Mathematics

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

Summer at the HUB Britiania Summer Camp

Speaker: 
Melania Alvarez
Date: 
Sat, Jul 2, 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.

Class: 
Educational
Subject: 
Mathematics

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

Optimal Investment for an Insurance Company

Speaker: 
Alexandru Badescu
Location: 
Calgary Place Tower (Shell)
University of Calgary, Calgary, Canada
Conference: 
Shell Lunchbox Lectures
Abstract: 

Optimal investment is a key problem in asset-liability management of an insurance company. Rather than allocating wealth optimally so as to maximize the overall investment return, an insurance company is interested in assessing the risk exposure where both assets and liabilities are included and minimizing the risk of mismatches between them. Different approaches for solving optimization problems by minimizing standard risk measures such as the value at risk (VaR) or the conditional value at risk (CVaR) have been proposed in the literature. In this paper we focus on some Solvency II applications by investigating several novel problems for jointly quantifying the optimal initial capital requirement and the optimal portfolio investment under various constraints.

Discussions on the convexity of these problems are also provided. Using a Monte Carlo simulation and a semi-parametric approach based on different assumptions for the loss distribution, we compute the insurer optimal capital needed to be efficiently invested in a portfolio formed by two or more assets. Finally, a detailed numerical experiment is conducted to assess the robustness and sensitivity of our optimal solutions relative to the model factors.

This paper was written in collaboration with Alexandru V. Asimit (Cass Business School, City University, UK), Tak Kuen Siu (Faculty of Business and Economics, Macquarie University, Australia)and Yuriy Zinchenko (Department of Mathematics and Statistics, University of Calgary).

Class: 
Applied
Subject: 
Mathematics
Econometrics
Applied Mathematics

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

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