Forthcoming Seminars

Thu, 02/06/2011 16:00	Chris Bell (Imperial College London)	Differential Equations and Applications Seminar	DH 1st floor SR
	Theory of ac voltammetry for reversible electrochemical systems using multiple scales analysis
	Voltammetry is a powerful method for interrogating electrochemical systems. A voltage is applied to an electrode and the resulting current response analysed to determine features of the system under investigation, such as concentrations, diffusion coefficients, rate constants and thermodynamic potentials. Here we will focus on ac voltammetry, where the voltage signal consists of a high frequency sine-wave superimposed on a linear ramp. Using multiple scales analysis, we find analytical solutions for the harmonics of the current response and show how they can be used to determine the system parameters. We also include the effects of capacitance due to the double-layer at the electrode surface and show that even in the presence of large capacitance, the harmonics of the current response can still be isolated using the FFT and the Hanning window.

Thu, 02/06/2011 16:00	Marco Streng (Warwick)	Number Theory Seminar
	Class invariants for quartic CM-fields
	I show how invariants of curves of genus 2 can be used for explicitly constructing class fields of certain number fields of degree 4.

Thu, 02/06/2011 16:30	Ed Green (Virginia Tech)	Representation Theory Seminar	L2
	Generalized Matrix Artin Algebras
	Last lecture of Bloc meeting

Thu, 02/06/2011 17:00	Carlo Toffalori - joint work with Gena Puninski (Florence - Moscow)	Logic Seminar	L3
	"Generalized lattices over local Dedekind-like rings"
	Recent papers by Butler-Campbell-Kovàcs, Rump, Prihoda-Puninski and others introduce over an order O over a Dedekind domain D a notion of "generalized lattice", meaning a D-projective O-module. We define a similar notion over Dedekind-like rings – a class of rings intensively studied by Klingler and Levy. We examine in which cases every generalized lattices is a direct sum of ordinary – i.e., finitely generated – lattices. We also consider other algebraic and model theoretic questions about generalized lattices.

Fri, 03/06/2011 12:00	John Calabrese (University of Oxford)	Junior Geometry and Topology Seminar	SR1
	Some random facts about the Weil conjectures
	I'll start by defining the zeta function and stating the Weil conjectures (which have actually been theorems for some time now). I'll then go on by saying things like "Weil cohomology", "standard conjectures" and "Betti numbers of the Grassmannian". Hopefully by the end we'll all have learned something, including me.

Fri, 03/06/2011 14:00	Prof K Foster (University of Oxford))	Mathematical Biology and Ecology Seminar	L2
	Social evolution in microbes

Fri, 03/06/2011 14:15	Prof Stefan Ankirchner (University of Bonn)	Nomura Seminar	DH 1st floor SR
	Cross hedging with futures in a continuous-time model with a stationary spread
	When managing risk, frequently only imperfect hedging instruments are at hand. We show how to optimally cross-hedge risk when the spread between the hedging instrument and the risk is stationary. At the short end, the optimal hedge ratio is close to the cross-correlation of the log returns, whereas at the long end, it is optimal to fully hedge the position. For linear risk positions we derive explicit formulas for the hedge error, and for non-linear positions we show how to obtain numerically effcient estimates. Finally, we demonstrate that even in cases with no clear-cut decision concerning the stationarity of the spread it is better to allow for mean reversion of the spread rather than to neglect it. The talk is based on joint work with Georgi Dimitroff, Gregor Heyne and Christian Pigorsch.

Fri, 03/06/2011 16:30	Prof Graeme Segal (Oxford)	Colloquia	L2
	‘Aspects of the work of Dan Quillen’.
	Graeme Segal shall describe some of Dan Quillen’s work, focusing on his amazingly productive period around 1970, when he not only invented algebraic K-theory in the form we know it today, but also opened up several other lines of research which are still in the front line of mathematical activity. The aim of the talk will be to give an idea of some of the mathematical influences which shaped him, of his mathematical perspective, and also of his style and his way of approaching mathematical problems.

Mon, 06/06/2011 12:00	Magdalena Larfors (LMU Munich)	String Theory Seminar	L3
	String compactifications on toric varieties
	In the absence of background fluxes and sources, compactifying string theories on Calabi-Yau three-folds leads to supersymmetric solutions. Turning on fluxes, e.g. to lift the moduli of the compactification, generically forces the three-fold to break the Calabi-Yau conditions, and instead fulfill the weaker geometrical condition of having a reduced structure group. In this talk I will demonstrate that three-dimensional smooth, compact, toric varieties can have reduced structure group, and thus be suitable for flux compactifications of string theory. Since the class of three-dimensional SCTV is large, this is promising for the construction of new, phenomenologically interesting string theory vacua.

Mon, 06/06/2011 14:15	M S Narasimhan (TIFR Bangalore)	Geometry and Analysis Seminar	L3
	Stability and canonical filtrations in arithmetic

Mon, 06/06/2011 14:15	Konstantinos Zygalakis (University of Oxford)	Stochastic Analysis Seminar	Oxford-Man Institute
	Modified equations, backward error analysis and numerical methods for stiff stochastic differential equations.
	: Backward error analysis is a technique that has been extremely successful in understanding the behaviour of numerical methods for ordinary differential equations. It is possible to fit an ODE (the so called modified equation) to a numerical method to very high accuracy. Backward error analysis has been of particular importance in the numerical study of Hamiltonian problems, since it allows to approximate symplectic numerical methods by a perturbed Hamiltonian system, giving an approximate statistical mechanics for symplectic methods. Such a systematic theory in the case of numerical methods for stochastic differential equations (SDEs) is currently lacking. In this talk we will describe a general framework for deriving modified equations for SDEs with respect to weak convergence. We will start by quickly recapping of how to derive modified equations in the case of ODEs and describe how these ideas can be generalized in the case of SDEs. Results will be presented for first order methods such as the Euler-Maruyama and the Milstein method. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we will derive a SDE that the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations and in the calculation of effective diffusivities will also be discussed, as well as the use of modified equations as a tool for constructing higher order methods for stiff stochastic differential equations. This is joint work with A. Abdulle (EPFL). D. Cohen (Basel), G. Vilmart (EPFL).

Mon, 06/06/2011 15:45	Herbert Spohn	Stochastic Analysis Seminar	Oxford-Man Institute
	The one-dimensional Kardar-Parisi -Zhang equation and its universality class
	In 1986 Kardar, Parisi, and Zhang proposed a stochastic PDE for the motion of driven interfaces, in particular for growth processes with local updating rules. The solution to the 1D KPZ equation can be approximated through the weakly asymmetric simple exclusion process. Based on work of Tracy and Widom on the PASEP, we obtain an exact formula for the one-point generating function of the KPZ equation in case of sharp wedge initial data. Our result is valid for all times, but of particular interest is the long time behavior, related to random matrices, and the finite time corrections. This is joint work with Tomohiro Sasamoto.

Mon, 06/06/2011 15:45	John Francis (Northwestern)	Topology Seminar	L3
	E_n-rings and factorization homology

Mon, 06/06/2011 17:00	Sasha Grigoryan (Bielefeld University)	Stochastic Analysis Seminar	Oxford-Man Institute
	To Be Announced

Mon, 06/06/2011
17:00

Jesenko Vukadinovic (City University of New York)

Partial Differential Equations Seminar

Gibson 1st Floor SR

Some Recent Results on the Doi-Smoluchowski Equation Which Arises in the Modeling of Nematic Liquid Crystals

The talk will address two recent results concerning the Doi-Smoluchowski equation and the Onsager model for nematic liquid crystals. The first result concerns the existence of inertial manifolds for the Smloluchowski equation both in the presence and in the absence of external flows. While the Doi-Smoluchowski equation as a PDE is an infinite-dimensional dynamical system, it reduces to a system of ODEs on a set coined inertial manifold, to which all other solutions converge exponentially fast. The proof uses a non-standard method, which consists in circumventing the restrictive spectral-gap condition, which the original equation fails to satisfy by transforming the equation into a form that does.

The second result concerns the isotropic-nematic phase transition for the Onsager model on the circle using more complicated potentials than the Maier-Saupe potential. Exact multiplicity of steady-states on the circle is proven for the two-mode truncation of the Onsager potential.

Tue, 07/06/2011 12:00	Gary Gibbons (DAMTP Cambridge)	Quantum Field Theory Seminar	L3
	What is the shape of a black hole

Tue, 07/06/2011
13:15

Aarom Lim (University of Oxford))

Junior Applied Mathematics Seminar

DH 1st floor SR

Modelling Viral Persistence in the Presence of Host Immunity in Chronic HTLV-I Infection

Human T-lymphotropic virus type I (HTLV-I) is a persistent human retrovirus characterised by a high proviral load and risk of developing ATL, an aggressive blood cancer, or HAM/TSP, a progressive neurological and inflammatory disease. Infected individuals typically mount a large, chronically activated HTLV-I-specific CTL response, yet the virus has developed complex mechanisms to evade host immunity and avoid viral clearance. Moreover, identification of determinants to the development of disease has thus far been elusive.

This model is based on a recent experimental hypothesis for the persistence of HTLV-I infection and is a direct extension of the model studied by Li and Lim (2011). A four-dimensional system of ordinary differential equations is constructed that describes the dynamic interactions among viral expression, infected target cell activation, and the human immune response. Focussing on the particular roles of viral expression and host immunity in chronic HTLV-I infection offers important insights to viral persistence and pathogenesis.

Tue, 07/06/2011 14:15	Dr John Methven (University of Reading))	Geophysical and Nonlinear Fluid Dynamics Seminar	Dobson Room, AOPP
	The slowly evolving background state extracted from atmospheric analyses

Tue, 07/06/2011 14:15	Prof Freddy Delbaen (ETH Zurich)	Nomura Seminar	Oxford-Man Institute
	BSDE with unbounded terminal value, uniqueness and existence of solutions

Tue, 07/06/2011 14:30	Gregory Sorkin (LSE)	Combinatorial Theory Seminar	L3
	Average-case performance of three-dimensional assignment heuristics
	The 2-dimensional assignment problem (minimum cost matching) is solvable in polynomial time, and it is known that a random instance of size n, with entries chosen independently and uniformly at random from [0,1], has expected cost tending to π^2/6. In dimensions 3 and higher, the "planar" assignment problem is NP-complete, but what is the expected cost for a random instance, and how well can a heuristic do? In d dimensions, the expected cost is of order at least n^{2-d} and at most ln n times larger, but the upper bound is non-constructive. For 3 dimensions, we show a heuristic capable of producing a solution within a factor n^ε of the lower bound, for any constant ε, in time of order roughly n^{1/ε}. In dimensions 4 and higher, the question is wide open: we don't know any reasonable average-case assignment heuristic.