Bendich, Paul L

I am a mathematician whose main research focus lies in adapting theory from ostensibly pure areas of mathematics, such as topology, geometry, and abstract algebra, into tools that can be broadly used in many data-centered
applications.
My initial training was in a recently-emerging field called topological data analysis (TDA). I have been
responsible for several essential and widely-used elements of its theoretical toolkit, with a particular
focus on building TDA methodology for use on stratified spaces. Some of this work involves the
creation of efficient algorithms, but much of it centers around theorem-proof mathematics, using proof techniques
not only from algebraic topology, but also from computational geometry, from probability, and from abstract
algebra. Recently, I have done foundational work on TDA applications in several areas, including to neuroscience, to multi-target tracking, to multi-modal data fusion, and to a probabilistic theory of database merging. I am also becoming involved in efforts to integrate TDA within deep learning theory and practice.