I'm Naya, a DPhil graduate in Mathematics from the University of Oxford and the Alan Turing Institute. Previously, I completed my MMath at Warwick University.

I have worked as a quant researcher at a hedge fund, and as a software developer at an investment bank.

Here, you can find out more about my research interests.

## Research

My research was a mixture of pure and applied topology, touching on themes from discrete Morse theory, knot theory and network analysis. My DPhil was supervised by Prof. Vidit Nanda. I was lucky enough to also spend some time at the Australian National University, first at a workshop under the supervision of Prof. Kathryn Hess, and then on a research visit.

Joint with Vidit Nanda

We construct an equivariant version of discrete Morse theory for simplicial complexes endowed with group actions. We use the discrete flow category of any such compatible matching to build the corresponding Morse complex of groups. Our main result establishes that the development of the Morse complex of groups recovers the original simplicial complex up to equivariant homotopy equivalence.

Joint with Daniele Celoria

We obtain a simple and complete characterisation of which matchings on the Tait graph of a knot diagram induce a discrete Morse function on the 2-sphere and simultaneously generalise Kauffman's Clock Theorem and Kenyon-Propp-Wilson’s correspondence.

Joint with Daniele Celoria

We associate to any simplicial complex a filtration, starting from the discrete Morse complex and finishing at the matching complex. This leads to the definition of several homology theories, which we compute in a number of examples. We completely determine the graded object associated to this filtration in terms of the homology of simpler complexes.

Joint with Agnese Barbensi, Dimos Goundaroulis, Barbara Mahler & Oliver Vipond

We analyse proteins forming open-ended trefoil knots by introducing a topologically inspired statistical metric that measures their entanglement. By looking directly at the geometry and topology of their native states, we are able to probe different folding pathways for such proteins.

Joint with Ana Garcia-Pulido, Kathryn Hess, Jane Tan, Katharine Turner & Bei Wang

It is often computationally expensive to determine topological features of the directed flag complex associated to a digraph. We introduce methods to measure how well graph pseudometrics capture the topology of a digraph, and apply them to various random digraph models.

## Projects

I'm currently working on a few projects, so hopefully you'll see more here soon...

### Knotoids

The knotoid distribution provides a 3D summary of the entanglement of a curve, most often used in the study of knotted proteins. knotoids is a command line tool to compute the distribution of a piecewise-linear curve by partitioning the surface of the sphere of projections, and calling Knoto-ID to classify a single point in each region.

## Teaching & Outreach

### Teaching

During my DPhil, I held a lectureship at St. Catherine's College, Oxford, where I was a tutor for the following courses:

Probability Linear Algebra I & II

Statistics & Data Analysis Constructive Mathematics

Analysis I, II & III Introduction to University Mathematics

Groups & Group Actions Introductory Calculus

I was also a Teaching Assistant in the Mathematics Department for Category Theory and Topology & Groups.

### Outreach

I was a lead organiser of Maths in Society at Oxford, a weekly speaker series covering topics such as formal proof verification, data science in energy systems, and the future of healthcare. Its purpose was to stimulate discussion among mathematicians about the impact of their research and future careers on society, with a focus on ethics. It was cut short by the pandemic, but you can follow this link to find out more. If you're currently a DPhil at Oxford, maybe you would consider restarting it!

A long time ago now, I volunteered with Code First Girls as a teaching assistant for their Introduction to Web Development course, and have volunteered with Stemettes at a hackathon for children aged 5-18 to build chatbots.

## Contact

nyerolemou [at] gmail [dot] com