My research interests revolve around developing the theoretical and computational foundations of Topological Data Analysis (TDA) and their applications. 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 TDA. I also often run into computational geometry & topology questions during my research. I want to expand the use of geometric and topological ideas to a broader range of data science and machine learning.
Email: woojin [AT] math.duke.edu
Zoom Research Meeting: https://duke.zoom.us/j/94227580431?pwd=NVVQQVdWYThXQ2QxNjgzc3NKZGJydz09
The list of my talks in the past can be found in my CV.
Jan/2023 The Joint Mathematics Meetings 2023 (SS. on Applied Topology: Theory and Implementation), Title: TBD
Nov/2022 Computational Persistence Workshop at Purdue University (virtual), Title: TBD
Oct/2022 International Conference on Advances in Interdisciplinary Statistics and Combinatorics at UNC at Greensboro, Title: TBD
July/23/2022. The discriminative power of the generalized rank invariant has been posted to arXiv (Joint work with N. Clause and F. Memoli).
July/23/2022. Bigraded Betti numbers and generalized persistence diagrams has been posted to arXiv (Joint work with Samantha Moore); It is a new version of the preprint posted on Nov, 2021. Submitted.
July/20/2022. Interleaving by parts: Join Decompositions of Interleavings and Join-Assemblage of Geodesics has been posted to arXiv. It is a new version of the preprint posted on Jan, 2021. Submitted.
Mar/14/2022. The full version of Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applications has been invited to a special issue of Discrete & Computational Geometry, devoted to best papers from SoCG 2022. arXiv
Mar/6/2022. I am co-organizing Workshop on Algebraic Combinatorics and Category Theory in Topological Data Analysis which takes place on March 12, 2022 (a substitute for the cancelled AMS Spring Southeastern Sectional Meeting ).
Feb/15/2022. Extracting Persistent Clusters via Möbius inversion has been posted to arXiv (Joint work with F. Memoli), a significant revision of work in 2018, titled previously Stable Signatures for Dynamic Graphs and Dynamic Metric Spaces via Zigzag Persistence. Submitted.
Feb/9/2022. Computing Generalized Rank Invariant for 2-Parameter Persistence Modules via Zigzag Persistence and its Applications has been accepted to SoCG 2022 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 (cancelled).
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.