University of Calgary

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...

I will provide a (very basic) tutorial on the Curry-Howard correspondence between proofs (in natural deduction) and terms in the typed -calculus. No prior knowledge of either will be presupposed.

Slightly altering and extending McGee’s semantics for conditionals, we define a ternary notion of logical consequence for the validity of natural language arguments. The ternary logical consequence can be regarded as a unification of two kinds of...

In genetic epidemiology, log-linear models of population risk may be used to study the effect of genotypes and exposures on the relative risk of a disease. Such models may also include gene-environment interaction terms that allow the genotypes to...

The COVID-19 pandemic has illustrated both the utility and limitation of using epidemic models for understanding and forecasting disease spread. One of the many difficulties in modelling epidemic spread is that caused by behavioural change in the...

Linkage analysis maps genes for a heritable trait by identifying genomic regions with excess relatedness among individuals with similar trait values.Analysis may be conducted in families, or in unrelated individuals from a population. Here, we focus...

The Eilenberg-Zilber (EZ) theorem is a powerful tool in homological algebra and algebraic topology, being a key ingredient in the Kunneth theorem. It also serves as the basis for defining the cup product, which in turn establishes cohomology as a...