Short Research Summary: 

My research combines algebra, topology, and data analysis. I study new forms of homology, such as multipersistent relative homology, U-homology, and weak U-homology, to better understand data that is noisy, uncertain, or incomplete. I also work in coding theory, cryptography, and ring and module theory, especially group rings and zero-divisor structures, to build strong mathematical tools that connect pure algebra with modern applications in data science and security.

Introductory book/lecture notes: 

(1) H. Edelsbrunner and J. Harer, Computational Topology: An Introduction. American Mathematical Society, 2010. (2) S.Y.Oudot, Persistence Theory: From Quiver Representations to Data Analysis, American Mathematical Society, 2015.

Mentee Assessment: 

Through online interview