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Mathematics

Gauge Theory and Khovanov Homology

Speaker: 
Edward Witten
Date: 
Fri, Feb 17, 2012
Location: 
PIMS, University of Washington
Abstract: 
After reviewing ordinary finite-dimensional Morse theory, I will explain how Morse generalized Morse theory to loop spaces, and how Floer generalized it to gauge theory on a three-manifold. Then I will describe an analog of Floer cohomology with the gauge group taken to be a complex Lie group (rather than a compact group as assumed by Floer), and how this is expected to be related to the Jones polynomial of knots and Khovanov homology.

Summer at the HUB Britiania Summer Camp

Speaker: 
Melania Alvarez
Date: 
Fri, Jul 1, 2011
Location: 
Britiannia Centre
Conference: 
Summer at the HUB
Abstract: 
PIMS was proud to support the 'Summer at the HUB' camp which took place in July-August 2011. Focus camps included Lego Simple Machines and Math, iPad Camp and Robo Meccano. Many thanks to Britannia Centre for providing this video.

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

Speaker: 
K. Soundararajan
Date: 
Fri, Jun 3, 2011
Location: 
University of Calgary, Calgary, Canada
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

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

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

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.
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