University of Calgary

PIMS Distinguished Chair Lectures 2006

In various scientific fields from astro- and high energy physics to neuroimaging, researchers observe entire images or functions rather than single observations. The integral geometric properties, notably the Euler characteristic of the level...

A colorful diagrammatic language for the 2-category of categories has been exposited in a recent monograph by Dan Marsden and Ralf Hinze. In this tutorial, we will demonstrate how to use the language, and we will emphasize its benefits for the study...

Acyclic models, as its commonly seen today, is a proof technique used to show when two chain complexes are chain equivalent or have isomorphic homology. It originated as a theorem by Eilenberg and MacLane (1953), where it was immediately used to show...

The aim of this talk about work in progress is to describe the local/separable factorization for restriction functors and for join restriction functors.

The formalization of string diagrams, in a 1991 paper by Andre Joyal and Ross Street, was a seminal event. They defined a basic diagrammatic language and proved its validity for rigorous mathematics in any monoidal category, and in doing so they laid...

Waldhausen’s S_\bullet-construction gives a way to define the algebraic K-theory space of a category with cofibrations. Specifically, the K-theory space of a category with cofibrations C can be defined as the loop space of the realization of the...

At a previous presentation Geoff Cruttwell asked me, if the vertical bundle of a principal bundle in a join restriction category is trivial. This was not just an interesting question on its own, it also pointed towards more going on with group...

Michael Drazin introduced the idea of a “pseudoinverse” for rings and semigroups in 1961. These inverses categorically are rather special as (like ordinary inverses) they are preserved by all functors when they exist. A category is Drazin when all...