Mon 24 May 2010
University of Edinburgh
JCMB 5215
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2.00pm |
Christos Papadimitropoulos
The Fourier restriction phenomenon in thin sets
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Mon 29 Mar 2010
University of Edinburgh
JCMB 6301
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2.00pm |
Gabriel Koch (Oxford)
An alternative approach to regularity for the Navier-Stokes equations
in critical spaces
Abstract
In an important recent paper, L. Escauriaza, G. Seregin and V. Sverak [ESS] show that solutions to the
Navier-Stokes equations (NSE) which remain bounded in $L3(R3)$ (a ``critical" space) cannot become singular in
finite time. This, coupled with a decay result for global solutions by I. Gallgher, D. Iftimie and F. Planchon,
is the same type of result which has been proved recently for ``critical" hyperbolic/dispersive equations by C.
Kenig and F. Merle. Their method (which relies on ``profile decompositions" for bounded sequences) is quite
general in nature and thus it is natural to ask whether it can be applied in the NSE setting to give an
alternative proof of [ESS]. In collaboration with C. Kenig this has been achieved in the special case of $\dot
H^{{1/2}}$ due to the profile decomposition of I. Gallagher in that setting. A similar decomposition has now
been established in $L3$ as well, and we therefore expect to be able to generalize our result soon to the more
general setting of [ESS].
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Thu 18 Mar 2010
Heriot-Watt University
EM G.44
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4.15pm |
Thomas Sorensen (Imperial College)
Regularity properties of Coulombic wavefunctions and their one-electron densities
Abstract
We review recent results on the regularity and structure of wavefunctions psi of the non-relativistic
Schroedinger operator describing atoms and molecules (that is, with Coulomb interactions). We also
discuss the regularity of the associated one-electron densities rho. In particular, we characterize
the structure of psi around 'two-particle coalescence points'. The method of proof of the
latter extends to the study of the structure of the solutions to the
multiconfiguration equations, and their densities, at the positions of the nuclei.
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Mon 15 Mar 2010
University of Edinburgh
JCMB 5215
|
2.00pm |
Nick Michalowski/Longo (Edinburgh)
Local Existence Theory for Ultra-hyperbolic Quasilinear Schrodinger Equations
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Thu 11 Mar 2010
Heriot-Watt University
EM G.44
|
4.15pm |
Hillel Raz (Cardiff University)
Local Operators and Locality Bounds in the Anharmonic Lattice
Abstract.
Local operators are defined as operators which act on local finite sets and outside of that set act as
the identity. In this talk we seek to answer the following question,
what happens to local operators under a
specific map that corresponds to the time evolution in
quantum mechanics. That is, we seek to find whether or not
such operators remain local and if so to what extent.
We do this by comparing the evolved local operator with
another local operator that is not evolved and
bounding a relation between the two of them. The result is known as
a locality bound, and bears the name of the two who first
discovered it - a Lieb-Robinson bound. We provide such a
bound in a few specific settings that come from physics, in particular in the anharmonic lattice.
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Mon 08 Mar 2010
University of Edinburgh
JCMB 5215
|
2.00pm |
Juan Antonio Barcelo (Madrid)
Limiting absortion principle for the Lame equation
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Thu 25 Feb 2010
Heriot-Watt University
EM G.44
|
3.30pm |
Jens Wirth (Imperial College)
Energy and dispersive estimates for hyperbolic systems
Abstract.
We consider hyperbolic t-dependent pseudo-different systems and present some results on energy and
dispersive estimates for their solutions based on a diagonalisation
procedure applied to their full symbol. Examples include
differential hyperbolic systems as well as hyperbolic differential equations of higher order.
David Dos Santos Ferreira (Universite Paris XIII)
On the linearized local Calderon problem
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Thu 18 Feb 2010
Heriot-Watt University
EM G.44
|
4.15pm |
Marko Lindner (TU Chemnitz)
Spectra of Jacobi operators: Analysis and approximation
Abstract.
We look at bounded linear operators on vector-valued
$\ell^p$ spaces and study their spectrum (in particular
the essential spectrum) and pseudospectra. Our operators
are given by infinite matrices with finitely many diagonals.
For the case of tridiagonal matrices, we moreover give
upper bounds on spectrum and pseudospectrum of the
infinite matrix A in terms of pseudospectra of certain
submatrices of A. The latter sets approximate the
(pseudo-)spectrum of A as $n$ goes to infinity.
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Mon 15 Feb 2010
University of Edinburgh
JCMB 5215
|
2.00pm |
Jim Wright (Edinburgh)
Some elementary number theory revisited
from a harmonic analyst's perspective
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Thu 11 Feb - Sat 13 Feb 2010
Heriot-Watt University
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all day |
CANPDE Crash-course in Analysis and Nonlinear PDEs
Yvan Martel (Universite de Versailles-Saint-Quentin-en-Yvelines)
Francesco Maggi (Universita di Firenze)
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Thu 28 Jan 2010
Heriot-Watt University
EM G.44
|
4.15pm |
Michael Ruzhansky (Imperial College)
Pseudo-differential operators and symmetries
Abstract.
In this talk we will describe an approach to pseudo-differential operators
on Lie groups and homogeneous spaces in terms of their representation
theory. This allows one to recapture global symbols of operators and
their main properties. The talk will be based on the recent monograph:
M. Ruzhansky and V. Turunen, Pseudo-differential operators and
symmetries, Birkhauser, Basel, 2010.
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Mon 18 Jan 2010
University of Edinburgh
5215 JCMB
|
2.00pm |
Martin Dindos (Edinburgh)
The BMO solvability of the elliptic boundary value problem and
the A-infinity condition
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Thu 19 Nov 2009
Heriot-Watt University
EM 1.70
|
2.15pm |
Nicholas Young (Leeds University)
Boundary interpolation problems in a half plane
Abstract.
A classical problem of function theory is to construct (when possible)
an analytic function f in the upper half plane Im z > 0 such that
Re f(z) is non-negative for all z and such that f satisfies some
interpolation conditions at points in the closed upper half plane.
I will describe an elementary method for the solution of such problems.
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Thu 12 Nov 2009
University of Edinburgh
4310 JCMB
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3.00pm |
Olga Maleva (Birmingham)
Differentiability of Lipschitz functions inside thin sets
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Tue 10 Nov 2009
University of Edinburgh
4310 JCMB
|
2.00pm |
Betsy Stovall (UCLA)
Quasi-extremals for certain generalized Radon transforms
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Thu 05 Nov 2009
Heriot-Watt University
EM 1.70
|
2.15pm |
David Rule (Heriot-Watt University)
Weighted norm inequalities for pseudodifferential operators
defined by amplitudes
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Mon 2 Nov 2009
University of Edinburgh
5215 JCMB
|
2.00pm |
Arghir Zarnescu (Oxford)
Mathematical problems of the Q-tensor theory
Abstract
The complexity of nematic liquid crystals is described, in Landau-de Gennes
theory, through functions defined on two or three-dimensional domains and
taking values into the set of Q-tensors, that is three-by-tree symmetric
traceless matrices.
The main mathematical challenges are caused by the necessity to finely
manipulate high dimensional objects. This large dimensionality of the
domain and target space allows for specific features inaccessible in lower
dimensions (for instance one needs at least a 2D domain to have a real
analytic matrix-valued function with discontinuous eigenvectors). Also, in 2D
domains, in the so-called ''constrained theory'', one can express lifting
questions in terms of familiar complex analysis problems, but in 3D one needs
to construct the appropriate analogue of the complex analytic language in
order to effectively deal with the lifting problem, and this is yet to be
done.
I will present some natural physical questions and recent advances in their
mathematical treatment, advances that involve a non-standard combination of
diverse tools from analysis, Riemannian geometry, regularity theory and
qualitative properties of elliptic and parabolic systems
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Wed 21 Oct 2009
ICMS
14 India Street
|
10:00 am |
PDE Mini-Symposium
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Thu 15 Oct - Fri 16 Oct 2009
Heriot-Watt University
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all day |
CANPDE Crash-course in Analysis and Nonlinear PDEs
Laszlo Szekelyhidi (Bonn)
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Mon 12 Oct 2009
University of Edinburgh
5215 JCMB
|
2.00pm |
Stefan Valdimarsson (Iceland)
Geometric Brascamp--Lieb gives the optimal best constant
Abstract
We will review the appearances of geometric data in Brascamp--Lieb inequalities. Then we will discuss
their role in furnishing the optimal best constant for the Brascamp--Lieb inequalities.
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Mon 4 Oct 2009
University of Edinburgh
5215 JCMB
|
2.00pm |
Axel Grunrock (Bonn)
Bilinear space-time estimates for linearized kp-type equations
with semiperiodic and periodic data
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Mon 28 Sep 2009
University of Edinburgh
5215 JCMB
|
2.00pm |
Aram Karakhanyan (University of Edinburgh)
On derivation of Euler-Lagrange equations for incompressible energy minimizers
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