University of Regina

I will provide an introduction to simplicial sets, which will serve as foundation for the rest of the lecture series. We will discuss examples and a few constructions, such as the function complex and geometric realization.

We will review how to do homotopy theory with model categories. As motivation for infinity-categories, we will discuss the benefits and drawbacks of working with model categories.

A common theme in homotopy theory is to record not just whether two objects are equivalent, but also *how* they are equivalent. For instance, we can consider maps between spaces, homotopies between maps, homotopies between homotopies, and so on. An...

I will start by giving a broad overview of our seminar so far, outlining the way in which characteristic classes arise from the cohomology of classifying spaces. When the coefficients for cohomology are the real numbers, the characteristic classes...

We consider cyclic partitions of the complete k-uniform hypergraph on a finite set V , minus a set of s edges, s ≥ 0. An s-almost t-complementary k-hypergraph is a k-uniform hypergraph with vertex set V and edge set E for which there exists a...

In this talk, we consider the non-penalty shrinkage and pretest estimation methods for the regression parameters of the generalized log-logistic proportional hazards (PH) model. This model, a simple extension of the log-logistic model (which...

In the first talk of this series, we saw how the first Stiefel-Whitney class is a complete invariant of real line bundles. Building on this, we will now study how to build a complete invariant for complex line bundles: the Chern class. Among other...

The synthetic analogue of the bar comonad controls the universal differentials in the bar spectral sequence of algebras over spectral operads. This can be viewed as a deformation of Koszul duality of such algebras. I will explain ongoing work with...

In topology, cohomology is an invariant we can assign to spaces. In algebra, there are also cohomology theories for various algebraic structures, such as group cohomology, Lie algebra cohomology, and André-Quillen cohomology of commutative rings...

We will see the definition and some examples of broken toric varieties and balloon animal maps between them. After an overview of some of the many different areas in which they appear, we look at how their geometry can be studied via complexes of...