I recently successfully defended my dissertation to recieve my Ph.D. in Applied Mathematics at the University of Arizona. My research interests are in the applications of topology to various data analysis problems. My passions outside of mathematics include Music and Web-Development/Design.


Analyzing Scalar Fields through Topological Similarity

I am currently being advised by Professor Joshua Levine of the Computer Science department on a project intended to study large-scale, multifaceted data sets using topological methods. The goal is to examine existing tools that are used to measure distance between topological structures (bottleneck distance for Persistence Diagrams and interleaving distance of Reeb Graphs, for example) with the intent to apply these metrics or modify them in a way that they become useful to the study of these data sets. We recently finished a survey of the existing Reeb graph metrics, which you can find here. Soon following, we took what we learned through this empirical survey to implement a distance between merge trees which we experimentally show to be both discriminative and stable. This work is currently in submission.

In addition to this line of work, we'd like to investigate the possibility of leveraging machine learning to (1) create similarity metrics through supervised training, (2) create similarity metrics through unsupervised training, and (3) aid in the computation of computationally complex metric such as interleaving distance and functional distortion distance on Reeb graphs. My CV can be found here.



MuView is an in-development visualization tool to aid in the exploratory analysis of music review data. It pulls review data from multiple music publication websites to create a dynamic, interactive experience for users to navigate the multitude of reviews.

Many current review aggregation sites have no way to make complex queries on the data (such as unions and intersections of sets). Even finding simple lists of the top rated albums by specific publications are difficult. This is an attempt to allow users to navigate the lanscape of review data in a more versatile way. The features include choosing your own publications to pull data from, sort by ratings, peform unions and intersections of multiple sets (groups) of albums, view year-end ranks for each album, and more

MuView is built in React.js and utilizes D3.js for dynamic data interactions. The prototype which includes data from 2018 (until I fetch more) is available here.


The real-time assessment (RTA) application is a prototype for a dashboard used to track and gain insights for tutoring large bodies of students. The main focus is that current test-based approaches fail to adequately assess students in that they 1) do not have a vaild way of capturing a students closeness to the solution and 2) do not keep track of underlying weaknesses which are the real cause for incorrect answers.

I, along with a colleague of mine, designed this application to couple with a company we co-founded in 2018, called TutorYard. We designed a tutoring scheme where the tutors would simply score a students progress. If the student has been doing better than the day before on a particular concept, the score goes up. Then, the tutor can take note of particular non-curriculum weaknesses, such as basic multiplication and division, or percentages. Then, classroom teachers would be granted access to this information to better assess their class as a whole. The prototype was constructed completely using React.js and D3.js. You can view the prototype for this application here (success may vary depending on the resolution of your screen). The source code can also be viewed here.