My research primarily focuses on eigenvalue problems in differential geometry and their extensions to discrete algorithms. I also work on the operads of moduli spaces of curves related to additional supersymmetric structures and the topological and combinatorial properties of their dual graphs. I work on building efficient feature representation and interpretability of machine learning algorithms. I am particularly interested in a data-driven approach to solve for the spectrum of the Laplace-Beltrami operator that enables deep neural networks to recognize global features of shapes and surfaces that were previously unseen using current state of the art computational techniques. Qualitative analysis of 3D data finds important applications in computer graphics, vision, and sensors, such as face recognition, medical image processing, and remote sensing. There are also various physical and cosmological applications that are naturally associated with geometric analysis and computation.