Research
Geometric methods, mathematical cognition, and applied modeling.
Topological and geometric structure in data, made concrete in public tooling.
Fractals and interactive exploration of Mandelbrot/Julia sets, the Fractal in TutoFractal.
How learners reason at the math-art boundary; AI in mathematics teaching.
Co-authored with Zheng Yang and Todd Edwards. A mixed-methods study of an AI learning partner in Calculus II, using a Taylor-series module to examine recursive mathematical understanding, reflection, and learner agency. Manuscript in development.
Co-editor of a proposed scholarly volume on human-AI mathematical interaction: student learning, teacher development, and AI as a research and design partner. Book project in development.
Reproducible tests of approximate algebraic structure in open GPT-2 representations: planted synthetic relations, spectral validation gates, and capacity probes at full residual dimension. Falsifiable protocol, not a product claim.
Probabilistic and ML tooling for operational decisions: validation and deployable interfaces matter as much as the model. Industry applications have included casino-analytics settings; details stay high-level here.