Forthcoming Seminars

Tue, 07/06/2011 15:45	Aaron Bertram (Utah)	Algebraic and Symplectic Geometry Seminar	L3
	Birational models of the Hilbert Scheme of Points in $P^2$ as Moduli of Bridgeland-stable Objects
	The effective cone of the Hilbert scheme of points in $P^2$ has finitely many chambers corresponding to finitely many birational models. In this talk, I will identify these models with moduli of Bridgeland-stable two-term complexes in the derived category of coherent sheaves on $P^2$ and describe a map from (a slice of) the stability manifold of $P^2$ to the effective cone of the Hilbert scheme that would explain the correspondence. This is joint work with Daniele Arcara and Izzet Coskun.

Tue, 07/06/2011 17:00	Alistair Bird (Lancaster)	Functional Analysis Seminar	L3
	Closed ideals of operators on generalized James spaces

Wed, 08/06/2011
10:15

Luca Giomi

OCCAM Wednesday Morning Event

OCCAM Common Room (RI2.28)

Active systems: from liquid crystals to living systems

Colonies of motile microorganisms, the cytoskeleton and its components, cells and tissues have much in common with soft condensed matter systems (i.e. liquid crystals, amphiphiles, colloids etc.), but also exhibit behaviors that do not appear in inanimate matter and that are crucial for biological functions.

These unique properties arise when the constituent particles are active: they consume energy from internal and external sources and dissipate it by moving through the medium they inhabit. In this talk I will give a brief introduction to the notion of "active matter" and present some recent results on the hydrodynamics of active nematics suspensions in two dimensions.

Wed, 08/06/2011 16:00	Dawid Kielak (University of Oxford)	Junior Geometric Group Theory Seminar	SR1
	Fusion, graphs and $\mathrm{Out}(F_n)$ .
	We will attempt to introduce fusion systems in a way comprehensible to a Geometric Group Theorist. We will show how Bass–Serre thoery allows us to realise fusion systems inside infinite groups. If time allows we will discuss a link between the above and $\mathrm{Out}(F_n)$ .

Thu, 09/06/2011 13:00	Ben Hambly	Mathematical Finance Internal Seminar	DH 1st floor SR
	From bid-stacks to swing options in electricity markets
	The aim of this work is to show how to derive the electricity price from models for the underlying construction of the bid-stack. We start with modelling the behaviour of power generators and in particular the bids that they submit for power supply. By modelling the distribution of the bids and the evolution of the underlying price drivers, that is the fuels used for the generation of power, we can construct an spede which models the evolution of the bids. By solving this SPDE and integrating it up we can construct a bid-stack model which evolves in time. If we then specify an exogenous demand process it is possible to recover a model for the electricity price itself. In the case where there is just one fuel type being used there is an explicit formula for the price. If the SDEs for the underlying bid prices are Ornstein-Uhlenbeck processes, then the electricity price will be similar to this in that it will have a mean reverting character. With this price we investigate the prices of spark spreads and swing options. In the case of multiple fuel drivers we obtain a more complex expression for the price as the inversion of the bid stack cannot be used to give an explicit formula. We derive a general form for an SDE for the electricity price. We also show that other variations lead to similar, though still not tractable expressions for the price.

Thu, 09/06/2011 14:00	Dr Daan Huybrechs (Catholic University of Leuven)	Computational Mathematics and Applications	Gibson Grd floor SR
	Several kinds of Chebyshev polynomials in higher dimensions
	Chebyshev polynomials are arguably the most useful orthogonal polynomials for computational purposes. In one dimension they arise from the close relationship that exists between Fourier series and polynomials. We describe how this relationship generalizes to Fourier series on certain symmetric lattices, that exist in all dimensions. The associated polynomials can not be seen as tensor-product generalizations of the one-dimensional case. Yet, they still enjoy excellent properties for interpolation, integration, and spectral approximation in general, with fast FFT-based algorithms, on a variety of domains. The first interesting case is the equilateral triangle in two dimensions (almost). We further describe the generalization of Chebyshev polynomials of the second kind, and many new kinds are found when the theory is completed. Connections are made to Laplacian eigenfunctions, representation theory of finite groups, and the Gibbs phenomenon in higher dimensions.

Thu, 09/06/2011 14:30	David Evans (Cardiff)	Representation Theory Seminar	L3
	Modular invariants, subfactors and the search for the exotic
	Subfactor theory provides a framework for studying modular invariant partition functions in conformal field theory, and candidates for exotic modular tensor categories and almost Calabi-Yau algebras. I will survey some joint work with Terry Gannon and Mathew Pugh.

Thu, 09/06/2011 16:00	Colin B MacDonald (University of Oxford)	Differential Equations and Applications Seminar	DH 1st floor SR
	Computing on surfaces with the Closest Point Method
	Solving partial differential equations (PDEs) on curved surfaces is important in many areas of science. The Closest Point Method is a new technique for computing numerical solutions to PDEs on curves, surfaces, and more general domains. For example, it can be used to solve a pattern-formation PDE on the surface of a rabbit. A benefit of the Closest Point Method is its simplicity: it is easy to understand and straightforward to implement on a wide variety of PDEs and surfaces. In this presentation, I will introduce the Closest Point Method and highlight some of the research in this area. Example computations (including the in-surface heat equation, reaction-diffusion on surfaces, level set equations, high-order interface motion, and Laplace–Beltrami eigenmodes) on a variety of surfaces will demonstrate the effectiveness of the method.

Thu, 09/06/2011 16:00	David Masser (Basel)	Number Theory Seminar	L3
	To Be Announced

Thu, 09/06/2011 16:00	David Masser	Logic Seminar Number Theory Seminar	L3
	Unlikely intersections for algebraic curves.
	In the last twelve years there has been much study of what happens when an algebraic curve in $n$ -space is intersected with two multiplicative relations $x_1^{a_1} \cdots x_n^{a_n}~=~x_1^{b_1} \cdots x_n^{b_n}~=~1 \eqno(\times)$ for $(a_1, \ldots ,a_n),(b_1,\ldots, b_n)$ linearly independent in ${\bf Z}^n$ . Usually the intersection with the union of all $(\times)$ is at most finite, at least in zero characteristic. In Oxford nearly three years ago I could treat a special curve in positive characteristic. Since then there have been a number of advances, even for additive relations $\alpha_1x_1+\cdots+\alpha_nx_n~=~\beta_1x_1+\cdots+\beta_nx_n~=~0 \eqno(+)$ provided some extra structure of Drinfeld type is supplied. After reviewing the zero characteristic situation, I will describe recent work, some with Dale Brownawell, for $(\times)$ and for $(+)$ with Frobenius Modules and Carlitz Modules.

Thu, 09/06/2011 17:00	Robert Boltje (Santa Cruz)	Representation Theory Seminar	L2
	The double Burnside ring and fusion systems

Fri, 10/06/2011 00:00		Mathematical Biology and Ecology Seminar
	No Seminar

Fri, 10/06/2011 11:15	Various	OCCAM Special Seminar	OCCAM Common Room (RI2.28)
	OCCAM Group Meeting
	James Kirkpatrick - "Drift Diffusion modelling of organic solar cells: including electronic disorder". Timothy Reis - "Moment-based boundary conditions for the Lattice Boltzmann method". Matthew Moore - "Introducing air cushioning to Wagner theory". Matthew Hennessy - “Organic Solar Cells and the Marangoni Instability”.

Fri, 10/06/2011 12:00	Michael Groechenig (University of Oxford)	Junior Geometry and Topology Seminar	SR1
	Fundamental groups and positive characteristic
	In spirit with John's talk we will discuss how topological invariants can be defined within a purely algebraic framework. After having introduced étale fundamental groups, we will discuss conjectures of Gieseker, relating those to certain "flat bundles" in finite characteristic. If time remains we will comment on the recent proof of Esnault-Sun.

Mon, 13/06/2011 12:00	Sara Pasquetti (QMUL)	String Theory Seminar	L3
	3D-partition functions on the sphere: exact evaluation and mirror symmetry
	Recently it has been shown that path integrals of N=4 theories on the three-sphere can be localised to matrix integrals. I will show how to obtain exact expressions of partition functions by an explicit evaluation of these matrix integrals.

Mon, 13/06/2011 14:15	Michael Thaddeus (Columbia)	Geometry and Analysis Seminar	L3
	"Moduli spaces of principal bundles on chains of projective lines."

Mon, 13/06/2011 14:15	Nizar Touzi (London)	Stochastic Analysis Seminar	Oxford-Man Institute
	Model independent bound for option pricing: a stochastic control aproach
	This problem is classically addressed by the so-called Skorohod Embedding problem. We instead develop a stochastic control approach. Unlike the previous literature, our formulation seeks the optimal no arbitrage bounds given the knowledge of the distribution at some (or various) point in time. This problem is converted into a classical stochastic control problem by means of convex duality. We obtain a general characterization, and provide explicit optimal bounds in some examples beyond the known classical ones. In particular, we solve completely the case of finitely many given marginals.

Mon, 13/06/2011 15:45	Chris Douglas (Oxford)	Topology Seminar	L3
	3-Dimensional Topological Field Theories associated to Fusion Categories

Mon, 13/06/2011 15:45	Keith Ball (University of Edinburgh)	Stochastic Analysis Seminar	Oxford-Man Institute
	"The Second Law of Probability: Entropy growth in the central limit process."
	The talk will explain how a geometric principle gave rise to a new variational description of information-theoretic entropy and how this led to the solution of a problem dating back to the 50's: whether the the central limit theorem is driven by an analogue of the second law of thermodynamics.

Mon, 13/06/2011 17:00	Adriana Garroni (Universita di Roma)	Partial Differential Equations Seminar	Gibson 1st Floor SR
	A variational derivation for continuum model for dislocations
	The main mechanism for crystal plasticity is the formation and motion of a special class of defects, the dislocations. These are topological defects in the crystalline structure that can be identify with lines on which energy concentrates. In recent years there has been a considerable effort for the mathematical derivation of models that describe these objects at different scales (from an energetic and a dynamical point of view). The results obtained mainly concern special geometries, as one dimensional models, reduction to straight dislocations, the activation of only one slip system, etc. The description of the problem is indeed extremely complex in its generality. In the presentation will be given an overview of the variational models for dislocations that can be obtained through an asymptotic analysis of systems of discrete dislocations. Under suitable scales we study the “variational limit” (by means of Gamma-convergence) of a three dimensional (static) discrete model and deduce a line tension anisotropic energy. The characterization of the line tension energy density requires a relaxation result for energies defined on curves.