Forthcoming Seminars

Wed, 27/04/2011
14:00

Duvan Henao (Université Pierre et Marie Curie - Paris VI)

Gibson 1st Floor SR

Isoperimetric inequalities and cavity interactions in nonlinear elasticity

We consider the problem of cavitation in nonlinear elasticity, or the formation of macroscopic cavities in elastic materials from microscopic defects, when subjected to large tension at the boundary.

The main goal is to determine the optimal locations where the body prefers the cavities to open, the preferred number of cavities, their optimal sizes, and their optimal shapes. To this aim it is necessary to analyze the elastic energy of an incompressible deformation creating multiple cavities, in a way that accounts for the interaction between the cavitation singularities. Based on the quantitative version of the isoperimetric inequality, as well as on new explicit constructions of incompressible deformations creating cavities of different shapes and sizes, we provide energy estimates showing that, for certain loading conditions, there are only the following possibilities:

only one cavity is created, and if the loading is isotropic then it is created at the centre
multiple cavities are created, they are spherical, and the singularities are well separated
there are multiple cavities, but they act as a single spherical cavity, they are considerably distorted, and the distance between the cavitation singularities must be of the same order as the size of the initial defects contained in the domain.

In the latter case, the formation of thin structures between the cavities is observed, reminiscent of the initiation of ductile fracture by void coalesence.

This is joint work with Sylvia Serfaty (LJLL, Univ. Paris VI).

Thu, 28/04/2011
14:00

Prof Bob Russell (Simon Fraser University)

Computational Mathematics and Applications

Gibson Grd floor SR

An Overview of Adaptive Mesh Generation and Variational Methods

Over the last several decades, many mesh generation methods and a plethora of adaptive methods for solving differential equations have been developed. In this talk, we take a general approach for describing the mesh generation problem, which can be considered as being in some sense equivalent to determining a coordinate transformation between physical space and a computational space. Our description provides some new theoretical insights into precisely what is accomplished from mesh equidistribution (which is a standard adaptivity tool used in practice) and mesh alignment. We show how variational mesh generation algorithms, which have historically been the most common and important ones, can generally be compared using these mesh generation principles. Lastly, we relate these to a variety of moving mesh methods for solving time-dependent PDEs.

This is joint work with Weizhang Huang, Kansas University

Mon, 02/05/2011 12:00		String Theory Seminar	L3
	No Seminar

Mon, 02/05/2011 17:00	Michael Ruzicka (Universitaet Freiburg)	Partial Differential Equations Seminar	Gibson 1st Floor SR
	Analysis of non-Newtonian Fluid Flows
	Fluids that are not adequately described by a linear constitutive relation are usually referred to as "non-Newtonian fluids". In the last 15 years we have seen a significant progress in the mathematical theory of generalized Newtonian fluids, which is an important subclass of non-Newtonian fluids. We present some recent results in the existence theory and in the error analysis for approximate solutions. We will also indicate how these techniques can be generalized to more general constitutive relations.

Tue, 03/05/2011 12:00	Keith Hannabuss	Quantum Field Theory Seminar	L3
	Algebras, Categories, and QED

Tue, 03/05/2011 14:15	Dr Andrew Thompson (DAMTP, University of Cambridge)	Geophysical and Nonlinear Fluid Dynamics Seminar	Dobson Room, AOPP
	Jet-topography interactions in the ocean

Tue, 03/05/2011 14:15	Lioudmilla Vostrikova (University of Angers)	Nomura Seminar	Oxford-Man Institute
	F-divergence minimal martingale measures and optimal portfolios for exponential Levy models with a change-point
	We study exponential Levy models with change-point which is a random variable, independent from initial Levy processes. On canonical space with initially enlarged filtration we describe all equivalent martingale measures for change- point model and we give the conditions for the existence of f-minimal equivalent martingale measure. Using the connection between utility maximisation and f-divergence minimisation, we obtain a general formula for optimal strategy in change-point case for initially enlarged filtration and also for progressively enlarged filtration when the utility is exponential. We illustrate our results considering the Black-Scholes model with change-point. Key words and phrases: f-divergence, exponential Levy models, change-point, optimal portfolio MSC 2010 subject classifications: 60G46, 60G48, 60G51, 91B70

Tue, 03/05/2011 14:30	Bruce Reed (McGill)	Combinatorial Theory Seminar	L3
	Hajos’ Conjecture is almost always true
	In 1961 Hajos conjectured that if a graph contains no subdivsion of a clique of order t then its chromatic number is less than t. In 1981, Erdos and Fajtlowicz showed that the conjecture is almost always false. We show it is almost always true. This is joint work with Keevash, Mohar, and McDiarmid.

Tue, 03/05/2011 15:45	Martijn Kool (Imperial)	Algebraic and Symplectic Geometry Seminar	L3
	A short proof of the Göttsche conjecture
	Counting the number of curves of degree $d$ with $n$ nodes (and no further singularities) going through $(d^2+3d)/2 - n$ points in general position in the projective plane is a problem which was already considered more than 150 years ago. More recently, people conjectured that for sufficiently large $d$ this number should be given by a polynomial of degree $2n$ in $d$. More generally, the Göttsche conjecture states that the number of $n$-nodal curves in a general $n$-dimensional linear subsystem of a sufficiently ample line bundle $L$ on a nonsingular projective surface $S$ is given by a universal polynomial of degree $n$ in the 4 topological numbers $L^2, L.K_S, (K_S)^2$ and $c_2(S)$. In a joint work with Vivek Shende and Richard Thomas, we give a short (compared to existing) proof of this conjecture.

Tue, 03/05/2011 17:00	Prof. Aner Shalev (Jerusalem)	Algebra Seminar	L2
	Word maps: properties, applications, open problems
	Word maps on groups were studied extensively in the past few years, in connection to various conjectures on profinite groups, finite groups, finite simple groups, etc. I will provide background, as well as very recent works (joint with Larsen, Larsen-Tiep, Liebeck-O'Brien-Tiep) on word maps with relations to representations (e.g. Gowers' method and character ratios), geometry and probability. Recent applications, e.g. to subgroup growth and representation varieties, will also be described. I will conclude with a list of problems and conjectures which are still very much open. The talk should be accessible to a wide audience.

Wed, 04/05/2011 10:10	Thomas Woolley (CMB)	OCCAM Wednesday Morning Event	OCCAM Common Room (RI2.28)
	Power spectra methods for stochastic reaction-diffusion equations on growing domains

Wed, 04/05/2011 11:30	David Stewart (University of Oxford)	Algebra Kinderseminar	ChCh, Tom Gate, Room 2
	Unbounding Ext

Wed, 04/05/2011 16:00	Dr Secil Tokgoz (Turkey)	Analytic Topology in Mathematics and Computer Science	L3
	Some results on submaximal spaces
	A topological space $(X,\tau)$ is submaximal if $\tau$ is the maximal element of $[{\tau}_{s}]$ . Submaximality was first defined and characterized by Bourbaki. Since then, some mathematicians presented several characterizations of submaximal spaces. In this paper, we will attempt to develop the concept of submaximality and offer some new results. Furthermore, some results concerning $\alpha$ -scattered space will be obtained.

Wed, 04/05/2011 16:00	Moritz Rodenhausen (University of Bonn)	Junior Geometric Group Theory Seminar	SR2
	Normal Forms, Factorability and Cohomology of HV-groups
	A factorability structure on a group G is a specification of normal forms of group elements as words over a fixed generating set. There is a chain complex computing the (co)homology of G. In contrast to the well-known bar resolution, there are much less generators in each dimension of the chain complex. Although it is often difficult to understand the differential, there are examples where the differential is particularly simple, allowing computations by hand. This leads to the cohomology ring of hv-groups, which I define at the end of the talk in terms of so called "horizontal" and "vertical" generators.

Thu, 05/05/2011 12:00	Lee Butler (Bristol)	Advanced Class Logic	L3
	"Wilkie's conjecture for definable curves."

Thu, 05/05/2011 12:30	Jose Rodrigo (University of Warwick)	OxPDE Lunchtime Seminar	Gibson 1st Floor SR
	On the evolution of almost-sharp fronts for the surface quasi-geostrophic equation
	I will describe recent work with Charles Fefferman on a construction of families of analytic almost-sharp fronts for SQG. These are special solutions of SQG which have a very sharp transition in a very thin layer. One of the main difficulties of the construction is the fact that there is no formal limit for the family of equations. I will show how to overcome this difficulty, linking the result to joint work with C. Fefferman and Kevin Luli on the existence of a "spine" for almost-sharp fronts. This is a curve, defined for every time slice by a measure-theoretic construction, that describes the evolution of the almost-sharp front.

Thu, 05/05/2011 13:00	Moritz Rodenhausen (University of Bonn)	Junior Geometry and Topology Seminar	SR1
	Normal Forms, Factorability and Cohomology of HV-groups
	A factorability structure on a group G is a specification of normal forms of group elements as words over a fixed generating set. There is a chain complex computing the (co)homology of G. In contrast to the well-known bar resolution, there are much less generators in each dimension of the chain complex. Although it is often difficult to understand the differential, there are examples where the differential is particularly simple, allowing computations by hand. This leads to the cohomology ring of hv-groups, which I define at the end of the talk in terms of so called "horizontal" and "vertical" generators.

Thu, 05/05/2011 13:00	Konstantinos Zygalakis (OCCAM)	Mathematical Finance Internal Seminar	DH 1st floor SR
	Effective Diffusive behaviour for passive tracers and inertial particles: Homogenization and numerical algorithms
	In this talk we will present results concerning the large scale long time behaviour of particles moving in a periodic (random) velocity field subject to molecular diffusion. The particle can be considered massless (passive tracer) or not (inertial particle). Under appropriate assumptions for the velocity field the large scale long time behavior of the particle is described by a Brownian motion with an effective diffusivity matrix K. We then present some numerical algorithms concerning the calculation of the effective diffusivity in the limit of vanishing molecular diffusion (stochastic geometric integrators). Time permitting we will discuss the case where the driving noise is no longer white but colored and study the effects of this change to the effective diffusivity matrix.

Thu, 05/05/2011
14:00

Prof Mike Giles (University of Oxford)

Computational Mathematics and Applications

Gibson Grd floor SR

Multilevel Monte Carlo method

Please note that this is a short notice change from the originally advertised talk by Dr Shahrokh Shahpar (Rolls-Royce plc.)

The new talk "Multilevel Monte Carlo method" is given by Mike Giles, Oxford-Man Institute of Quantitative Finance, Mathematical Institute, University of Oxford.

Joint work with Rob Scheichl, Aretha Teckentrup (Bath) and Andrew Cliffe (Nottingham)

Thu, 05/05/2011 16:00	Leon Danon (University of Warwick)	Differential Equations and Applications Seminar	DH 1st floor SR
	Collective human behaviour and epidemics: what (else) can we learn from mobile phone data?
	Human behaviour can show surprising properties when looked at from a collective point of view. Data on collective behaviour can be gleaned from a number of sources, and mobile phone data are increasingly becoming used. A major challenge is combining behavioural data with health data. In this talk I will describe our approach to understanding behaviour change related to change in health status at a collective level.