
Fields Institute Colloquium/Seminar in Applied Mathematics
20092010
Organizing Committee 

Jim Colliander (Toronto)
Walter Craig (McMaster)
Catherine Sulem (Toronto) 
Robert McCann (Toronto)
Adrian Nachman (Toronto)
Mary Pugh (Toronto)

The Fields Institute Colloquium/Seminar in Applied Mathematics
is a monthly colloquium series for mathematicians in the areas of
applied mathematics and analysis. The series alternates between
colloquium talks by internationally recognized experts in the field,
and less formal, more specialized seminars.In recent years, the
series has featured applications to diverse areas of science and
technology; examples include superconductivity, nonlinear wave
propagation, optical fiber communications, and financial modeling.
The intent of the series is to bring together the applied mathematics
community on a regular basis, to present current results in the
field, and to strengthen the potential for communication and collaboration
between researchers with common interests. We meet for one session
per month during the academic year. The organizers welcome suggestions
for speakers and topics.
200910
Past Seminars

June
2 , 2010
Wednesday, 2:10 PM

Alex Tamasan (University of Central Florida)
Recovering the electrical conductivity from interior data
In this talk I will present a new method to reconstruct the
conductivity of a body from interior knowledge of the magnitude
of the current density field generated while maintaining a
specific boundary voltage. The problem reduces to the Dirichlet
problem for the 1Laplacian (a degenerate elliptic equation),
and it is equivalent to finding specific minimal surfaces
in a conformal metric. An implicit compatibility relation
between the interior data and the boundary data is not captured
by the degenerate elliptic PDE. Instead, we formulate and
study a minimization problem. Under certain conditions, level
sets of minimizers of the functional are area minimizers (in
the particular metric), fact which allows us to treat the
case when partial interior data is available. In the end I
will show some numerical results based on implementation of
the theory. This is joint work with Adrian Nachman of U Toronto
and Alexander Timonov of U South Carolina Upstate.

PAST TALKS

FRIDAY,
OCTOBER 9
2:00 p.m. 
**
Special Seminar Announcement**

PDE/Applied Math/Analysis Seminar
John Ball, University of Oxford
'The Qtensor theory of liquid crystals'
Bahen Centre, BA6183 
October
13th, 2009
2:10 p.m.
Bahen 6183
( 40 St. George St.) 
Robert
V. Moody, University of Victoria (http://www.math.ualberta.ca/~rvmoody/rvm/)
Symmetry, diffraction, and the homometry problem
Diffraction has been the mainstay of experimental crystallography
for nearly a hundred years. Recent interest in quasicrystals
and aperiodic tilings has brought fresh insights into the
nature of diffraction and its relation to symmetry, especially
in the case of pure point diffraction.
In this talk I will try to make a case for diffraction as
an encoding of symmetry and then delve into the famous inverse
problem of unravelling the information about a structure from
information about its diffraction.
The diffraction is a measure. Which pure point measures can
occur as diffraction patterns and given such a measure how
does one find and classify all the structures that could have
produced it? This is the homometry problem. In answering it
we arrive naturally in the setting of certain stochastic processes.
The complexity of the classification revolves around the set
of extinctions in the diffraction.
The talk will be aimed at a general mathematical audience.

November
4th, 2009
2:10 p.m.
Fields Institute,
Room 230 
Elliot
Lieb, Princeton University
A second look at the second law of thermodynamics
The increase of entropy was regarded as perhaps the most
perfect and unassailable law in physics and it was even supposed
to have philosophical import. Einstein, like most physicists
of his time, regarded the second
law of thermodynamics as one of the major achievements of
the field, and it entered his work in several ways. The essence
of the second law is the statement that all processes can
be quantified by an entropy
function whose increase is a necessary and sufficient condition
for a process to occur. As a fundamental physical law no deviation,
however tiny, is permitted and its consequences are farreaching.
Current wisdom regards the second law as a consequence of
statistical mechanics but the entropy principle, which was
discovered before statistical mechanics was invented, ought
to be derivable from a few logical principles without recourse
to Carnot cycles, ideal gases and other assumptions about
such things as 'heat', 'hot' and 'cold', 'temperature', 'reversible
processes', etc. Like conservation of energy (the ``first''
law), the existence of a law so precise and so modelindependent
must have a logical foundation that is independent of the
details of the constitution of matter. In this lecture the
foundations of the subject and the construction (with J. Yngvason)
of entropy from a few simple principles will be presented.
(No previous familiarity with the subject is required.)
A summary can be found in:
"A Guide to Entropy and the Second Law of Thermodynamics",
Notices of the Amer. Math. Soc. vol 45 571581 (1998).
http://www.ams.org/notices/199805/lieb.pdf.
This paper received the American Mathematical Society 2002
Levi Conant prize for ``the best expository paper published
in either the Notices of the AMS or the Bulletin of the AMS
in the preceding five years''.

December 9, 2009
2:10 p.m.
Fields Institute, Room 210 
Jose Francisco Rodrigues (University of Lisbon / CMAF)
Constrained ReactionDiffusion and Transport Systems:
the Nmembrane and Multiphase Problems
We analyse vector valued diffusion and transport equations
with a class of constraints of unilateral and bilateral type.
Using the variational inequality approach we characterize
explicitly the associated Lagrange multipliers by reducing
the problems to semilinear systems coupled through the characteristic
functions of the coincident sets of the Nmembranes problem,
analogously to the obstacle problem. In collaboration with
Lisa Santos, we obtain new results to the system associated
with the Gibbs simplex for multiphase problems. We also discuss
the stability of the solutions and their coincident sets,
in particular, the asymptotic behaviour in time for the respective
evolution problems.

**PLEASE NOTE CHANGE IN DATE AND TIME**
January 14, 2010
11:00 a.m.
Fields Institute, Stewart Library 
Ivana Alexandrova (East Carolina University)
Resonances for Magnetic Scattering by Two Solenoidal Fields
at Large Separation
We consider the problem of quantum resonances in magnetic
scattering by two solenoidal fields at large separation in
two dimensions. We study the distribution of resonances near
the real axis when the distance between two centers of fields
goes to infinity. We give a sharp lower bound on resonance
widths in terms of backward amplitude calculated explicitly
for scattering by each solenoidal field. The study is based
on a new type of complex scaling method. As an application,
we also discuss the relation to semiclassical resonances in
scattering by two solenoidal fields. This is joint work with
Hideo Tamura.

January
20, 2010
2:10 p.m.
Fields Institute, Stewart Library 
Andrew Belmonte
http://www.math.psu.edu/belmonte/
W. G. Pritchard Laboratories
Department of Mathematics
Penn State University, USA
Sinking Amid Bubbles
The transient and steady state motion of a solid sphere falling
through a fluid depends to a large degree on the material
properties of the fluid medium, be it Newtonian, Stokes, viscoelastic,
or something more complicated. A field of rising bubbles provides
a convenient way to slow down or even reverse the sedimentation
of a heavy sphere, as utilized in some industrial situations.
I will present an experimental and mathematical study of a
single sphere descending through such a bubbly fluid (Reynolds
numbers around 1000) in a quasi2D geometry, focusing on two
transitions: from falling to floating, and the onset of a
diffusive lateral motion. This is joint work with Michael
Higley (now at NJIT).

***MOVED TO APPLIED MATH/PDE/ANALYSIS
SEMINAR ON JANUARY 29TH***
January 27, 2010
3:10 p.m.
Fields Institute, Room 210 
Eric Carlen (Rutgers)
http://www.math.rutgers.edu/~carlen/
Rate of relaxation to stable profiles for some fourth
order evolution equations equations
We will explain recent work on obtaining strong stability
results, with rate of relaxation bounds, on stationary profiles
for a class of forth order equations of thin film and CahnHilliard
type. The talk is based on joint work with Carvalho, Orlandi,
and Suleyman.

JANUARY 2010***
2:10 p.m.
Fields Institute,
Room 230 
Jeff Schenker, Michigan State University
TBA

April
14, 2010
2:10 p.m.
Fields Room 230 
Albert
Fathi (Ecole Normale Superieure de Lyon)
DenjoySchwartz and HamiltonJacobi
Given a C2 Hamiltonian H(xp), C2strictly convex in the moment
variable, it has been shown by Patrick Bernard that one can
always find C1 strict subsolutions with locally Lipschitz
derivative of the HamiltonJacobi equation. After explaining
the general background, the talk will concentrate on the constraints
imposed on smoother critical subsolutions by the implications
of the classical DenjoySchwartz theory of Dynamical Systems
on surfaces.

May
26, 2010
Wednesday, 2:10 PM
Where: BA6183 (NOTE SPECIAL LOCATION) 
Dr Garry Newsam
Defence Science and Technology Organisation (DSTO) AUSTRALIA
New Theories of Imagery and Implications for Image
Segmentation
Analysis has constructed a rich hierarchy of function spaces
but it is not often obvious where real objects fit within
it. The talk will review the evolution of views on where one
particular class of objects, images, sits within the hierarchy
and consider the implications for one particular image processing
problem, image segmentation. The nub of the talk is that the
last decade has seen the emergence of an surprising consensus:
images are not in any of the standard function spaces but
are really distributions. This unexpected characterisation
appears to be the only way to accommodate the consistent empirical
observations that key properties of images are essentially
scaleinvariant. The result has strong implications for how
image processing problems such as deblurring or computation
of depth from motion should be formulated; the talk will conclude
with a brief discussion of what it might mean for image segmentation
based on minimising the MumfordShah functional.

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