Ph.D. Candidate in Computer Science
Stony Brook University
I am a Ph.D. candidate at Stony Brook University working at the intersection of computational geometry, abstract algebra, and symbolic mathematics. My research reimagines foundational mathematical operations to simplify complex problems, particularly in geometric computation.
Submitted to Inventiones mathematicae
Abstract: We propose performing arithmetic directly on geometric objects (e.g., line segments, rectangles) rather than their numerical measures. This avoids indeterminate forms like 0/0 in calculus and aligns with polynomial ring structures in abstract algebra.
Contribution: Eliminates the need for limit processes in differentiation while preserving geometric object integrity.