makes G acyclic) has size at least $m^2/2n^2+m/2n$ , and this bound is tight. Using this result, we show how to find subgraphs of high minimum degrees, and also long cycles in Eulerian digraphs. These results were motivated by a conjecture of Bollobás and Scott. Joint work with Ma, Shapira, Sudakov and Yuster

Tue, 08/05/2012 15:45		Algebraic and Symplectic Geometry Seminar
	No seminar

Tue, 08/05/2012 17:00	Professor G. A. Jones (Southampton)	Algebra Seminar	L2
	Groups and Beauville surfaces

Wed, 09/05/2012 10:15	Brian Duffy, Simon Walton	OCCAM Wednesday Morning Event	OCCAM Common Room (RI2.28)
	Glyph-Based Video Visualization Techniques

Wed, 09/05/2012 12:30	Apala Majumdar (OCCAM)	OxPDE Lunchtime Seminar	Gibson 1st Floor SR
	Passage from mean-field to continuum to liquid crystal theories
	In this talk, we make quantitative comparisons between two widely-used liquid crystal modelling approaches - the continuum Landau-de Gennes theory and mesoscopic mean-field theories, such as the Maier-Saupe and Onsager theories. We use maximum principle arguments for elliptic partial differential equations to compute explicit bounds for the norm of static equilibria within the Landau-de Gennes framework. These bounds yield an explicit prescription of the temperature regime within which the LdG and the mean-field predictions are consistent, for both spatially homogeneous and inhomogeneous systems. We find that the Landau-de Gennes theory can make physically unrealistic predictions in the low-temperature regime. In my joint work with John Ball, we formulate a new theory that interpolates between mean-field and continuum approaches and remedies the deficiencies of the Landau-de Gennes theory in the low-temperature regime. In particular, we define a new thermotropic potential that blows up whenever the mean-field constraints are violated. The main novelty of this work is the incorporation of spatial inhomogeneities (outside the scope of mean-field theory) along with retention of mean-field level information.

Wed, 09/05/2012 15:00	Howard Elman (Department of Computer Science University of Maryland)	Special Seminar	Taught Course Center
	"Efficient Solution Algorithms for Partial Differential Equations with Random Coefficients"

Thu, 10/05/2012 12:00	Laura Schaposnik	Junior Geometry and Topology Seminar	L3
	Spectral data for the Hitchin fibration
	We shall dedicate the first half of the talk to introduce classical Higgs bundles and describe the fibres of the corresponding Hitchin fibration in terms of spectral data. Then, we shall define principal Higgs bundles and look at some examples. Finally, we consider the particular case of $SL(2,R)$ , $U(p,p)$ and $Sp(2p,2p)$ Higgs bundles and study their spectral data. Time permitting, we shall look at different applications of our new methods.