Scientific

Time and chance happeneth to them all: Mutation, selection and recombination

Speaker: 
Steven Evans
Date: 
Sat, Oct 15, 2011
Location: 
PIMS, University of Washington
Conference: 
Pacific Northwest Probability Seminar
Abstract: 

Many multi-cellular organisms exhibit remarkably similar patterns of aging and mortality. Because this phenomenon appears to arise from the complex interaction of many genes, it has been a challenge to explain it quantitatively as a response to natural selection. I survey attempts by me and my collaborators to build a framework for understanding how mutation, selection and recombination acting on many genes combine to shape the distribution of genotypes in a large population. A genotype drawn at random from the population at a given time is described in our model by a Poisson random measure on the space of loci, and hence its distribution is characterized by the associated intensity measure. The intensity measures evolve according to a continuous-time, measure-valued dynamical system. I present general results on the existence and uniqueness of this dynamical system, how it arises as a limit of discrete generation systems, and the nature of its equilibria.

Class: 
Scientific
Subject: 
Mathematics
Probability

Gauge Theory and Khovanov Homology

Speaker: 
Edward Witten
Date: 
Sat, Feb 18, 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.

Class: 
Scientific
Subject: 
Mathematics
Differential Geometry and Geometric Analysis
Topology
Physics
Mathematical Physics
Particle Physics and Quantum Field Theory

Ranks of elliptic curves

Speaker: 
Brian Conrey
Date: 
Thu, Jun 2, 2011
Location: 
PIMS, University of Calgary
Conference: 
Analytic Aspects of L-functions and Applications to Number Theory
Abstract: 

We show how to use conjectures for moments of L-functions to get insight into the frequency of rank 2 elliptic curves within a family of quadratic twists.

Class: 
Scientific
Subject: 
Mathematics
Number Theory

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
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
Class: 
Scientific
Subject: 
Mathematics
Number Theory

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
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
Class: 
Scientific
Subject: 
Mathematics
Number Theory

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
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: 
Scientific
Subject: 
Mathematics
Number Theory

PIMS/UBC Distinguished Colloquium: Dusa McDuff

Conference: 
PIMS/UBC Distinguished Colloquium Series
Date: 
Fri, Nov 4, 2011
Reference: 
Embedding questions in symplectic geometry
Class: 
Scientific
Subject: 
Mathematics

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.

Conference: 
Hugh C. Morris Lecture
Date: 
Mon, Nov 7, 2011
Reference: 
Hugh C. Morris Lecture: George Papanicolaou
Class: 
Scientific
Subject: 
Mathematics

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

Speaker: 
Ram Murty
Date: 
Thu, Jun 2, 2011
Location: 
PIMS, University of Calgary
Conference: 
Analytic Aspects of L-functions and Applications to Number Theory
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: 
Scientific
Subject: 
Mathematics
Number Theory

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

Speaker: 
Ram Murty
Date: 
Thu, Jun 2, 2011
Location: 
PIMS, University of Calgary
Conference: 
Analytic Aspects of L-functions and Applications to Number Theory
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.

Class: 
Scientific
Subject: 
Mathematics
Number Theory

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