Transformation Groups Seminar

Speaker: Sayantan Roy Chowdhury (Western)

"Toric regularity (cancelled)"

Time: 10:30

Room: MC 204

Algebraic Geometry

Speaker: Greg Reid (Western)

"WAG: Linear PDE's with constant coefficients"

Time: 15:30

Room: MC 107

Colloquium

Speaker: George Shillcock (University of Oxford)

"Evolution Theory Talk - Division of labour"

Time: 15:40

Room: MC 204

A collective evolves division of labour when its members all benefit by specialising to perform complementary tasks. It is observed across various scales of biological organisation at the origins of multicellularity and eusociality. It is, therefore, of interest to understand the conditions which favour the evolution of division of labour by natural selection. By focusing our attention to collectives that reproduce clonally, such as many plants and bacteria, we may safely model collectives as fitness maximisers faced with a constrained optimisation.

Geometry and Topology

Speaker: Steven Amelotte (Western)

"Homotopy types of moment-angle complexes and minimal free resolutions of Stanley-Reisner rings"

Time: 15:30

Room: MC 107

Toric topology assigns to each finite simplicial complex K a space with a torus action, called the moment-angle complex, whose equivariant topology neatly reflects combinatorial properties of K and homological properties of the Stanley-Reisner ring of K. A central result in the subject identifies the cohomology of the moment-angle complex with the Koszul homology of the corresponding Stanley-Reisner ring. In this talk, I'll describe how cohomology operations induced by the torus action can be used to extend this result to a topological interpretation of the entire minimal free resolution of the Stanley-Reisner ring, and then outline some work in progress which aims to identify the homotopy types of certain moment-angle complexes in terms of this data. (This is all based on joint work with Ben Briggs.)

Pizza Seminar

Speaker: Lindi Wahl (Western)

"Generating predictions: the power and elegance of generating functions. "

Time: 17:00

Room: MC 107

Like other transform methods, generating functions sometimes offer a lens through which an otherwise complicated problem has a surprisingly elegant solution. I'll offer a quick introduction to probability generating functions and show how we can take advantage of some really beautiful theorems to make practical predictions -- like the probability that COVID-19 has driven the Yamagata flu strain to extinction.

Ph.D. Presentation

Speaker: Third-year Ph.D. students (Western)

"TBA"

Time: 15:30

Room: MC 107

Graduate Seminar

Speaker: Thomas Thorbjornsen (Western)

"The Synthetic Fundamental Group of the Circle"

Time: 16:30

Room: MC 107

Homotopy type theory is a foundation for mathematics that is well-suited to do homotopy theory. Unlike ZFC, we no longer have access to the law of excluded middle or the axiom of choice. Many mathematicians find it daunting and off-putting to work without these axioms, but great opportunity is created amidst the challenge.

In this talk we will investigate how we can do homotopy theory in homotopy type theory. We will construct the fundamental group of the circle by using the tools provided by Martin-Löf type theory, Voevodsky’s univalence axiom, and higher inductive types. In particular, we will look at the underlying language of type theory and its identity types, how fiber bundles are expressed as type families, and the essential role played by the univalence axiom.