Research

Academic Interests

I am interested in applied problems within computational topology. Namely the application of tools from topological data analysis (TDA) to problems in sensor networks and machine learning.

Sensor Networks

I have been working on simulating the dynamics of coordinate-free 3D mobile sensor networks. This is a continuation of work in collaboration with Henry Adams at the University of Florida.

Topological Deep Learning

There has been a recent push to utilize features detected by topological methods to help improve deep learning architectures. To the right, we have a few examples of topological features that one can use to describe global characteristics of data.

The first two columns are Persistence Diagrams and their corresponding Persistence Barcodes which contain topological descriptions of point clouds sampled from six tori, three of genus 1 and three of genus 2 with varying thicknesses.

The third and fourth columns show a transformation of the persistence diagram which is then converted into a persistence image (before normalization) which can be vectorized and fed as a feature.

The last column is the persistence landscape which can also be vectorized by keeping track of the critical points.

Temporal Link Prediction

Given a collection of observations of a temporal network, when can we predict future links that will appear? This problem arises in network science with applications to detecting failures in power grids, social network dynamics, and fraud detection. I am interested in using techniques from deep learning to explore these problems and use topological tools to assist the models in maintaining global characteristics.

Publications

(Coming soon) Below you will find my writing organized by publication type and year. For questions on any specific publication, feel free to reach out to me.

2024

Coming soon......

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