Scientific

Kirchhoff Scattering Inversion

Author: 
Chuck Ursenbach
Date: 
Tue, Aug 1, 2006
Location: 
University of Calgary, Calgary, Canada
Conference: 
Seismic Imaging Summer School
Abstract: 

• These lectures will introduce the theory of Kirchhoff migration and imaging from an inversion perspective
• They are intended to teach some geophysics to mathematicians and some mathematics to geophysicists
• Recommended reference: Bleistein, Cohen & Stockwell, 2001, “Mathematics of Multidimensional Seismic Imaging, Migration, and Inversion”

Notes: 
PDF icon Ursenbach_Chuck.pdf
Class: 
Scientific
Subject: 
Geophysics

String Theory Compactification with/without Torsion

Author: 
Piljin Yi
Date: 
Thu, Jun 1, 2006
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
Summer School on Strings, Gravity, and Cosmology
Abstract: 

Topics:

• Geometry and Holomony
• Supersymmetry, Spinors, and Calabi-Yau
• Flux and Backreaction
• Energetics of Heterotic Flux Compactification
• Strominger System and Heterotic Flux as a Torsion
• A Supersymmetric Solution to Heterotic Flux Compactification
• Global Issues: Index Counting, Smoothness, etc

Notes: 
PDF icon Yi.pdf
Class: 
Scientific
Subject: 
General Relativity and Cosmology
Particle Physics and Quantum Field Theory

Aperiodicity: Lessons from Various Generalizations

Author: 
C. Radin
Date: 
Thu, Aug 1, 2002
Location: 
University of Victoria, Victoria, Canada
Conference: 
Aperiodic Order, Dynamical Systems, Operator Algebras and Topology
Abstract: 

This is a slightly expanded version of a talk given at the Workshop on Aperiodic Order, held in Victoria, B.C. in August, 2002. The general subject of the talk was the densest packings of simple bodies, for instance spheres or polyhedra, in Euclidean or hyperbolic spaces, and describes recent joint work with Lewis Bowen. One of the main points was to report on our solution of the old problem of treating optimally dense packings of bodies in hyperbolic spaces. The other was to describe the general connection between aperiodicity and nonuniqueness in problems of optimal density.

Notes: 
PDF icon Radin_Charles.pdf
Class: 
Scientific
Subject: 
Dynamical Systems
Operator Algebras

Random Walk in Random Scenery

Author: 
Frank den Hollander
Date: 
Fri, Feb 3, 2006
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

In this talk we consider a random walk on a randomly colored lattice and ask what are the properties of the sequence of colors encountered by the walk.

Notes: 
PDF icon denhollander_3feb.pdf
Class: 
Scientific
Subject: 
Probability

Phase Transitions for Interacting Diffusions

Author: 
Frank den Hollander
Date: 
Wed, Jan 18, 2006
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

In the present talk we focus on the ergodic behavior of systems of interacting diffusions.

Notes: 
PDF icon denhollander_18jan.pdf
Class: 
Scientific
Subject: 
Dynamical Systems
Probability

Lectures on Integer Partitions

Author: 
Herbert S. Wilf
Date: 
Thu, Jun 1, 2000
Location: 
University of Victoria, Victoria, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

What I’d like to do in these lectures is to give, first, a review of the classical theory of integer partitions, and then to discuss some more recent developments. The latter will revolve around a chain of six papers, published since 1980, by Garsia-Milne, Jeff Remmel, Basil Gordon, Kathy O’Hara, and myself. In these papers what emerges is a unified and automated method for dealing with a large class of partition identities.

By a partition identity I will mean a theorem of the form “there are the same number of partitions of n such that . . . as there are such that . . ..” A great deal of human ingenuity has been expended on finding bijective and analytical proofs of such identities over the years, but, as with some other parts of mathematics, computers can now produce these bijections by themselves. What’s more, it seems that what the computers discover are the very same bijections that we humans had so proudly been discovering for all of those years.

These lectures are intended to be accessible to graduate students in mathematics and computer science.

Notes: 
PDF icon Wilf.pdf
Class: 
Scientific
Subject: 
Combinatorics

Torsion invariants of 3-manifolds

Author: 
Vladimir Turayev
Date: 
Mon, Jan 20, 2003
Location: 
University of Calgary, Calgary, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

This series of six lectures is intended for a general audience. The aim of the lectures is to survey the theory of torsions of 3-dimensional manifolds. The torsions were introduced by Kurt Reidemeister in 1935 to give a topological classification of lens spaces. Recent interest in torsions is due to their connections with the Seiberg-Witten invariants of 4-manifolds and the Floer-type homology of 3-manifolds. The lectures will cover the above topics.

Notes: 
PDF icon Turaev.pdf
Class: 
Scientific
Subject: 
Topology

Algebraic Z^d-actions

Author: 
Klaus Schmidt
Date: 
Fri, Nov 1, 2002
Location: 
University of Victoria, Victoria, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 
This is a written account of five Pacific Institute for the Mathematical Sciences Distinguished Chair Lectures given at the Mathematics Department, University of Victoria, BC, in November 2002. The lectures were devoted to the ergodic theory of $\mathbb Z^d$--actions, i.e. of several commuting automorphisms of a probability space. After some introductory remarks on more general $\mathbb Z^d$-actions the lectures focused on ‘algebraic’ $\mathbb Z^d$-actions, their sometimes surprising properties, and their deep connections with algebra and arithmetic. Special emphasis was given to some of the very recent developments in this area, such as higher order mixing behaviour and rigidity phenomena.
Notes: 
PDF icon Schmidt.pdf
Class: 
Scientific
Subject: 
Group Theory
Probability

Entropy and Orbit Equivalence

Author: 
Daniel J. Rudolph
Date: 
Fri, Oct 1, 2004
Location: 
University of Victoria, Victoria, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

In these notes we first offer an overview of two core areas in the dynamics of probability measure preserving systems, the Kolmogorov-Sinai theory of entropy and the theory of orbit equivalence. Entropy is a nontrivial invariant that, said simply, measures the exponential growth rate of the number of orbits in a dynamical system, a very rough measure of the complexity of the orbit structure. On the other hand, the core theorem of the orbit theory of these systems, due to Henry Dye, says that any two free and ergodic systems are orbit equivalent, that is to say can be regarded as sitting on the same set of orbits. The goal we set out to reach now is to explain and understand the seeming conflict between these two notions.

Notes: 
PDF icon Rudolph.pdf
Class: 
Scientific
Subject: 
Dynamical Systems
Probability

On Hilbert's Tenth Problem

Author: 
Yuri Matiyasevich
Date: 
Tue, Feb 1, 2000
Location: 
University of Calgary, Calgary, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

Dr. Matiyasevich is a distinguished logician and mathematician based at the Steklov Institute of Mathematics at St. Petersburg. He is known for his outstanding work in logic, number theory and the theory of algorithms.

At the International Congress of Mathematicians in Paris in 1900 David Hilbert presented a famous list of 23 unsolved problems. It was 70 years later before a solution was found for Hilbert's tenth problem. Matiyasevich, at the young age of 22, acheived international fame for his solution.

Notes: 
PDF icon Matiyasevich.pdf
Class: 
Scientific
Subject: 
Number Theory
Algebra

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