Forthcoming Seminars

Fri, 06/02/2009
16:30 		Professor Ivar Ekeland (University of British Columbia) Colloquia Add to calendar L2
Time inconsistency in the calculus of variations
In classical economic theory, one discounts future gains or losses at a constant rate: one pound in t years is worth exp(-rt) pounds today. There are now very good reasons to consider non-constant discount rates. This gives rise to a problem of time-inconsistency: a policy which is optimal today will no longer be optimal tomorrow. The concept of optimality then no longer is useful. We introduce instead a concept of equilibrium solution, and characterize it by a non-local variant of the Hamilton-Jacobi equation. We then solve the classical Ramsey model of endogenous growth in this framework, using the central manifold theorem
Mon, 09/02/2009
12:00 		Jarah Evslin (Trieste) String Theory Seminar Add to calendar L3
Topology changing T-dualities
We define an action of ordinary and Narain T-duality on an arbitrary torus bundle by applying Buscher and Narain's formulations patchwise. In general it changes the topology of the compactification manifold and its NS 3-form flux, for example in the case of a circle bundle it interchanges the Chern class with a pushforward of the flux. It nonetheless provides a candidate duality of the full string theory because it preserves several topological and geometric invariants such as the twisted K-theory in type II and the tadpole and supersymmetry conditions in non-Kahler heterotic compactifications.
Mon, 09/02/2009
14:15 		Dr Jan Obloj (Oxford) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Azema-Yor processes: three characterisation theorems
We study the class of Azema-Yor processes which are of the form F(M_t)-f(M_t)(X_t-M_t), where F'=f, X_t is a semimartingale with no positive jumps and M_t is its running maximum. We show that these processes arise as unique strong solutions to the Bachelier SDE which we also show is equivalent to the DrawDown SDE. The proofs are greatly simplified thanks to (algebraic) group property of the set of AY processes indexed by functions. We then restrict our attention to the case when X is a martingale. It turns out that the AY martingales are the only local martingales of the form H(X_t,M_t) for a Borel function H. Furthermore, they can also be characterised by their optimal properties: all uniformly integrable martingales whose maximum dominates a given target are dominated by an AY martingale in the concave ordering of terminal values. We mention how these results find direct applications in portfolio optimisation/insurance theory. Joint work with Laurent Cararro and Nicole El Karoui
Mon, 09/02/2009
15:45 		TBA Topology Seminar Add to calendar L3
BOS Day in Bristol
Mon, 09/02/2009
15:45 		Dr Nikolaos Zygouras (Warwick) Stochastic Analysis Seminar Add to calendar Oxford-Man Institute
Pinning-depinning transition in Random Polymers
Random polymers are used to model various physical ( Ising inter- faces, wetting, etc.) and biological ( DNA denaturation, etc.) phenomena They are modeled as a one dimensional random walk (Xn), with excursion length distribution P(E1 = n) = (n)=nc, c > 1, and (n) a slowly varying function. The polymer gets a random reward, whenever it visits or crosses an interface. The random rewards are realised as a sequence of i.i.d. variables (Vn). Depending on the relation be- tween the mean value of the disorder Vn and the temperature, the polymer might prefer to stick on the interface (pinning) or undergo a long excursion away from it (depinning). In this talk we will review some aspects of random polymer models. We will also discuss in more detail the pinning-depinning transition of the 'Pinning' model and also its relation to other directed polymer models
Mon, 09/02/2009
16:00 		Johan Bredberg (Oxford) Junior Number Theory Seminar Add to calendar SR1
Dirichlet's Approximation Theorem
This talk will introduce Dirichlet's Theorem on the approximation of real numbers via rational numbers. Once this has been established, a stronger version of the result will be proved, viz Hurwitz's Theorem.
Mon, 09/02/2009
17:00 		Kenneth Falconer (St. Andrews) Partial Differential Equations Seminar Add to calendar Gibson 1st Floor SR
Self-affine sets - Dimensions and Dynamics
The talk will survey some recent and not so recent work on the Hausdorff and box dimension of self-affine sets and related attractors and repellers that arise in certain dynamical systems.
Tue, 10/02/2009
12:00 		Igor Rodnianski (Princeton) Relativity Seminar Add to calendar L3
Boundedness and decay of scalar waves on Kerr and more general black holes
I will review our current mathematical understanding of waves on black hole backgrounds, starting with the classical boundedness theorem of Kay and Wald on Schwarzschild space-time and ending with recent boundedness and decay theorems on a wider class of black hole space-times.
Tue, 10/02/2009
14:30 		Christina Goldschmidt (Oxford) Combinatorial Theory Seminar Add to calendar L3
The scaling limit of critical random graphs
Consider the Erdos-Renyi random graph $ G(n,p) $ inside the critical window, so that $ p = n^{-1} + \lambda n^{-4/3} $ for some real \lambda. In this regime, the largest components are of size $ n^{2/3} $ and have finite surpluses (where the surplus of a component is the number of edges more than a tree that it has). Using a bijective correspondence between graphs and certain "marked random walks", we are able to give a (surprisingly simple) metric space description of the scaling limit of the ordered sequence of components, where edges in the original graph are re-scaled by $ n^{-1/3} $. A limit component, given its size and surplus, is obtained by taking a continuum random tree (which is not a Brownian continuum random tree, but one whose distribution has been exponentially tilted) and making certain natural vertex identifications, which correspond to the surplus edges. This gives a metric space in which distances are calculated using paths in the original tree and the "shortcuts" induced by the vertex identifications. The limit of the whole critical random graph is then a collection of such metric spaces. The convergence holds in a sufficiently strong sense (an appropriate version of the Gromov-Hausdorff distance) that we are able to deduce the convergence in distribution of the diameter of $ G(n,p) $, re-scaled by $ n^{-1/3} $, to a non-degenerate random variable, for $ p $ in the critical window. This is joint work (in progress!) with Louigi Addario-Berry (Universite de Montreal) and Nicolas Broutin (INRIA Rocquencourt).
Tue, 10/02/2009
15:45 		Young-Houn Kiem (Seoul National University) Algebraic and Symplectic Geometry Seminar Add to calendar L3
Moduli theoretic compactifications of the space of smooth rational curves
The space of smooth rational curves of degree d in projective space admits various moduli theoretic compactifications via GIT, stable maps, stable sheaves, Hilbert scheme and so on. I will discuss how these compactifications are related by explicit blow-ups and -downs for d<4.
Tue, 10/02/2009
17:00 		Ivan Marin (Université Paris 7) Algebra Seminar Add to calendar L2
Some algebraic aspects of KZ systems
Wed, 11/02/2009
11:30 		George Wellen (University of Oxford) Algebra Kinderseminar Add to calendar
A PID that is not Euclidean (Held in ChCh, Tom Gate, Room 2)
It is well-known that Euclidean domains are PIDs; examples proving that the inclusion is strict are not commonly known. Here is one.
Thu, 12/02/2009
11:00 		Dr Myles Allen (Oxford University) Applied Dynamical Systems and Inverse Problems Seminar Add to calendar DH 3rd floor SR
Relative Likelihood vs Bayes in Climate Prediction
Thu, 12/02/2009
12:00 		Arman Taghavi-Chabert (Oxford) Junior Geometry and Topology Seminar Add to calendar SR1
An Introduction to the Penrose transform
Thu, 12/02/2009
14:00 		Dr Raphael Hauser (Computing Laboratory, Oxford) Computational Mathematics and Applications Add to calendar Comlab
A new perspective on the complexity of interior point methods for linear programming
The aim of this talk is to render the power of (short-step) interior-point methods for linear programming (and by extension, convex programming) intuitively understandable to those who have a basic training in numerical methods for dynamical systems solving. The connection between the two areas is made by interpreting line-search methods in a forward Euler framework, and by analysing the algorithmic complexity in terms of the stiffness of the vector field of search directions. Our analysis cannot replicate the best complexity bounds, but due to its weak assumptions it also applies to inexactly computed search directions and has explanatory power for a wide class of algorithms. Co-Author: Coralia Cartis, Edinburgh University School of Mathematics.
Thu, 12/02/2009
16:00 		Hung Bui (Oxford) Number Theory Seminar Add to calendar L3
Gaps between zeros of the Rieman zeta-function
Thu, 12/02/2009
16:30 		Jim Woodhouse (Cambridge) Differential Equations and Applications Seminar Add to calendar DH 1st floor SR
Why is brake squeal so twitchy. Modelling and sensitivity studies of friction-driven vibration
Friction-driven vibration occurs in a number of contexts, from the violin string to brake squeal and machine tool vibration. A review of some key phenomena and approaches will be given, then the talk will focus on a particular aspect, the "twitchiness" of squeal and its relatives. It is notoriously difficult to get repeatable measurements of brake squeal, and this has been regarded as a problem for model testing and validation. But this twitchiness is better regarded as an essential feature of the phenomenon, to be addressed by any model with pretensions to predictive power. Recent work examining sensitivity of friction-excited vibration in a system with a single-point frictional contact will be described. This involves theoretical prediction of nominal instabilities and their sensitivity to parameter uncertainty, compared with the results of a large-scale experimental test in which several thousand squeal initiations were caught and analysed in a laboratory system. Mention will also be made of a new test rig, which attempts to fill a gap in knowledge of frictional material properties by measuring a parameter which occurs naturally in any linearised stability analysis, but which has never previously been measured.

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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