I am interested in the theoretical foundations for persistence theory in topological data analysis and their applications to dynamical systems. For my research, I primarily exploit concepts from algebraic & combinatorial topology, (algebraic) combinatorics, metric geometry, commutative algebra, representation theory, and category theory, blending these with ideas of persistence in topological data analysis. I also often run into computational geometry & topology questions during my research.
Email: woojin [AT] math.duke.edu
Zoom Research Meeting: https://duke.zoom.us/j/94227580431?pwd=NVVQQVdWYThXQ2QxNjgzc3NKZGJydz09
Nov/30/2021. Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applications has been posted to arXiv (Joint work with T. Dey and F. Memoli).
Oct/05/2021. Samantha Moore (a Ph.D. candidate at Univ. of North Carolina at Chapel Hill) is giving a poster presentation about our work “Generalized Persistence Diagrams as an Extension of Elder-Rule-Staircodes” in AATRN poster session, on Oct 8, 2021 (Friday).
Sep/11/2021. I am co-organizing Special Session on Algebraic Combinatorics and Category Theory in Topological Data Analysis in AMS Spring Southeastern Sectional Meeting (March 11-13) with Alex McCleary, Amit Patel, and Facundo Memoli.
July/13/2021. Generalizd Persistence Generalized persistence diagrams for persistence modules over posets has been accepted for publication in Journal of Applied and Computational Topology. arXiv preprint.
Apr/09/2021. I will give a contributed lecture titled The Persistent Topology of Dynamic Data at MSRI Hot Topic workshop: Topological Insights in Neuroscience (May 3-11, 2021).
Mar/31/2021. I will give an invited talk in Metrics in Multiparameter Persistence, Lorentz Center (Jul 19-23, 2021).