I am an Associate Professor of Computer Science at the North Carolina State University. My research is in geometric algorithms. I am most interested in the intersection of geometric algorithms and topological data analysis.
Watch the video of my talk on Sensors and Samples: A Homological Approach at the Institute for Advanced Study Workshop on Topology. Here is a talk I gave on Mesh Generation and Topological Data Analysis .
From the work of Bauer and Lesnick, it is known that there is no functor from the category of pointwise finite-dimensional persistence modules to the category of barcodes and overlap matchings. In this work, we introduce sub-barcodes and show that there is a functor from the category of factorizations of persistence module homomorphisms to a poset of barcodes ordered by the sub-barcode relation. Sub-barcodes and factorizations provide a looser alternative to bottleneck matchings and interleavings that can g