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Mathematics

Special values of Artin L-series (3 of 3)

Speaker: 
Ram Murty
Date: 
Wed, Jun 1, 2011
Location: 
PIMS, University of Calgary
Conference: 
Analytic Aspects of L-functions and Applications to Number Theory
CRG: 
L-functions and Number Theory (2010-2013)
Abstract: 

Dirichlet’s class number formula has a nice conjectural generalization in the form of Stark’s conjectures. These conjectures pertain to the value of Artin L-series at s = 1. However, the special values at other integer points also are interesting and in this context, there is a famous conjecture of Zagier. We will give a brief outline of this and display some recent results.

This lecture is part of a series of 3.

Artin’s holomorphy conjecture and recent progress (2 of 3)

Speaker: 
Ram Murty
Date: 
Tue, May 31, 2011
Location: 
PIMS, University of Calgary
Conference: 
Analytic Aspects of L-functions and Applications to Number Theory
CRG: 
L-functions and Number Theory (2010-2013)
Abstract: 

Artin conjectured that each of his non-abelian L-series extends to an entire function if the associated Galois representation is nontrivial and irreducible. We will discuss the status of this conjecture and discuss briefly its relation to the Langlands program.

This lecture is part of a series of 3.

Introduction to Artin L-series (1 of 3)

Speaker: 
Ram Murty
Date: 
Mon, May 30, 2011
Location: 
PIMS, University of Calgary
Conference: 
Analytic Aspects of L-functions and Applications to Number Theory
CRG: 
L-functions and Number Theory (2010-2013)
Abstract: 

After defining Artin L-series, we will discuss the Chebotarev density theorem and its applications.

This lecture is part of a series of 3.

Small Number and the Old Canoe (Squamish)

Speaker: 
Veselin Jungic
Speaker: 
Mark Maclean
Speaker: 
Rena Sinclair
Date: 
Sun, Nov 22, 2009
Location: 
Simon Fraser University, Burnaby, Canada
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
BIRS First Nations Math Education Workshop
Abstract: 
N.B. This video is a translation into Squamish by T'naxwtn, Peter Jacobs of the Squamish Nation In Small Num­ber and the Old Canoe math­e­mat­ics is present through­out the story with the hope that this expe­ri­ence will make at least some mem­bers of our young audi­ence, with the moderator’s help, rec­og­nize more math­e­mat­ics around them in their every­day lives. We use terms like smooth, shape, oval, and sur­face, the math­e­mat­i­cal phrase­ol­ogy like, It must be at least a hun­dred years old, the artist skill­fully presents reflec­tion (sym­me­try) of trees in water, and so on. The idea behind this approach is to give the mod­er­a­tor a few open­ings to intro­duce or empha­size var­i­ous math­e­mat­i­cal objects, con­cepts, and ter­mi­nol­ogy. The short film is a lit­tle math sus­pense story and our ques­tion is related only to one part of it. The aim of the ques­tion is to lead to an intro­duc­tion at an intu­itive level of the con­cept of a func­tion and the essence of the prin­ci­ple of inclusion-exclusion as a count­ing tech­nique. The authors would also like to give their audi­ence an oppor­tu­nity to appre­ci­ate that in order to under­stand a math ques­tion, one often needs to read (or in this case, watch) a prob­lem more than once. For additional details see http://mathcatcher.irmacs.sfu.ca/story/small-number-and-old-canoe

Small Number and the Old Canoe

Speaker: 
Veselin Jungic
Speaker: 
Mark Maclean
Speaker: 
Rena Sinclair
Date: 
Sun, Nov 22, 2009
Location: 
Simon Fraser University, Burnaby, Canada
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
BIRS First Nations Math Education Workshop
Abstract: 
In Small Num­ber and the Old Canoe math­e­mat­ics is present through­out the story with the hope that this expe­ri­ence will make at least some mem­bers of our young audi­ence, with the moderator’s help, rec­og­nize more math­e­mat­ics around them in their every­day lives. We use terms like smooth, shape, oval, and sur­face, the math­e­mat­i­cal phrase­ol­ogy like, It must be at least a hun­dred years old, the artist skill­fully presents reflec­tion (sym­me­try) of trees in water, and so on. The idea behind this approach is to give the mod­er­a­tor a few open­ings to intro­duce or empha­size var­i­ous math­e­mat­i­cal objects, con­cepts, and ter­mi­nol­ogy. The short film is a lit­tle math sus­pense story and our ques­tion is related only to one part of it. The aim of the ques­tion is to lead to an intro­duc­tion at an intu­itive level of the con­cept of a func­tion and the essence of the prin­ci­ple of inclusion-exclusion as a count­ing tech­nique. The authors would also like to give their audi­ence an oppor­tu­nity to appre­ci­ate that in order to under­stand a math ques­tion, one often needs to read (or in this case, watch) a prob­lem more than once. For additional details see http://mathcatcher.irmacs.sfu.ca/story/small-number-and-old-canoe

Small Number Counts to 100 (Cree)

Speaker: 
Veselin Jungic
Speaker: 
Mark Maclean
Speaker: 
Rena Sinclair
Date: 
Sun, Nov 22, 2009
Location: 
Simon Fraser University, Burnaby, Canada
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
BIRS First Nations Math Education Workshop
Abstract: 
This short animation movie is a math education resource based on Aboriginal culture. For more information, visit: http://www.math.sfu.ca/~vjungic/SmallNumber.html This version of the video was recorded by Dr. Eldon Yellowhorn of the Pikani First Nation in Blackfoot. Special Thanks To: Banff International Research Station for Mathematical Innovation and Discovery Department of Mathematics, Simon Fraser University Pacific Institute For Mathematical Sciences Sean O'Reilly, Arcana Studios The IRMACS Centre, Simon Fraser University

Hugh C. Morris Lecture: George Papanicolaou

Speaker: 
George Papanicolaou
Date: 
Mon, Nov 7, 2011
Location: 
PIMS, University of British Columbia
Conference: 
Hugh C. Morris Lecture
Abstract: 
N.B. The audio introduction of this lecture has not been properly captured. The quantification of uncertainty in large-scale scientific and engineering computations is rapidly emerging as a research area that poses some very challenging fundamental problems which go well beyond sensitivity analysis and associated small fluctuation theories. We want to understand complex systems that operate in regimes where small changes in parameters can lead to very different solutions. How are these regimes characterized? Can the small probabilities of large (possibly catastrophic) changes be calculated? These questions lead us into systemic risk analysis, that is, the calculation of probabilities that a large number of components in a complex, interconnected system will fail simultaneously. I will give a brief overview of these problems and then discuss in some detail two model problems. One is a mean field model of interacting diffusion and the other a large deviation problem for conservation laws. The first is motivated by financial systems and the second by problems in combustion, but they are considerably simplified so as to carry out a mathematical analysis. The results do, however, give us insight into how to design numerical methods where detailed analysis is impossible.

Embedding questions in symplectic geometry

Speaker: 
Dusa McDuff
Date: 
Fri, Nov 4, 2011
Location: 
PIMS, University of British Columbia
Conference: 
PIMS/UBC Distinguished Colloquium
Abstract: 
As has been known since the time of Gromov's Nonsqueezing Theorem, symplectic embedding questions lie at the heart of symplectic geometry. In the past few years we have gained significant new insight into the question of when there is a symplectic embedding of one basic geometric shape (such as a ball or ellipsoid)into another (such as an ellipsoid or torus). After a brief introduction to symplectic geometry, this talk will describe some of this progress, with particular emphasis on results in dimension four.

On Hilbert's 10th Problem - Part 4 of 4

Speaker: 
Yuri Matiyasevich
Date: 
Wed, Mar 1, 2000
Location: 
PIMS, University of Calgary
Conference: 
Mini Courses by Distinguished Chairs
Abstract: 

A Diophantine equation is an equation of the form $ D(x_1,...,x_m) $ = 0, where D is a polynomial with integer coefficients. These equations were named after the Greek mathematician Diophantus who lived in the 3rd century A.D.

Hilbert's Tenth problem can be stated as follows:
Determination of the Solvability of a Diophantine Equation. Given a diophantine equation with any number of unknown quantities and with rational integral numerical coefficients, devise a process according to which it can be determined by a finite number of operations whether the equation is solvable in rational integers.

This lecture is part 4 of a series of 4.

N.B. This video was transferred from an old encoding of the original media. The audio and video quality may be lower than normal.

On Hilbert's 10th Problem - Part 3 of 4

Speaker: 
Yuri Matiyasevich
Date: 
Wed, Mar 1, 2000
Location: 
PIMS, University of Calgary
Conference: 
Mini Courses by Distinguished Chairs
Abstract: 

A Diophantine equation is an equation of the form $ D(x_1,...,x_m) $ = 0, where D is a polynomial with integer coefficients. These equations were named after the Greek mathematician Diophantus who lived in the 3rd century A.D.

Hilbert's Tenth problem can be stated as follows:
Determination of the Solvability of a Diophantine Equation. Given a diophantine equation with any number of unknown quantities and with rational integral numerical coefficients, devise a process according to which it can be determined by a finite number of operations whether the equation is solvable in rational integers.

This lecture is part 3 of a series of 4.

N.B. This video was transferred from an old encoding of the original media. The audio and video quality may be lower than normal.

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