Research Overview

My research lies at the intersection of topology and theoretical computer science, where I explore how complex structures can be understood, represented, and computed. I focus especially on how topological data analysis (TDA) can extract meaningful patterns from high-dimensional or noisy data, and how tools from complexity theory and parameterized algorithms can make these computations more efficient and scalable.

These themes converge in my work on problems like homology localization and path planning in configuration spaces, where topological and computational perspectives meet. Complexity theory helps identify what makes these problems difficult, while parameterized complexity allows us to isolate the core challenges and design algorithms that adapt to the structure of the data.

I'm also branching into applied robotics, where topology and complexity theory offer powerful tools for motion planning, configuration space analysis, and spatial reasoning. Locally, I collaborate with colleagues who bring deep expertise in this area, and I’m excited to explore the connections between discrete math, geometry, and real-world robotics.

Alongside my theoretical work, I am developing a research program in pedagogy, focused on fostering a paradigm shift toward democratic education in higher education (and beyond). Since no fully realized framework yet exists, I approach this as both a theoretical and practical endeavor—building foundational concepts, mapping existing approaches, and drawing on my own classroom practice. This includes creating a theoretical model, assembling a literature survey, developing a practical guidebook, and conducting empirical studies. My goal is to help shape a pedagogy rooted in agency, community, responsibility, and freedom—values that align closely with the way I approach both research and supervision.