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
Higher gauge theory, non-Abelian Wilson surfaces and a generalization of 2-form electrodynamics
17:00
14:15
The solutions to a class of non-linear stochastic partial
differential equations
Abstract
In this talk, we consider a class of non-linear stochastic partial
differential equations. We represent its solutions as the weighted
empirical measures of interacting particle systems. As a consequence,
a simulation scheme for this class of SPDEs is proposed. There are two
sources of error in the scheme, one due to finite sampling of the
infinite collection of particles and the other due to the Euler scheme
used in the simulation of the individual particle motions. The error
bound, taking into account both sources of error, is derived. A
functional limit theorem is also derived. The results are applied to
nonlinear filtering problems.
This talk is based on joint research with Kurtz.
16:30
Representation theory and combinatorics, from Young tableaux to the loop Grassmannian
Abstract
A little more than 100 years ago, Issai Schur published his pioneering PhD
thesis on the representations of the group of invertible complex n x n -
matrices. At the same time, Alfred Young introduced what later came to be
known as the Young tableau. The tableaux turned out to be an extremely useful
combinatorial tool (not only in representation theory). This talk will
explore a few of these appearances of the ubiquitous Young tableaux and also
discuss some more recent generalizations of the tableaux and the connection
with the geometry of the loop grassmannian.
14:30
14:15
From wetting to filling and back again: wedge covariance and non-local interfacial models
17:00
LS-galleries and MV-cycles
Abstract
Let $G$ be a complex semisimple algebraic group. We give an interpretation
of the path model of a representation in terms of the geometry of the affine
Grassmannian for $G$.
In this setting, the paths are replaced by LS--galleries in the affine
Coxeter complex associated to the Weyl group of $G$.
The connection with geometry is obtained as follows: consider a
Bott--Samelson desingularization of the closure of an orbit
$G(\bc[[t]]).\lam$ in the affine Grassmannian. The points of this variety can
be viewed as galleries of a fixed type in the affine Tits building associated
to $G$. The retraction of the Tits building onto the affine Coxeter complex
induces in this way, a stratification of the $G(\bc[[t]])$--orbit, indexed by
certain folded galleries in the Coxeter complex.
The connection with representation theory is given by the fact that the
closures of the strata associated to LS-galleries are the
Mirkovic-Vilonen--cycles, which form a basis of the representation $V(\lam)$
for the Langland's dual group $G^\vee$.
16:30
16:30