17:00
15:45
Front Fluctuations for the one dimensional Stochastic Cahn Hilliard Equation
Abstract
We consider the Cahn Hilliard Equation in the line, perturbed by
the space derivative of a space--time white noise. We study the
solution of the equation when the initial condition is the
interface, in the limit as the intensity of the noise goes to zero
and the time goes to infinity conveniently, and show that in a scale
that is still infinitesimal, the solution remains close to the
interface, and the fluctuations are described by a non Markovian
self similar Gaussian process whose covariance is computed.
14:15
Rough Paths and applications to support theorems
Abstract
After a brief introduction to the basics of Rough Paths I'll
explain recent work by Peter Friz, Dan Stroock and myself proving that a
Brownian path conditioned to be uniformly close to a given smooth path
converges in distribution to that path in the Rough Path metric. The Stroock
Varadhan support theorem is an immediate consequence.
The novel part of the argument is to
obtain the estimate in a way that is independent of the particular norm used
in the Euclidean space when one defines the uniform norm on path space.
14:15
14:30
14:00
09:00
14:30
Getting Connected: the pros and cons of networks in populations with limited resources
14:15
Simulating the Mean-Reverting Square Root Process, with Applications to Option Valuation
16:30
Recent developments in numerical simulation of failure in metals subjected to impact loading
Abstract
The seminar will address issues related to numerical simulation
of non-linear behaviour of solid materials to impact loading.
The kinematic and constitutive aspects of the transition from
continuum to discontinuum will be presented as utilised
within an explicit finite element development framework.
Material softening, mesh sensitivity and regularisation of
solutions will be discussed.
12:00
Special Holonomy Manifolds and Quartic String Corrections
Abstract
At the leading order, the low-energy effective field equations in string
theory admit solutions of the form of products of Minkowski spacetime and a
Ricci-flat Calabi-Yau space. The equations of motion receive corrections at
higher orders in \alpha', which imply that the Ricci-flat Calabi-Yau space is
modified. In an appropriate choice of scheme, the Calabi-Yau space remains
Kahler, but is no longer Ricci-flat. We discuss the nature of these
corrections at order {\alpha'}^3, and consider the deformations of all the
known cohomogeneity one non-compact Kahler metrics in six and eight
dimensions. We do this by deriving the first-order equations associated with
the modified Killing-spinor conditions, and we thereby obtain the modified
supersymmetric solutions. We also give a detailed discussion of the boundary
terms for the Euler complex in six and eight dimensions, and apply the
results to all the cohomogeneity one examples. Additional material will be
presented concerning the case of holonomy G_2.
17:00
12:00