DANIEL TOLOSA
RESEARCH PROJECTS
ALGEBRAIC TOPOLOGY
(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.
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.
MATHEMATICAL BIOLOGY
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.
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.
Alexandria Volkening, mentor and collaborator, on the day of my PhD defense.
