Here you can find information about talks I have given.
Persistent homology is a tool used to extract topological invariants from datasets. It has applications in a number of non-mathematical disciplines (notably medicine and biology). In this talk, I'll give an introduction to peristent homology, and explore some financial applications
The centre of a group $G$ is the subgroup of $G$ consisting of those elements $z$ such that $zg = gz$ for all $g$ in $G$. It's not immediately clear how we would mimic such a definition in a context where our algebraic structures don't have elements. There are a number of different approaches to making this generalisation, and the aim of this talk is to introduce and compare these from a categorical perspective.
The Euler characteristic is an invariant of manifolds which is preserved under an equivalence relation called bordism. The set of bordism classes of manifolds admits a commutative ring structure, and this invariant lifts to a ring homomorphism. In fact, bordism defines a homology theory, and gives rise to a topological object called a ring spectrum. In this talk, I will discuss the problem of lifting the Euler characteristic ring homomorphism to a map of ring spectra, and the various difficulties involved when considering commutativity.