# Mathematics

## Moments of zeta and L-functions on the critical Line I (2 of 3)

I will discuss techniques to get upper and lower bounds for moments of zeta and L-functions. The lower bounds are unconditional and the upper bounds in general rely on the Riemann Hypothesis. In several cases of low moments, one can obtain asymptotics, and I may discuss a couple of such recent cases.

This lecture is part of a series of 3

## Distribution of Values of zeta and L-functions (1 of 3)

I will discuss the distribution of values of zeta and L-functions when restricted to the right of the critical line. Here the values are well understood by probabilistic models involving “random Euler products”. This fails on the critical line, and the L-values here have a different flavor here with Selberg’s theorem on log normality being a representative result.

This lecture is part of a series of 3

## PIMS/UBC Distinguished Colloquium: Dusa McDuff

## Inaugural Hugh C Morris Lecture - George Papanicolaou

PIMS was pleased to present the inaugural lecture in the new Hugh C Morris series with speaker George Papanicolaou from Stanford University.

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

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)

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)

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)

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

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)

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