Forthcoming Seminars

Mon, 21/05/2012 14:15	CHRISTIAN BAYER (University of Vienna)	Stochastic Analysis Seminar	Oxford-Man Institute
	Some applications of the Ninomiya-Victoir scheme in the context of financial engineering
	Based on ideas from rough path analysis and operator splitting, the Kusuoka-Lyons-Victoir scheme provides a family of higher order methods for the weak approximation of stochastic differential equations. Out of this family, the Ninomiya-Victoir method is especially simple to implement and to adjust to various different models. We give some examples of models used in financial engineering and comment on the performance of the Ninomiya-Victoir scheme and some modifications when applied to these models.

Mon, 21/05/2012 14:15	Andre Neves (Imperial College)	Geometry and Analysis Seminar	L3
	The Willmore problem

Mon, 21/05/2012 15:45	DEJAN VELUSCEK (ETH Zurich)	Stochastic Analysis Seminar	Oxford-Man Institute
	Extrapolation methods for weak approximation schemes
	We will give a quick overview of the semigroup perspective on splitting schemes for S(P)DEs which present a robust, "easy to implement" numerical method for calculating the expected value of a certain payoff of a stochastic process driven by a S(P)DE. Having a high numerical order of convergence enables us to replace the Monte Carlo integration technique by alternative, faster techniques. The numerical order of splitting schemes for S(P)DEs is bounded by 2. The technique of combining several splittings using linear combinations which kills some additional terms in the error expansion and thus raises the order of the numerical method is called the extrapolation. In the presentation we will focus on a special extrapolation of the Lie-Trotter splitting: the symmetrically weighted sequential splitting, and its subsequent extrapolations. Using the semigroup technique their convergence will be investigated. At the end several applications to the S(P)DEs will be given.

Mon, 21/05/2012 15:45	Cornelia Drutu (Oxford)	Topology Seminar	L3
	Equivalent notions of rank for manifolds of non-positive curvature and for mapping class groups of surfaces
	In Riemannian geometry there are several notions of rank defined for non-positively curved manifolds and with natural extensions for groups acting on non-positively curved spaces. The talk shall explain how various notions of rank behave for mapping class groups of surfaces. This is joint work with J. Behrstock.

Mon, 21/05/2012 16:00	Daniel Kotzen	Junior Number Theory Seminar	SR1
	The least quadratic non-residue

Mon, 21/05/2012 17:00	Claude Bardos (Paris VII Denis Diderot)	Partial Differential Equations Seminar	Gibson 1st Floor SR
	Euler equation as a limit of solutions of Boltzmann or Navier-Stokes equation
	Recent results (starting with Scheffer and Shnirelman and continuing with De Lellis and Szekelhyhidi ) underline the importance of considering solutions of the incompressible Euler equations as limits of solutions of more physical examples like Navier-Stokes or Boltzmann. I intend to discuss several examples illustrating this issue.

Tue, 22/05/2012 12:00	Tony Padilla (Nottingham)	Quantum Field Theory Seminar	L3
	From classical duals to cleaning Lambda

Tue, 22/05/2012 14:30	Jozef Skokan (LSE)	Combinatorial Theory Seminar	L3
	Strong Ramsey saturation for cycles
	We call a graph $H$ Ramsey-unsaturated if there is an edge in the complement of $H$ such that the Ramsey number $r(H)$ of $H$ does not change upon adding it to $H$ . This notion was introduced by Balister, Lehel and Schelp who also showed that cycles (except for $C_4$ ) are Ramsey-unsaturated, and conjectured that, moreover, one may add any chord without changing the Ramsey number of the cycle $C_n$ , unless $n$ is even and adding the chord creates an odd cycle. We prove this conjecture for large cycles by showing a stronger statement: If a graph $H$ is obtained by adding a linear number of chords to a cycle $C_n$ , then $r(H)=r(C_n)$ , as long as the maximum degree of $H$ is bounded, $H$ is either bipartite (for even $n$ ) or almost bipartite (for odd $n$ ), and $n$ is large. This motivates us to call cycles strongly Ramsey-unsaturated. Our proof uses the regularity method.

Tue, 22/05/2012 15:45	Timo Schurg (Bonn)	Algebraic and Symplectic Geometry Seminar	L3
	From perfect obstruction theories to commutative differential graded algebras
	A perfect obstruction theory for a commutative ring is a morphism from a perfect complex to the cotangent complex of the ring satisfying some further conditions. In this talk I will present work in progress on how to associate in a functorial manner commutative differential graded algebras to such a perfect obstruction theory. The key property of the differential graded algebra is that its zeroth homology is the ring equipped with the perfect obstruction theory. I will also indicate how the method introduced can be globalized to work on schemes without encountering gluing issues.

Tue, 22/05/2012 17:00	Dr. M. de Visscher (City)	Algebra Seminar	L2
	On simple modules for the Brauer algebra

Wed, 23/05/2012 10:15	Samuel Isaacson (Boston University)	OCCAM Wednesday Morning Event	OCCAM Common Room (RI2.28)
	Relationships between several particle-based stochastic reaction-diffusion models
	Particle-based stochastic reaction-diffusion models have recently been used to study a number of problems in cell biology. These methods are of interest when both noise in the chemical reaction process and the explicit motion of molecules are important. Several different mathematical models have been used, some spatially-continuous and others lattice-based. In the former molecules usually move by Brownian Motion, and may react when approaching each other. For the latter molecules undergo continuous time random-walks, and usually react with fixed probabilities per unit time when located at the same lattice site. As motivation, we will begin with a brief discussion of the types of biological problems we are studying and how we have used stochastic reaction-diffusion models to gain insight into these systems. We will then introduce several of the stochastic reaction-diffusion models, including the spatially continuous Smoluchowski diffusion limited reaction model and the lattice-based reaction-diffusion master equation. Our work studying the rigorous relationships between these models will be presented. Time permitting, we may also discuss some of our efforts to develop improved numerical methods for solving several of the models.

Wed, 23/05/2012 11:30	Dawid Kielak	Algebra Kinderseminar
	An introduction to sheaf cohomology – St Hugh's, 80WR18

Thu, 24/05/2012 12:00	Rosalinda Juer	Junior Geometry and Topology Seminar	L3
	Unoriented cobordism categories and Klein TQFTs
	The mid 1980s saw a shift in the nature of the relationship between mathematics and physics. Differential equations and geometry applied in a classical setting were no longer the principal players; in the quantum world topology and algebra had come to the fore. In this talk we discuss a method of classifying 2-dim invertible Klein topological quantum field theories (KTQFTs). A key object of study will be the unoriented cobordism category $\mathscr{K}$ , whose objects are closed 1-manifolds and whose morphisms are surfaces (a KTQFT is a functor $\mathscr{K}\rightarrow\operatorname{Vect}_{\mathbb{C}}$ ). Time permitting, the open-closed version of the category will be considered, yielding some surprising results.

Thu, 24/05/2012 12:30	Mikhail Feldman (University of Wisconsin)	OxPDE Lunchtime Seminar	Gibson 1st Floor SR
	Regularity and stability of solutions to shock reflection problem
	We discuss shock reflection problem for compressible gas dynamics, and von Neumann conjectures on transition between regular and Mach reflections. Then we will talk about some recent results on existence, regularity and geometric properties of regular reflection solutions for potential flow equation. In particular, we discuss optimal regularity of solutions near sonic curve, and stability of the normal reflection soluiton. Open problems will also be discussed. The talk will be based on the joint work with Gui-Qiang Chen, and with Myoungjean Bae.

Thu, 24/05/2012 13:00	N/A	Mathematical Finance Internal Seminar	DH 1st floor SR
	Open Problem Session

Thu, 24/05/2012 14:00	Dr Elias Jarlebring (KTH Stockholm)	Computational Mathematics and Applications	Gibson Grd floor SR
	A linear eigenvalue algorithm for nonlinear eigenvalue problems
	The Arnoldi method for standard eigenvalue problems possesses several attractive properties making it robust, reliable and efficient for many problems. We will present here a new algorithm equivalent to the Arnoldi method, but designed for nonlinear eigenvalue problems corresponding to the problem associated with a matrix depending on a parameter in a nonlinear but analytic way. As a first result we show that the reciprocal eigenvalues of an infinite dimensional operator. We consider the Arnoldi method for this and show that with a particular choice of starting function and a particular choice of scalar product, the structure of the operator can be exploited in a very effective way. The structure of the operator is such that when the Arnoldi method is started with a constant function, the iterates will be polynomials. For a large class of NEPs, we show that we can carry out the infinite dimensional Arnoldi algorithm for the operator in arithmetic based on standard linear algebra operations on vectors and matrices of finite size. This is achieved by representing the polynomials by vector coefficients. The resulting algorithm is by construction such that it is completely equivalent to the standard Arnoldi method and also inherits many of its attractive properties, which are illustrated with examples.

Thu, 24/05/2012 16:00	James Newton (Cambridge)	Number Theory Seminar	L3
	Weights in Serre's conjecture for Hilbert modular forms

Thu, 24/05/2012 16:00	Anne Juel (Manchester)	Industrial and Applied Mathematics Seminar	DH 1st floor SR
	Bubble instabilities in rigid and flexible vessels
	The displacement of a liquid by an air finger is a generic two-phase flow that underpins applications as diverse as microfluidics, thin-film coating, enhanced oil recovery, and biomechanics of the lungs. I will present two intriguing examples of such flows where, firstly, oscillations in the shape of propagating bubbles are induced by a simple change in tube geometry, and secondly, flexible vessel boundaries suppress viscous fingering instability. 1) A simple change in pore geometry can radically alter the behaviour of a fluid displacing air finger, indicating that models based on idealized pore geometries fail to capture key features of complex practical flows. In particular, partial occlusion of a rectangular cross-section can force a transition from a steadily-propagating centred finger to a state that exhibits spatial oscillations via periodic sideways motion of the interface at a fixed location behind the finger tip. We characterize the dynamics of the oscillations and show that they arise from a global homoclinic connection between the stable and unstable manifolds of a steady, symmetry-broken solution. 2) Growth of complex dendritic fingers at the interface of air and a viscous fluid in the narrow gap between two parallel plates is an archetypical problem of pattern formation. We find a surprisingly effective means of suppressing this instability by replacing one of the plates with an elastic membrane. The resulting fluid-structure interaction fundamentally alters the interfacial patterns that develop and considerably delays the onset of fingering. We analyse the dependence of the instability on the parameters of the system and present scaling arguments to explain the experimentally observed behaviour.

Thu, 24/05/2012 17:00	Pierre Simon (Ecole Normale Superiore)	Logic Seminar	L3
	S-independence in NIP theories
	I will explain how to define a notion of stable-independence in NIP theories, which is an attempt to capture the "stable part" of types.

Fri, 25/05/2012
11:00

David Howey (Department of Engineering Science, University of Oxford)

Industrial and Interdisciplinary Workshops

DH 1st floor SR

Parameter estimation for electrochemical cells

Please note the unusual start-time.

In order to run accurate electrochemical models of batteries (and other devices) it is necessary to know a priori the values of many geometric, electrical and electrochemical parameters (10-100 parameters) e.g. diffusion coefficients, electrode thicknesses etc. However a basic difficulty is that the only external measurements that can be made on cells without deconstructing and destroying them are surface temperature plus electrical measurements (voltage, current, impedance) at the terminals. An interesting research challenge therefore is the accurate, robust estimation of physically realistic model parameters based only on external measurements of complete cells. System identification techniques (from control engineering) including ‘electrochemical impedance spectroscopy’ (EIS) may be applied here – i.e. small signal frequency response measurement. However It is not clear exactly why and how impedance correlates to SOC/ SOH and temperature for each battery chemistry due to the complex interaction between impedance, degradation and temperature.

I will give a brief overview of some of the recent work in this area and try to explain some of the challenges in the hope that this will lead to a fruitful discussion about whether this problem can be solved or not and how best to tackle it.