Research
Topological Data Analysis, Geometric Data Analysis, Manifold Learning, Machine Learning, Statistics
Interests
My research work is at the intersection of statistics, geometry, and topology. I look at data science and machine learning from a geometric point of view, often specifically with a mathematically rigorous lens. I am interested in modeling data both as a smooth manifold and a singular manifold. Topological and geometric data analysis have found applications in diabetes research, data visualisation, neuroscience, cosmology and quantum physics.
Publications:
- Tangent space and dimension estimation with Wasserstein distance, SIAGA
- Strange random topology of the circle, SoCG
- Cover learning for large-scale topology representation, ICML
- Complete intersections with given Hilbert polynomials, Journal of Commutative Algebra
- HADES: Fast singularity detection with local measure comparison, (under review)
- Geometry of navigation identifies genetic-risk and clinical Alzheimer's disease (under review)
- Fibers of point cloud persistence (under review)
- Milnor K-Theory and Shintani cocycle (preprint)
