Pacific Institute for the Mathematical Sciences - PIMS

The 34-th Annual Canadian Operator Symposium (COSy) will take place
at the University of Calgary campus from May 29th to June 2, 2006.

The meeting will be an occasion to celebrate the 65-th birthday of
Peter
Rosenthal, University of Toronto.

This will be the fifth of a sequence of conferences on Scientific Computing and
Applications held in the Pacific Rim region. All of them have the goal of bringing
together mathematicians, scientists and engineers working in the field
of scientific computing and its applications to solve scientific and industrially
oriented problems and to provide a forum for the participants to meet and
exchange ideas of common interest in an informal atmosphere.

The focus of this particular conference will be on the problems and methods
related to image processing, financial applications and modelling of
multiphase flows.
The goal of the conference is twofold.
The theoretical areas of interest include
fundamental methods and algorithms for solving PDE's and linear systems
of equations. On the other hand, it will try to attract the attention of
the applied community, in particular the oil sands industry, banking
and medical imaging, to present and discuss the applications of scientific
computing to practical problems. The theoretical topics of interest are
(but not limited to): Finite Element, Finite Volume Element and Finite
Volume Methods for partial differential equations, splitting techniques
and stabilized methods, iterative solvers and preconditioning techniques
for large scale systems, methods for systems with a special structure,
parallel algorithms and performance analysis.

MindRap uses an innovative learning process that involves technology, music, art, performing, writing, collaboration, culture, self-esteem, and mentoring. High school students learn how to create animated multimedia modules that include their own artwork, music, and stories to teach a basic math or science skill. Cultural information and achievements are used to motivate and inspire both the students who are creating the modules as well as those who are the intended audience. Throughout the process the students are guided by professional writers, artists, musicians, and educators. The student's creations are then published on a website portal that can be accessed by teachers and students all the over the world. The target of the after school program is at-risk inner city students. We will discuss this project and the various branches of work that have sprouted from its core.

On behalf of the University of Alberta, the Department of Mathematical and Statistical Sciences invited the mathematical graduate student community to the 2006 Young Researchers Conference for Mathematical and Statistical Sciences.

Alejandro Adem (University of British Columbia)

A Stringy Product for Twisted Orbifold K-theory

Given an orbifold X with inertia orbifold LX, we construct a product for the twisted K-theory of LX which extends the orbifold cohomology product of Chen & Ruan. The twisting arises from the "inverse transgression" of elements in $H^4(BX, Z)$. This is joint work with Y.Ruan and B.Zhang.

Simon Brendle (Stanford University)

Global convergence of the Yamabe flow

Let $M$ be a compact manifold of dimension $n \geq 3$. Along the Yamabe flow, a Riemannian metric on $M$ is deformed such that $\frac{\partial g}{\partial t} = -(R_g - r_g) \, g$, where $R_g$ is the scalar curvature associated with the metric $g$ and $r_g$ denotes the mean value of $R_g$. It is known that the Yamabe flow exists for all time. Moreover, if $3 \leq n \leq 5$ or $M$ is locally conformally flat, then the solution approaches a metric of constant scalar curvature as $t \to \infty$. I will describe how this result can be generalized to higher dimensions. The key ingredient in the proof is a new construction of test functions whose Yamabe energy is less than that of the round sphere.

Jim Bryan (University of British Columbia)

Donaldson-Thomas and Gromov-Witten invariants of orbifolds and their crepant resolutions

A well known principle in physics asserts that string theory on an orbifold X is equivalent to string theory on Y, any crepant resolution of X. Donaldson-Thomas and Gromov-Witten theory are mathematical counterparts of type IIA and type IIB topological string theory and so it is expected that one can recover the Gromov-Witten or Donaldson-Thomas invariants of Y from those on X. We will mathematically formulate and discuss these correspondences and illustrate them with some examples.

Ben Chow (UC San Diego)

On the works of D. Glickenstein and F. Luo on semi-discrete curvature flows

Yong-Geun Oh (University of Wisconsin-Madison)

Lagrangian currents, Calabi invariants and non-simpleness of the area-preserving homeomorphism group of S^2

In this talk, I will introduce the notion of `hamiltonian limits' of the Hamiltonian flows, and define the continuous Hamiltonian flows and their associated Hamiltonian functions, which I call `topological Hamiltonians'. I will give the proof of the uniqueness of the topolocgical Hamiltonian associated to continuous Hamiltonian flows. The uniquessness proof uses the method of geometric measure theory and some $C^0$ symplectic geometry. I will discuss some implication of this study in a well-known conjecture in the dynamical systems on the simpleness of the area preserving homeomorphism group $S^2$.

Gang Tian (Princeton University)

Kahler-Ricci flow and complex Monge-Ampere equation