# Mathematics

## Disconnecting the G_2 Moduli Space

Little is currently known about the global properties of the moduli space of a closed 7-manifold, ie the space of Riemannian metrics with holonomy modulo diffeomorphisms. A holonomy metric has an associated -structure, and I will define a Z/48 valued homotopy invariant of a -structure in terms of the signature and Euler characteristic of a Spin(7)-coboundary. I will describe examples of manifolds with holonomy metrics where the invariant is amenable to computation in terms of eta invariants, and which are candidates for having a disconnected moduli space. This is joint work in progress with Diarmuid Crowley and Sebastian Goette.

## Universal torsion, L^2-invariants, polytopes and the Thurston norm

We introduce universal torsion which is defined for -acyclic manifolds with torsion free fundamental group and takes values in certain -groups of a skew field associated to the integral group ring. It encompasses well-know invariants such as the Alexander polynomial and -torsion. We discuss also twisted -torsion and higher order Alexander polynomials which can also be derived from the universal invariant and assign certain polytopes to the universal torsion. This gives especially in dimension 3 interesting invariants which recover for instance the Thurston norm.

## Introduction to the Farrell-Jones Conjecture

## Decision problems, curvature and topology

## PIMS Symposium on the Geometry and Topology of Manifolds

## Nassif Ghoussoub Receives Honorary Degree from the University of Victoria

## PIMS-SFU Undergraduate Summer School on Rigorous Computing

## A topological look at the vector (cross) product in three dimensions

## It’s All in the Follow Through – what research in math education says ... and doesn’t say

## Robustness of Design: A Survey

When an experiment is conducted for purposes which include fitting a particular model to the data, then the ’optimal’ experimental design is highly dependent upon the model assumptions - linearity of the response function, independence and homoscedasticity of the errors, etc. When these assumptions are violated the design can be far from optimal, and so a more robust approach is called for. We should seek a design which behaves reasonably well over a large class of plausible models. I will review the progress which has been made on such problems, in a variety of experimental and modelling scenarios - prediction, extrapolation, discrimination, survey sampling, dose-response, etc