University of Regina

Given a category C with a class of "weak equivalences" W, Dwyer and Kan constructed a simplicial localization of C that turns the morphisms in W into equivalences. We will go over this construction, its properties, and some tools to compute the...

In this talk, I will explain the concepts of limits and colimits in the context of infinity categories. As a warm-up, I will start by recalling these notions in the setting of ordinary categories. I will also compare these concepts with homotopy (co...

$L_\infty$ algebras, i.e. Lie algebras up to homotopy coherent homotopy, appear in a variety of contexts, including string theory and deformation theory. Over the last several decades, the outlines of a Lie theory for such objects has appeared in...

Similar to how the integers can be equipped with an ordering that is invariant with respect to addition, many groups can be equipped with an ordering that is invariant under the group operation. But aside from being a curious generalization of a...

In classical homotopy theory, graphs are treated as 1-dimensional CW complexes. But since the classical notions of continuous maps and their homotopies do not respect the discrete nature of graphs, this fails to capture the full combinatorial...

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...