University of Regina

In this third part, we will discuss orientations of manifolds, Poincaré duality, and the intersection product.

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.

A $P$-matrix is a matrix all of whose principal minors are positive. In this talk, we demonstrate that the fractional powers of a $P$-matrix are also $P$-matrices. This insight allows us to affirmatively address a longstanding conjecture raised in [D...

A matrix is called totally positive if all of its minors are positive. These matrices are important in mathe- matics, but checking whether a large matrix is totally positive can be challenging. In this talk, we explore whether certain matrices...

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...