Unlike the classical tools and methods that data scientists have historically employed to analyze data, topological data analysis (TDA) provides a tool for analyzing the shape of data. One of the central tasks in TDA is finding the proper representation of a given data cloud. Such representation contains algebraic and geometric features of the data cloud, and one can understand the shape of the data using those features. Moreover, one can evaluate the difference or similarity between two data clouds by measuring the similarity of their barcodes.

I am interested in both theoretical and applied aspects of Topological Data Analysis and Topological Robotics. On the theoretical side, in particular, I am currently developing my understanding and pursuing my research in the following topics:

• projective and injective modules over the incidence algebra on a (locally-finite) poset;

• exact structures of persistence modules over a (locally-finite) poset.

Publications and Preprints

Persistent Homology of Configuration Spaces of Trees

arXiv: 2310.05303, October, 2023. 80 pages.