Forthcoming Seminars

Thu, 09/02/2012 16:00	Dave Platt (Bristol University)	Number Theory Seminar	L3
	Degree 1 L-functions and the Discrete Fourier Transform
	I will review the basic properties of the DFT and describe how these can be exploited to efficiently compute degree 1 L-functions.

Thu, 09/02/2012 17:00	Mike Prest (Manchester)	Logic Seminar	L3
	Categories of additive imaginaries and spectra
	To each additive definable category there is attached its category of pp-imaginaries. This is abelian and every small abelian category arises in this way. The connection may be expressed as an equivalence of 2-categories. We describe two associated spectra (Ziegler and Zariski) which have arisen in the model theory of modules.

Fri, 10/02/2012 00:00		Mathematical Biology and Ecology Seminar
	No Seminar

Fri, 10/02/2012 11:30	Various	OCCAM Special Seminar	OCCAM Common Room (RI2.28)
	OCCAM Group Meeting
	Jean Charles Seguis - The fictitious domain method applied to hybrid simulations in biology Chris Farmer - Data assimilation and parameter estimation Mark Curtis - Stokes' flow, singularities and sperm

Fri, 10/02/2012 14:15	Catherine Donnelly (Heriot-Watt)	Nomura Seminar	DH 1st floor SR
	Good-deal bounds in a regime-switching diffusion market
	We consider the pricing of a maturity guarantee, which is equivalent to the pricing of a European put option, in a regime-switching market model. Regime-switching market models have been empirically shown to fit long-term stockmarket data better than many other models. However, since a regime-switching market is incomplete, there is no unique price for the maturity guarantee. We extend the good-deal pricing bounds idea to the regime-switching market model. This allows us to obtain a reasonable range of prices for the maturity guarantee, by excluding those prices which imply a Sharpe Ratio which is too high. The range of prices can be used as a plausibility check on the chosen price of a maturity guarantee.

Fri, 10/02/2012 14:30	Dr. James Maddison (AOPP University of Oxford)	Mathematical Geoscience Seminar	DH 3rd floor SR
	Ocean Eddy Parameterisation and Conservation Principles
	Ocean climate models are unlikely routinely to have sufficient resolution to resolve the turbulent ocean eddy field. The need for the development of improved mesoscale eddy parameterisation schemes therefore remains an important task. The current dominant mesoscale eddy closure is the Gent and McWilliams scheme, which enforces the down-gradient mixing of buoyancy. While motivated by the action of baroclinic instability on the mean flow, this closure neglects the horizontal fluxes of horizontal momentum. The down-gradient mixing of potential vorticity is frequently discussed as an alternative parameterisation paradigm. However, such a scheme, without careful treatment, violates fundamental conservation principles, and in particular violates conservation of momentum. A new parameterisation framework is presented which preserves conservation of momentum by construction, and further allows for conservation of energy. The framework has one dimensional parameter, the total eddy energy, and five dimensionless and bounded geometric parameters. The popular Gent and McWilliams scheme exists as a limiting case of this framework. Hence the new framework enables for the extension of the Gent and McWilliams scheme, in a manner consistent with key physical conservations.

Fri, 10/02/2012 16:30	Professor Karen Vogtmann (Cornell University)	Colloquia	L2
	The topology and geometry of automorphism groups of free groups
	Free groups, free abelian groups and fundamental groups of closed orientable surfaces are the most basic and well-understood examples of infinite discrete groups. The automorphism groups of these groups, in contrast, are some of the most complex and intriguing groups in all of mathematics. I will give some general comments about geometric group theory and then describe the basic geometric object, called Outer space, associated to automorphism groups of free groups. This Colloquium talk is the first of a series of three lectures given by Professor Vogtmann, who is the European Mathematical Society Lecturer. In this series of three lectures, she will discuss groups of automorphisms of free groups, while drawing analogies with the general linear group over the integers and surface mapping class groups. She will explain modern techniques for studying automorphism groups of free groups, which include a mixture of topological, algebraic and geometric methods.

Mon, 13/02/2012 12:00	Sanjaye Ramgoolam (Queen Mary University of London)	String Theory Seminar	L3
	Quantum states to brane geometries via fuzzy moduli space
	The moduli space of supersymmetric (eighth-BPS) giant gravitons in $AdS_5 \times S^5$ is a limit of projective spaces. Quantizing this moduli space produces a Fock space of oscillator states, with a cutoff $N$ related to the rank of the dual $U(N)$ gauge group. Fuzzy geometry provides the ideal set of techniques for associating points or regions of moduli space to specific oscillator states. It leads to predictions for the spectrum of BPS excitations of specific worldvolume geometries. It also leads to a group theoretic basis for these states, containing Young diagram labels for $U(N)$ as well as the global $U(3)$ symmetry group. The problem of constructing gauge theory operators corresponding to the oscillator states and some recent progress in this direction are explained.

Mon, 13/02/2012
14:15

Mykhaylo Shkolnikov (Stanford, USA)

Stochastic Analysis Seminar

Oxford-Man Institute

"On diffusions interacting through their ranks"

Abstract: We will discuss systems of diffusion processes on the real line, in which the dynamics of every single process is determined by its rank in the entire particle system. Such systems arise in mathematical finance and statistical physics, and are related to heavy-traffic approximations of queueing networks. Motivated by the applications, we address questions about invariant distributions, convergence to equilibrium and concentration of measure for certain statistics, as well as hydrodynamic limits and large deviations for these particle systems. Parts of the talk are joint works with Amir Dembo, Tomoyuki Ichiba, Ioannis Karatzas, Soumik Pal and Ofer Zeitouni

Mon, 13/02/2012
14:15

Mykhaylo Shkolnikov (Stanford, USA)

Stochastic Analysis Seminar

Oxford-Man Institute

"On diffusions interacting through their ranks"

Mon, 13/02/2012 14:15	Daniel Waldram (Imperial College)	Geometry and Analysis Seminar	L3
	Supergravity as generalized geometry

Mon, 13/02/2012 15:45	FLORENT BENAYCH-GEORGES (Pierre and Marie Curie University)	Stochastic Analysis Seminar	Oxford-Man Institute
	Finite rank perturbations of random matrices and free probability theory
	Abstract : The question adressed in this talk is the following one : how are the extreme eigenvalues of a matrix X moved by a small rank perturbation P of X ? We shall consider this question in its generic apporach, i.e. when the matrices X and P are chosen at random independently and in isotropic ways. We shall give a general answer, uncovering a remarkable phase transition phenomenon: the limit of the extreme eigenvalues of the perturbed matrix differs from the original matrix if and only if the eigenvalues of the perturbing matrix are above a certain critical threshold. We also examine the consequences of this eigenvalue phase transition on the associated eigenvectors and generalize our results to examine the case of multiplicative perturbations or of additive perturbations for the singular values of rectangular matrices.

Mon, 13/02/2012 15:45	Karen Vogtmann (Cornell)	Topology Seminar	L3
	The topology and geometry of automorphism groups of free groups II
	Free groups, free abelian groups and fundamental groups of closed orientable surfaces are the most basic and well-understood examples of infinite discrete groups. The automorphism groups of these groups, in contrast, are some of the most complex and intriguing groups in all of mathematics. In these lectures I will concentrate on groups of automorphisms of free groups, while drawing analogies with the general linear group over the integers and surface mapping class groups. I will explain modern techniques for studying automorphism groups of free groups, which include a mixture of topological, algebraic and geometric methods.

Mon, 13/02/2012 16:00	Jan Tuitman	Junior Number Theory Seminar	SR1
	An introduction to p-adic cohomology
	In this talk we will give an introduction to the theory of p-adic (or rigid) cohomology. We will first define the theory for smooth affine varieties, then sketch the definition in general, next compute a simple example, and finally discuss some applications.

Mon, 13/02/2012 17:00	Bryce McLeod (OxPDE, University of Oxford)	Partial Differential Equations Seminar	Gibson 1st Floor SR
	The problem of wedge entry

Tue, 14/02/2012 12:00	Stefan Pokorski (Warsaw)	Quantum Field Theory Seminar	L3
	With or without a Higgs

Tue, 14/02/2012 14:15	Liz Stephens (University of Bristol)	Geophysical and Nonlinear Fluid Dynamics Seminar	Dobson Room, AOPP
	'An 80 % chance of confusion'- or - Can people make use of probabilistic weather forecasts?

Tue, 14/02/2012 14:30	Tobias Mueller, Amsterdam	Combinatorial Theory Seminar	L3
	Line arrangements and geometric representations of graphs
	A dot product representation of a graph assigns to each vertex $s$ a vector $v(s)$ in ${\bf R}^k$ in such a way that $v(s)^T v(t)$ is greater than $1$ if and only $st$ is an edge. Similarly, in a distance representation $\|v(s)-v(t)\|$ is less than $1$ if and only if $st$ is an edge. I will discuss the solution of some open problems by Spinrad, Breu and Kirkpatrick and others on these and related geometric representations of graphs. The proofs make use of a connection to oriented pseudoline arrangements. (Joint work with Colin McDiarmid and Ross Kang)