University of Regina

A basic aim of homological algebra is to establish invariants for various algebraic objects. This is achieved by constructing resolutions for these objects. These resolutions can be intractable, however for quadratic algebras one obtains a simpler...

The advent of topological materials, a form of physical matter with unusual but useful properties, has brought with it unexpected new connections between pure mathematics on the one side and physics, chemistry, and material science on the other side...

A classic theorem of Quillen established an equivalence of homotopy theory between (certain) DG Lie algebras and DG coalgebras. Both are models for (simply-connected) rational homotopy theory. A generalization of Quillen's result by Hinich provided a...

In the previous talk, we saw a few examples of deformation functors. In this third part, we will discuss some properties of deformation functors and more examples. We will revisit examples coming from DG Lie algebras.

In the previous talk, we got comfortable with the category of Artin local rings. In this second part, we will move on to functors of Artin rings, deformation functors, and some examples. Time permitting, we will discuss Schlessinger's theorem, giving...

In recent years, machine learning procedures have attracted much attention in National Statistical Offices (e.g., Statistics Canada). In particular, random forests are currently being scrutinized as an alternative to traditional imputation procedures...

In Manak's talk, we learned what a deformation functor is. We will explore this notion more in depth and look at some examples. Deformation functors allow us to make the idea of a "formal moduli problem" more precise. Time permitting, we will discuss...

Before the winter break we saw a number of key structures of deformation theory: differential graded Lie algebras, the Maurer-Cartan equation and its gauge group, and L-infinity algebras. In this talk, we will see how such structures arise in the...

What are L-infinity algebras? What is their relevance to deformation theory? How are they an improvement over differential graded Lie algebras? These are the questions I will attempt to answer as we go over the basics of L-infinity algebras.

Let B be a normed space and let A be a subspace. When does a continuous linear functional on A admit a unique norm-preserving extension to B? If A and B are C*-algebras and the functional is a so-called pure state, this question was at the heart of a...