Mathematics faculty and graduate students are invited to attend the PhD Preliminary Exam of Tatum Rask.

Advisor:  Dr. Amit Patel

Committee:  Dr. Chris Peterson, Dr. Clayton Shonkwiler, Dr. Dustin Tucker

Title:  Persistent Laplacians and Möbius Homology

Abstract:  This dissertation proposal outlines a project studying the Laplacian obtained from Möbius homology. We first synthesize previous work in the field of harmonic persistent homology and the persistent Laplacian. We focus on papers by Basu and Cox on harmonic barcodes; Mémoli, Wan, and Wang on the persistent Laplacian; and Gülen, Mémoli, and Wan on Grassmannian persistence diagrams. After highlighting the common threads and important ideas from these papers, we will introduce a new notion of a persistent Laplacian. This Laplacian is obtained through Möbius homology, defined by Patel and Skraba. The proposal will explore connections between this new Laplacian and prior results, highlighting potential avenues for future research.