Current Appointments & Affiliations
Phillip Griffiths Assistant Research Professor
·
2024 - Present
Mathematics,
Trinity College of Arts & Sciences
Assistant Research Professor of Mathematics
·
2024 - Present
Mathematics,
Trinity College of Arts & Sciences
Recent Publications
Persistent cup product structures and related invariants
Journal Article Journal of Applied and Computational Topology · March 2024 AbstractOne-dimensional persistent homology is arguably the most important and heavily used computational tool in topological data analysis. Additional information can be extracted from datasets by studying multi-dimensiona ... Full text CitePersistent homotopy groups of metric spaces
Journal Article Journal of Topology and Analysis · January 1, 2024 In this paper, we study notions of persistent homotopy groups of compact metric spaces. We pay particular attention to the case of fundamental groups, for which we obtain a more precise description via a persistent version of the notion of discrete fundame ... Full text CiteEPHEMERAL PERSISTENCE FEATURES AND THE STABILITY OF FILTERED CHAIN COMPLEXES
Journal Article Journal of Computational Geometry · January 1, 2024 We strengthen the usual stability theorem for Vietoris-Rips (VR) persistent homology of finite metric spaces by building upon constructions due to Usher and Zhang in the context of filtered chain complexes. The information present at the level of filtered ... Full text CiteRecent Grants
Persistent invariants and their properties
ResearchPrincipal Investigator · Awarded by American Mathematical Society · 2024 - 2026View All Grants
Education, Training & Certifications
Ohio State University ·
2023
Ph.D.