
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES

Fields
Institute Applied Mathematics Colloquium/Seminar
201314


Organizing
Committee
Jim
Colliander (U
of Toronto)
Walter Craig (McMaster)
Catherine Sulem (U of Toronto)

Robert
McCann (U of Toronto)
Adrian Nachman (U of Toronto)
Mary Pugh (U of Toronto)
Huaxiong
Huang (York) 



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.
Upcoming
Talks 2014 

TBA 
Previous
Talks 
March 18
12 noon,
Stewart Library

Henry Wente, University of Toledo
Bifurcation and symmetrybreaking for a problem in capillary theory
Consider a liquid drop in contact with a solid. An equilibrium configuration
is determined by minimizing the surface area of the drop subject to
a volume constraint. The free surface of such a drop will have constant
mean curvature. We focus on an easily visualized example where there
is a symmetrybreaking bifurcation at a critical juncture and where
stability is lost as the volume is increased. We examine the nature
of the bifurcation family.

January
22,
3:10 p.m.
Room 230 
Bob Finn, Stanford
Developments toward the Mariotte Problem
During the 17th Century Edme Mariotte observed that objects floating
on a liquid surface can attract or repel each other, and he attempted
(without success!) to develop physical laws describing the phenomenon.
Initial steps toward a consistent theory appeared with Laplace, who
in 1806 examined the configuration of two infinite vertical parallel
plates of possibly differing materials, partially immersed in an infinite
liquid bath and rigidly constrained. This can be viewed as an instantaneous
snapshot of an idealized special case of the Mariotte observations.
Using the then novel concept of surface tension, Laplace identified
particular choices of materials and of plate separation, for which
the plates would either attract or repel each other.
The present work returns to that twoplate configuration from a more
geometrical point of view, and yields characterization of all modes
of behavior that can occur. The results include algorithms for evaluating
the forces with arbitrary precision, and embrace also some surprises,
notably the remarkable variety of occurring behavior patterns despite
the relatively few relevant parameters. A striking limiting discontinuity
appears as the plates approach each other.
All results described are exact consequences of the underlying (nonlinear)
equations. No simplifying hypotheses are introduced; the conclusions
depend essentially on the specific nonlinearity. A message is conveyed,
that small configurational changes can have large observational consequences,
and thus easy answers in less restrictive circumstances should not
be expected.

November
29
Friday
2:10 p.m.
Stewart Library, 
Achim
Kempf, Waterloo
New methods for spectral geometry: hearing the shape of things 
November
22
Friday
2:10 p.m.
Stewart Library 
Efim
Pelinovsky, Nizhny Novgorod State Technical University

November 18
Monday
2:10 p.m.
Stewart Library

Werner Kirsch (FernUniversität in Hagen and Bochum)
Mathematics and Politics: Analysis of power and fair representation
in complex voting systems
Both in national and international politics there are various decision
making processes of considerable complexity, for example the process
to amend the Canadian constitution, decision making in the European
Community, and the election of the US president via the electoral
college. In this talk we introduce methods to quantify the power of
various actors. We will also discuss the question of a fair representation
of the citizens in this process, for example the question how many
electors a state should have in the electoral college. Our main example
will be the Council of Ministers of the EU, but the results will apply
to many other examples. The talk will emphasize the mathematical results,
but most of it will be accessible to nonmathematicians as well

Oct 17
4:10 p.m.
* Location:
MP Room 102
McLennan Physical Laboratories
255 Huron Street

Sharon
C. Glotzer (University of Michigan)
Packing & Assembling Polyhedra

Mon, July 8
1:10 p.m.
Stewart Library

Ricardo Barros, IMPA (Instituto Nacional de Matematica Pura
e Aplicada, Brazil)
Twodimensional Nonlinear Internal Wave
Large amplitude internal solitary waves excited typically by the
interaction of tidal currents with bottom topography have been observed
frequently in coastal oceans through insitu measurements and satellite
images. Although there has been a considerably intensive research
on nonlinear internal waves, most of the existing work is devoted
strictly to the onedimensional case. To study the evolution of twodimensional
large amplitude internal waves in a twolayer system with variable
bottom topography, we derive a fully twodimensional strongly nonlinear
model. This is a generalization of the onedimensional model of Choi,
Barros & Jo (2009) that is known to be free from shear instability
for a wide range of physical parameters. After investigating shear
instability of the regularized model for flat bottom, weakly twodimensional
and weakly nonlinear limits are discussed.

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