A list of past colloquia with abstracts is available here.

9 October 2009, room S-3.01	Jürgen Berndt (King's College London)   Cohomogeneity one actions   Abstract: The cohomogeneity of the action of a group on a space is the dimension of the orbit space. Cohomogeneity one actions are therefore actions with a one-dimensional orbit space. The general theory of such actions has been studied since several decades. It is well known that transitive actions allow us to reformulate geometric problems in terms of algebraic equations. Similarly, cohomogeneity one actions can be used to reformulate geometric problems in terms of ordinary differential equations. In recent years this has been successfully applied to the construction of geometric structures on manifolds or other spaces. In the talk I will give an introduction to the general theory of cohomogeneity one actions in the context of isometric actions, and discuss a few applications and classification results.
23 October 2009, room K3.11	Nick Trefethen (University of Oxford)   Four bugs on a rectangle   Abstract: Four bugs start at t=0 at the vertices of a 2x1 rectangle. Each one chases the bug to its left with speed 1. What's the shape of the ensuing spiral? You may think this sounds like a problem made famous by Martin Gardner in Scientific American, but it is remarkably different because of the rectangular initial condition. This talk will describe the bugs' extraordinary paths with the help of some unusual asymptotic analysis, joint work with James Lottes and S. J. Chapman. By the time the first circuit of the origin is completed, the scale of the configuration has shrunk by a factor that I think will surprise you, and the surprise leads to interesting questions about symmetry, well-posedness, and the meaning of large numbers.
20 November 2009, room K3.11	Damiano Brigo (Fitch Ratings and Imperial College)   Credit derivatives pre- and in-crisis: Stochastic dynamical models including extreme scenarios   Abstract: We illustrate Credit Index Options and Collateralized Debt Obligations (CDO), showing the basic arbitrage-free definitions of the quantities impacting the relevant payouts, and discussing different approaches in general. We focus first on a partial filtration formula for credit index options, improving the methodology currently used in the market by allowing us to remove singularities due to vanishing numeraires in the Radon Nikodym derivative leading to the pricing formula. We then introduce the arbitrage-free generalized Poisson dynamic Loss (GPL) model, capable of consistently calibrating all the CDO tranches for all the maturities at the same time. We show examples with market data both pre- and in- crisis, illustrating how the credit crisis started in 2007 impacts the models and the products valuation. We conclude by pointing out that mathematical subtleties are not to be underestimated, highlighting their impact on valuation.
27 November 2009, room K2.31	Dinesh Singh (University of Delhi)   Harmonic Analysis on the Unit Circle: A Personal Perspective   Abstract: This talk surveys - based on my personal learnings and preferences - about a hundred years of harmonic analysis on the unit circle starting with the work of Fatou and looking at some very recent aspects.
22 January 2010, room K3.11	June Barrow-Green (Open University)   The British use of mathematics in the First World War   Abstract: 'This is a Mathematical War' declared Sir George Greenhill in his Presidential address to the Mathematical Association in January 1915. Two years later his words were echoed at the front by a young British soldier who found himself fighting in a 'war of guns and mathematics'. Were these accurate descriptions or isolated observations? What effect did the war have on British mathematicians and on their subject? To answer these questions, I shall consider the extent to which British mathematicians were encouraged to contribute their talent to the war effort and the nature of their contributions.
12 February 2010, room K3.11	Philip Candelas (Oxford)   Calabi-Yau Manifolds in Physics and Number Theory   Abstract: Calabi-Yau manifolds have many remarkable properties owing to their connection to string theory and supersymmetry. These manifolds possess certain parameters which, over C, describe the complex structure. The periods, which are integrals of the unique holomorphic form over a homology basis, provide natural coordinates on this parameter space. It is a curious fact that there are two communities that think that they 'own' these periods. These are string theorists and number theorists, each being largely unaware of the other's existence. I will try to explain the importance of the periods to each of these communities.
5 March 2010, room K3.11	John Cardy (Oxford)   Random Planar Curves, Schramm-Loewner Evolution and Conformal Field Theory   Abstract: I review the two different approaches to studying the scaling limit of critical two-dimensional lattice models, through Conformal Field Theory and Schramm-Loewner Evolution, and how they are interrelated through the identification of suitable holomorphic observables.

• LMS/EPSRC short course: Topics in Arithmetic Geometry, 2006
• LMS/EPSRC short course: Topics in Algebraic Number Theory, 2002
• Short course in Financial Mathematics, 2001

To read some past lectures, click on the year and then on the lecture. Some information about the upcoming summer school can be obtained by clicking on its year. To register for an upcoming summer school, contact

Pat Evans
Senate House
Malet Street
London WC1E7HU
e-mail: p.evans@academic.lon.ac.uk
Phone: 020-7862 8034 (direct line)
FAX: 020-7862 8049

2005   A Mathematics Pot-Pourri III   

(June 17, 2005)

2004   A Mathematics Pot-Pourri II   

(June 25, 2004)

2003   A Mathematics Potpourri    

(June 27, 2003)

2002   Financial Mathematics   

(June 25, 2002)

2001   History of Mathematics   

(June 27 - 28, 2001)

Speakers included Prof. Jeremy Gray

2000   Numbers and Codes   

(June 29-30, 2000)

Speakers included Prof. Sir Andrew Wiles

1999   Chaos   

(June 21-23 1999)

Speakers included Sir Christopher Zeeman and Sir Robert May

2009 (Thursday 30 April)

2008 (Thursday 8 May)      

2007 (Thursday 26 April)      

2006 (Wednesday, May 3)      

2005 (Thursday, April 28)      

2004 (Thursday, April 29)