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(PhD thesis)

 An interplay of Topology, Algebra and Combinatorics comes together in a cyclic theory for a categorical model for the free loopspace with its circle action. In particular, we produce a small model for computing the equivariant homology of the free loopspace.

Preprint: click here

Advisor: Dr. Manuel Rivera.

Image: 2015, Nissim Ben Aderet. His pieces are made from a single closed line, hence his entire work consists of points on the free loopspace of a canvas.


We are working on a multi-analyte machine-learning-based classifier for Alzheimer's Disease(AD) that uses cell-free mRNA data to tell subjects whether or not they have AD. We explore the measurement uncertainty and accuracy of the classifier — it's very important to hold these type of classifiers to high standards, people's health and treatments may depend on it!
This work was done at The Data Mine - Purdue University , in collaboration with our corporate partner Molecular Stethoscope


We implement methods from Topological Data Analysis to study cell-based pattern formation. We apply our methods to zebrafish, which get their name from their characteristic striped pattern, and study their variation in time, as well as their large-scale statistical variability.

Collaborators: Dr. Alexandria Volkening.

Image: Fish and Scales, 1959, M.C. Escher.

WhatsApp Image 2023-01-19 at 5.16.30 PM.jpeg

Three generations of math!

This picture was taken at the conference in honor of Four Decades of the Einstein Chair Seminar at CUNY.

From left to right: Dennis Sullivan, Manuel Rivera, DT, Sofía Martínez.

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