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.
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.
DATA SCIENCE FOR CLINICAL DIAGNOSTICS
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.
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.