University of Regina

In this second part, we will look at more examples of cohomology rings. We will then focus on manifolds and discuss de Rham cohomology, orientations, Poincaré duality, and the intersection product.

Characteristic classes are certain cohomology classes that we assign to vector bundles. In this talk, we will first familiarize ourselves with cohomology. We will go over singular cohomology of spaces, the cup product, the cap product, along with...

Can you embed the real projective plane in three-dimensional space? Motivated by this and similar questions, I will introduce the correspondence between real line bundles and hypersurfaces, the first Stiefel-Whitney class, and Poincare duality. In...

In this talk, I will discuss recent progress on the directed Oberwolfach problem. A directed variant of the famous Oberwolfach problem, the directed Oberwolfach problem considers the fol- lowing scenario. Given m people and t round tables of size m1...

For a successful analysis a suitable representation of data by objects amenable for statistical methods is fundamental. There has been an explosion of applications in which homological representations of data played a significant role. I will present...

Generalized geometry, introduced by Hitchin in the early 2000s, has not only grown into a formalism for understanding previously mysterious constructions in physics (especially in supersymmetric sigma models) but has also led to the discovery of new...

A symmetric monoidal category is a category equipped with a monoidal product that is uniquely commutative up to isomorphism. In this way the iterated monoidal product has an action from the symmetric groups. We can generalize this notion by allowing...

The Bar and Cobar functors pair up to form an adjunction between the category of dg-algebras and dg-coalgebras. This adjunction can be used as a tool to provide a quasi-free resolution for any dg-algebra. We work out such a resolution for the case of...

I will review some of the basic machinery used in formulating characteristic classes for coherent sheaves on complex manifolds. The main ideas go back to the fundamental work of Toledo and Tong in the 70s. A natural extension of their ideas leads to...

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...