14:15
14:15
16:30
16:30
16:15
Conditioning in optimization and variational analysis
Abstract
Condition numbers are a central concept in numerical analysis.
They provide a natural parameter for studying the behavior of
algorithms, as well as sensitivity and geometric properties of a problem.
The condition number of a problem instance is usually a measure
of the distance to the set of ill-posed instances. For instance, the
classical Eckart and Young identity characterizes the condition
number of a square matrix as the reciprocal of its relative distance
to singularity.
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We present concepts of conditioning for optimization problems and
for more general variational problems. We show that the Eckart and
Young identity has natural extension to much wider contexts. We also
discuss conditioning under the presence of block-structure, such as
that determined by a sparsity pattern. The latter has interesting
connections with the mu-number in robust control and with the sign-real
spectral radius.
12:00
Moduli Kahler Potential for M-theory on a G_2 Manifold
Abstract
I present a calculation of the moduli Kahler potential for M-theory
on a G_2 manifold in a large radius approximation. The result is used to
analyze moduli dynamics and moduli stabilization in the context of the
associated four-dimensional effective theory.
12:00
17:00
The Aviles Giga functional
Abstract
Take any region omega and let function u defined inside omega be the
distance from the boundary, u solves the iconal equation \lt|Du\rt|=1 with
boundary condition zero. Functional u is also conjectured (in some cases
proved) to be the "limiting minimiser" of various functionals that
arise models of blistering and micro magnetics. The precise formulation of
these problems involves the notion of gamma convergence. The Aviles Giga
functional is a natural "second order" generalisation of the Cahn
Hilliard model which was one of the early success of the theory of gamma
convergence. These problems turn out to be surprisingly rich with connections
to a number of areas of pdes. We will survey some of the more elementary
results, describe in detail of one main problems in field and state some
partial results.
15:45
Surface measures on paths in an embedded Riemannian manifold
Abstract
We construct and study different surface measures on the space of
paths in a compact Riemannian manifold embedded into the Euclidean
space. The idea of the constructions is to force a Brownian particle
in the ambient space to stay in a small neighbourhood of the manifold
and then to pass to the limit. Finally, we compare these surface
measures with the Wiener measure on the space of paths in the
manifold.
12:00
Gauge theory for commutative but non-associative fuzzy spaces
Abstract
I discuss gauge theories for commutative but non-associative algebras
related to the SO(2k+1) covariant finite dimensional fuzzy 2k-sphere
algebras. A consequence of non-associativity is that gauge fields and
gauge parameters have to be generalized to be functions of coordinates as
well as derivatives. The usual gauge fields depending on coordinates only
are recovered after a partial gauge fixing.The deformation parameter for
these commutative but non-associative algebras is a scalar of the rotation
group. This suggests interesting string-inspired algebraic deformations of
spacetime which preserve Lorentz-invariance.
The talk will be based on hepth/0310153
16:30
16:15
Multiphysics modelling in FEMLAB
Abstract
The seminar will focus on mathematical modelling of physics phenomena,
with applications in e.g. mass and heat transfer, fluid flow, and
electromagnetic wave propagation. Simultaneous solutions of several
physics phenomena described by PDEs - multiphysics - will also be
presented and discussed.
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All models will be realised through the use of the MATLAB based finite
element package FEMLAB. FEMLAB is a multiphysics modelling environment
with built-in PDE solvers for linear, non-linear, time dependent and
eigenvalue problems. For ease-of-use, it comprises ready-to-use applications
for various physics phenomena, and tailored applications for Structural
Mechanics, Electromagnetics, and Chemical Engineering. But in addition,
FEMLAB facilitates straightforward implementation of arbitrary coupled
non-linear PDEs, which brings about a great deal of flexibility in problem
definition. Please see http://ww.uk.comsol.com for more info.
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FEMLAB is developed by the COMSOL Group, a Swedish headquartered spin-off
from the Royal Institute of Technology (KTH) in Stockholm, with offices
around the world. Its UK office is situated in The Oxford Science Park.
14:45