The Department of Mathematics and Statistics provides excellent undergraduate programs, as well as advanced instruction at the graduate and research levels. Find out more about our degree programs.
September 27, 2016 2:30 PM
Presented by : Bob Paré (Dalhousie)
Topic : The secret double life of graphs
Abstract : By graphs I mean, as do most category theorists, what graph theorists might call directed multigraphs. A category is such a graph with an appropriate multiplication on its edges. In fact, a precise way to say this is that the forgetful functor from the category of (small) categories to graphs, which has a left adjoint, is monadic. This is of course well-known. What is perhaps less well-known isthat the left adjoint, the paths functor, is comonadic. So one could say that graphs are categories with costructure. Here we have a nice comonad on Cat which is not a 2-comonad, and this is a bit troubling. However, Cat is not a mere 2-category but a double category, and the paths comonad lifts to a lax comonad on that. Considering the coalgebras on this gives a notion of "proarrow of graphs" thus giving a double category of graphs over which the double category of categories is monadic. We will study some of the properties of this double catecory.
Mathematics Colloquium Announcement
September 29, 2016 2:30 PM
Presented by : Karl Dilcher and Richard Nowakowski
Topic : Title: Richard K. Guy turns 100
Richard Guy has influenced many mathematicians over his long career, which isn't over yet. We will talk about the importance of "Unsolved Problems in Number Theory", "Reviews in Number Theory", "Book of Numbers", "Strong Law of Small Numbers" and "Winning Ways" as well as others.