In the field of geometry processing, I work to make sense of existing geometric data and provide interfaces to put that data to further use. Today, we find many sources of geometric data and increasingly find useful applications affecting our daily lives. Climate analysis, self-driving cars, 3d-printed prosthetics, virtual dressing rooms and video games all share the essential tasks of collecting, processing and utilizing geometric data.

Unfortunately, barriers stand between geometric data and the people who want to analyze and understand that data. Potential consumers and content creators cannot access or edit geometry because of poor human-computer interfaces. Meanwhile, some data never reaches its intended users because processing breaks down due to lack of robustness to noise.

My long-term research goal is to dismantle the barriers between humans and geometry. In this talk, I will show how I attack this problem on both fronts. I bring ideas from differential geometry and finite-element analysis to model geometric problems more intuitively and more robustly. Meanwhile, I pursue better user interfaces to reduce human effort and increase creative or scientific exploration of geometric data. I will present my work in robust geometry processing, higher-order PDEs, real-time shape articulation, and fabricating user interfaces. Each parallel branch of investigation, while self-motivating, complements the others, and together they invite exciting new directions for future research.