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Mathematics

Nassif Ghoussoub Receives Honorary Degree from the University of Victoria

Speaker: 
Nassif Ghoussoub
Date: 
Fri, Jun 12, 2015
Location: 
University of Victoria
Abstract: 
Dr. Nassif Ghoussoub received the honorary degree of DSc at UVic's convocation ceremonies on June 12, 2015. Ghoussoub is a world-leading mathematician who has played a critical role in building Canadian networks for the support of education and research in mathematical sciences. He is the founder of the Pacific Institute for Mathematical Sciences (PIMS), the Banff International Research Station (BIRS) and a co-founder of Mathematics of Information Technology and Complex Systems (MITACS). PIMS has transformed mathematics among research universities in western Canada by encouraging regional research initiatives. BIRS has gained an international reputation as a premier venue for mathematics conferences. MITACS, an offshoot of PIMS, promotes collaboration among mathematicians working in industry and academia. Ghoussoub, a math professor at the University of British Columbia, is a world leader in the field of partial differential equations.

A topological look at the vector (cross) product in three dimensions

Speaker: 
Peter Zvengrowski
Date: 
Sat, May 9, 2015
Location: 
PIMS, University of Lethbridge
Conference: 
Alberta Mathematics Dialog
Abstract: 
The vector product (or cross product) of two vectors in 3-dimensional real space $\mathbb{R}^3$ is a standard item covered in most every text in calculus, advanced calculus, and vector calculus, as well as in many physics and linear algebra texts. Most of these texts add a remark (or “warning”) that this vector product is available only in 3-dimensional space. In this talk we shall start with some of the early history, in the nineteenth century, of the vector product, and in particular its relation to quaternions. Then we shall show that in fact the 3-dimensional vector product is notthe only one, indeed the Swiss mathematician Beno Eckmann (a frequent visitor to Alberta) discovered a vector product in 7-dimensional space in 1942. Further- more, by about 1960 deep advances in topology implied that there were no further vector products in any other dimension. We shall also, following Eckmann, talk about the generalization to r-fold vector products for $r\geq 1$ (the familiar vector product is a 2-fold vector product), and give the complete results for which dimensions n and for which $r$ these can exist. In the above work it is clear that the spheres $S^3$, $S^7$ play a special role (as well as their “little cousin” $S^1$). In the last part of the talk we will briefly discuss how these special spheres also play a major part in the recent solution of the Kervaire conjecture by Hill, Hopkins, and Ravenel, as well as their relation to the author’s own research on the span of smooth manifolds.

It’s All in the Follow Through – what research in math education says ... and doesn’t say

Speaker: 
Rob Craigen
Date: 
Sat, May 9, 2015
Location: 
PIMS, University of Lethbridge
Conference: 
Alberta Mathematics Dialog
Abstract: 
We’ll be examining a few classic cases of how educational research has been handled that explain a lot about how we got where we are in public school math education today.

Robustness of Design: A Survey

Speaker: 
Doug Wiens
Date: 
Fri, May 8, 2015
Location: 
PIMS, University of Lethbridge
Conference: 
Alberta Mathematics Dialog
Abstract: 

When an experiment is conducted for purposes which include fitting a particular model to the data, then the ’optimal’ experimental design is highly dependent upon the model assumptions - linearity of the response function, independence and homoscedasticity of the errors, etc. When these assumptions are violated the design can be far from optimal, and so a more robust approach is called for. We should seek a design which behaves reasonably well over a large class of plausible models. I will review the progress which has been made on such problems, in a variety of experimental and modelling scenarios - prediction, extrapolation, discrimination, survey sampling, dose-response, etc

Measurement, Mathematics and Information Technology

Speaker: 
M. Ram Murty
Date: 
Fri, May 8, 2015
Location: 
PIMS, University of Lethbridge
Conference: 
Alberta Mathematics Dialog
Abstract: 

In this talk, we will highlight the importance of measurement, discuss what can and cannot be measured. Focusing on the measurement of position, importance, and shape, we illustrate by discussing the mathematics behind, GPS, Google and laser surgery. The talk will be accessible to a wide audience.

A Triangle has Eight Vertices (but only one center)

Speaker: 
Richard Guy
Date: 
Fri, May 8, 2015
Location: 
PIMS, University of Lethbridge
Conference: 
Alberta Mathematics Dialog
Abstract: 
Quadration regards a triangle as an orthocentric quadrangle. Twinning is an involution between orthocentres and circumcentres. Together with variations of Conway’s Extraversion, these give rise to symmetric sets of points, lines and circles. There are eight vertices, which are also both orthocentres and circumcentres. Twelve edges share six midpoints, which, with six diagonal points, lie on the 50-point circle, better known as the 9-point circle. There are 32 circles which touch three edges and also touch the 50-point circle. 32 Gergonne points, when joined to their respective touch-centres, give sets of four segments which concur in eight deLongchamps points, which, with the eight centroids, form two harmonic ranges with the ortho- and circum-centres on each of the four Euler lines. Corresponding points on the eight circumcircles generate pairs of parallel Simson-Wallace lines, each containing six feet of perpendiculars. In three symmetrical positions these coincide, with twelve feet on one line. In the three orthogonal positions they are pairs of parallel tangents to the 50-point circle, forming the Steiner Star of David. This three-symmetry is shared with the 144 Morley triangles which are all homothetic. Time does not allow investigation of the 256 Malfatti configurations, whose 256 radpoints probably lie in fours on 64 guylines, eight through each of the eight vertices.

From Euler to Born and Infeld, Fluids and Electromagnetism

Author: 
Yann Brenier
Date: 
Wed, Jun 10, 2015
Location: 
Centre Bernoulli, EFP-Lausanne
Conference: 
Marsden Memorial Lecture
Abstract: 

As the Euler theory of hydrodynamics (1757), the Born-Infeld theory of electromagnetism (1934) enjoys a simple and beautiful geometric structure. Quite surprisingly, the BI model which is of relativistic nature, shares many features with classical hydro- and magnetohydro-dynamics. In particular, I will discuss its very close connection with Moffatt’s topological approach to Euler equations, through the concept of magnetic relaxation.

 

The Marsden Memorial Lecture Series is dedicated to the memory of Jerrold E Marsden (1942-2010), a world-renowned Canadian applied mathematician. Marsden was the Carl F Braun Professor of Control and Dynamical Systems at Caltech, and prior to that he was at the University of California (Berkeley) for many years. He did extensive research in the areas of geometric mechanics, dynamical systems and control theory. He was one of the original founders in the early 1970’s of reduction theory for mechanical systems with symmetry, which remains an active and much studied area of research today.

 

This lecture is part of the Centre Interfacultaire Bernoulli Workshop on Classic and Stochastic Geometric Mechanics, June 8-12, 2015, which in turn is a part of the CIB program on

Geometric Mechanics, Variational and Stochastic Methods, 1 January to 30 June 2015.

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