SCIENTIFIC PROGRAMS AND ACTIVITIES

April 18, 2014
THE FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
Fields Institute Applied Mathematics Colloquium/Seminar
2013-14

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)

OVERVIEW

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 super-conductivity, 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 symmetry-breaking 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 symmetry-breaking 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 two-plate 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 non-mathematicians 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)
Two-dimensional 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 in-situ 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 one-dimensional case. To study the evolution of two-dimensional large amplitude internal waves in a two-layer system with variable bottom topography, we derive a fully two-dimensional strongly nonlinear model. This is a generalization of the one-dimensional 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 two-dimensional and weakly nonlinear limits are discussed.


 

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