Mathematics

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

Speaker: 
K. Soundararajan
Date: 
Thu, Jun 2, 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: 

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

  1. Lecture 1: distribution-values-zeta-and-l-functions-1-3
  2. Lecture 2: Moments of zeta and L-functions on the Critical Line, I
  3. Lecture 3: Moments of zeta and L-functions on the critical line, II
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Distribution of Values of zeta and L-functions (1 of 3)

Speaker: 
K. Soundararajan
Date: 
Thu, Jun 2, 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: 

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

  1. Lecture 1: distribution-values-zeta-and-l-functions-1-3
  2. Lecture 2: Moments of zeta and L-functions on the Critical Line, I
  3. Lecture 3: Moments of zeta and L-functions on the critical line, II
Class: 

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.

Class: 

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.

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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.

Class: 

Small Number and the Old Canoe (Squamish)

Speaker: 
Veselin Jungic
Mark Maclean
Rena Sinclair
Date: 
Sun, Nov 22, 2009
Location: 
Simon Fraser University, Burnaby, Canada
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

Class: 
Subject: 

Small Number and the Old Canoe

Speaker: 
Veselin Jungic
Mark Maclean
Rena Sinclair
Date: 
Sun, Nov 22, 2009
Location: 
Simon Fraser University, Burnaby, Canada
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

Class: 
Subject: 

Small Number Counts to 100 (Cree)

Speaker: 
Veselin Jungic
Mark Maclean
Rena Sinclair
Date: 
Sun, Nov 22, 2009
Location: 
Simon Fraser University, Burnaby, Canada
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

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Subject: 

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