Here you can find information about talks I have given.
In higher algebra, commutativity is a structure rather than a property, with different strengths of commutativity parametrised by $E_n$ operads. Homotopy-commutative ring spectra of characteristic 2 are characterised by their homology, making calculations in this context a bit more convenient. In this talk I will introduce the relevant theory and discuss some examples of this phenomenon, as well as calculations which can be used to construct algebraic models of geometrically-constructed ring spectra.
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.
See above for abstract and notes.
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 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.