Scientific

Mathematics and the Planet Earth: a Long Life Together II

Speaker: 
Ivar Ekeland
Date: 
Wed, Jul 17, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Mathematics of Planet Earth 2013
Abstract: 

When Colombus left Spain in 1492, sailing West, he knew that the Earth was round and was expecting to land in Japan. Seventeen centuries earlier, around 200 BC, Eratosthenes had shown that its circumference was 40,000 km, just by a smart use of mathematics, without leaving his home town of Alexandria. Since then, we have learned much more about Earth: it is a planet, it has an inner structure, it carries life , and at every step mathematics have been a crucial tool of discovery and understanding. Nowadays, concerns about the human footprint and climate change force us to bring all this knowledge to bear on the global problems facing us. This is the last challenge for mathematics: can we control change?
This is a two-part lecture, investigating how our idea of the world has influenced the development of mathematics. In the first lecture on July 15, I will describe the situation up to the twentieth century, in the second one on July 17 I will follow up to the present time and the global challenges humanity and the planet are facing today.
 

Class: 
Scientific
Subject: 
Mathematics
Atmospheric and Oceanic Physics: Climate Modelling
Econometrics
Environmental Science
Applied Mathematics

Mathematics and the Planet Earth: a Long Life Together I

Speaker: 
Ivar Ekeland
Date: 
Mon, Jul 15, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Mathematics of Planet Earth 2013
Abstract: 

When Colombus left Spain in 1492, sailing West, he knew that the Earth was round and was expecting to land in Japan. Seventeen centuries earlier, around 200 BC, Eratosthenes had shown that its circumference was 40,000 km, just by a smart use of mathematics, without leaving his home town of Alexandria. Since then, we have learned much more about Earth: it is a planet, it has an inner structure, it carries life , and at every step mathematics have been a crucial tool of discovery and understanding. Nowadays, concerns about the human footprint and climate change force us to bring all this knowledge to bear on the global problems facing us. This is the last challenge for mathematics: can we control change?

This is a two-part lecture, investigating how our idea of the world has influenced the development of mathematics. In the first lecture (July 15), I will describe the situation up to the twentieth century, in the second one (July 17) I will follow up to the present time and the global challenges humanity and the planet are facing today.

Class: 
Scientific
Subject: 
Mathematics
Atmospheric and Oceanic Physics: Climate Modelling
Econometrics
Environmental Science
Applied Mathematics

Taking Advantage of Degeneracy in Cone Optimization: with Applications to Sensor Network Localization

Author: 
Henry Wolkowicz
Date: 
Thu, Aug 8, 2013 to Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Reference: 
Workshop on Numerical Linear Algebra and Optimization- Photo Gallery
Abstract: 

Taking Advantage of Degeneracy in Cone Optimization: with Applications to Sensor Network Localization

Notes: 
PDF icon NLO Henry Wolkowicz.pdf
Class: 
Scientific
Subject: 
Numerical Analysis

Search Games and Optimal Kakeya Sets

Author: 
Yuval Peres
Date: 
Fri, Sep 6, 2013
Location: 
PIMS, University of British Columbia
Abstract: 

Search Games and Optimal Kakeya Sets: Yuval Peres
Based on joint work with Y. Babichenko, R. Peretz, P. Sousi and P. Winkler

Notes: 
PDF icon PIMS-UBC- YPeres.pdf
Class: 
Scientific
Subject: 
Probability

Solving linear systems by orthogonal tridiagonalization (GMINRES and/or GLSQR)

Author: 
Michael Saunders
Date: 
Thu, Aug 8, 2013 to Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Reference: 
Workshop on Numerical Linear Algebra and Optimization- Photo Gallery
Abstract: 

A general matrix A can be reduced to tridiagonal form by orthogonal
transformations on the left and right: UTAV = T. We can arrange that the
rst columns of U and V are proportional to given vectors b and c. An iterative
form of this process was given by Saunders, Simon, and Yip (SINUM 1988) and
used to solve square systems Ax = b and ATy = c simultaneously. (One of the
resulting solvers becomes MINRES when A is symmetric and b = c.)

The approach was rediscovered by Reichel and Ye (NLAA 2008) with emphasis
on rectangular A and least-squares problems Ax ~ b. The resulting solver was
regarded as a generalization of LSQR (although it doesn't become LSQR in
any special case). Careful choice of c was shown to improve convergence.

In his last year of life, Gene Golub became interested in \GLSQR" for
estimating cTx = bTy without computing x or y. Golub, Stoll, and Wathen
(ETNA 2008) revealed that the orthogonal tridiagonalization is equivalent to a
certain block Lanczos process. This reminds us of Golub, Luk, and Overton
(TOMS 1981): a block Lanczos approach to computing singular vectors.

Notes: 
PDF icon NLO Saunders.pdf
Class: 
Scientific
Subject: 
Numerical Analysis

Complex Fluids and Flows in Industry and Nature II- Photo Gallery

Date: 
Wed, Jul 24, 2013 to Fri, Jul 26, 2013
Class: 
Scientific
Subject: 
Mathematics

On solving indefinite least squares problems via anti-triangular factorizations

Author: 
Paul Van Dooren
Date: 
Thu, Aug 8, 2013 to Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Reference: 
Workshop on Numerical Linear Algebra and Optimization- Photo Gallery
Abstract: 

On solving indefinite least squares problems via anti-triangular factorizations:
Nicola Mastronardi, IAC-CNR, Bari, Italy and Paul Van Dooren, UCL, Louvain-la-Neuve, Belgium

Notes: 
PDF icon NLO Paul Van Dooren.pdf
Class: 
Scientific
Subject: 
Numerical Analysis

Eigenvalue avoided crossings

Author: 
Nick Trefethen
Date: 
Thu, Aug 8, 2013 to Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Reference: 
Workshop on Numerical Linear Algebra and Optimization- Photo Gallery
Abstract: 

Eigenvalue avoided crossings

Notes: 
PDF icon NLO Nick Trefethen.pdf
Class: 
Scientific
Subject: 
Numerical Analysis

Communication-­ Avoiding Algorithms for Linear Algebra and Beyond

Author: 
James Demmel
Date: 
Thu, Aug 8, 2013 to Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Reference: 
Workshop on Numerical Linear Algebra and Optimization- Photo Gallery
Abstract: 

Communication-­ Avoiding Algorithms for Linear Algebra and Beyond

Notes: 
PDF icon NLO James Demmel.pdf
Class: 
Scientific
Subject: 
Numerical Analysis

The Higher Order Generalized Singular Value Decomposition

Author: 
Charles Van Loan
Date: 
Thu, Aug 8, 2013 to Sat, Aug 10, 2013
Location: 
PIMS, University of British Columbia
Conference: 
Workshop on Numerical Linear Algebra and Optimization
Reference: 
Workshop on Numerical Linear Algebra and Optimization- Photo Gallery
Abstract: 

Suppose you have a collection of data matrices each of which has the same number of columns. The HO-GSVD can be used to identify common features that are implicit across the collection. It works by identifying a certain (approximate) invariant subspace of a matrix that is a challenging combination of the collection matrices. In describing the computational process I will talk about the Higher Order
CS decomposition and a really weird optimization problem that I bet you have never seen before! Joint work with Orly Alter, Priya Ponnapalli, and Mike Saunders.

Notes: 
PDF icon NLO Charles Van Loan.pdf
Class: 
Scientific
Subject: 
Numerical Analysis

Pages