University of Regina

The classification of 2-dimensional TQFTs was obtained by cutting up surfaces into disks, cylinders, and pairs of pants. In higher dimension, such a decomposition of n-manifolds is not available. We need to cut up manifolds not only along codimension...

Topological K-theory is an assignment of algebraic data to a topological space. It is a homotopy invariant and satisfies the Eilenberg-Steenrod axioms for a generalized cohomology theory. In this talk I give a rapid introduction to vector bundles...

When the same topic appears in both mathematics and physics, there are often stark differences between how that topic is conceptualized and studied in each discipline. In this talk we will examine what it means to a physicist for a field theory to be...

In Arnaud's talk, we saw that the 2-dimensional TQFT category is equivalent to the category of commutative Frobenius algebras with isomorphisms. In this sequel to Arnaud's talk, we take a closer look at Frobenius algebras. We will explore their...

It is well-known in quantum information theory that a positive operator valued measure (POVM) is the most general kind of quantum measurement. A quantum probability is a normalised POVM, namely a function on certain subsets of a (locally compact and...

In Allen's talk, we learned that the deformations of an algebra A can be classified by certain Hochschild cohomology classes. In this talk, we will see that the Hochschild cochains of A can be endowed with a differential graded (DG) Lie algebra...

If A is an algebra over a field k, and R is an augmented commutative k-algebra, then an R-deformation of A is (intuitively) an R-algebra B whose underlying k-algebra structure is isomorphic to that of A. Two R-deformations of A are considered...

The fundamental principle of derived deformation theory is that a formal “space” (i.e. a formal moduli problem) can be encoded by a differential graded Lie algebra. The plan for our learning seminar this term will be to unpack and understand this...

Periods are integrals of differential forms, and their study spans many branches of mathematics, including diophantine geometry, differential algebra, and algebraic geometry. If one restricts their attention to periods arising over OQ, then the...

Functional data analysis (FDA) is a growing statistical field for analyzing curves, images, or any multidimensional functions, in which each random function is treated as a sample element. Functional data is found commonly in many applications such...