My research focuses on developing novel machine learning methodologies informed by tools from advanced mathematics, with a focus on applications in biomedical discovery.

Machine Learning for Biomedical Discovery

I develop principled ML methods grounded in geometry and topology to extract meaningful insights from complex biomedical data.

Key Areas:

• Optimal Transport & Generative Modeling: Flow matching, Schrödinger bridges, and deep generative models for cellular development
• Diffusion Geometry & Manifold Learning: High-dimensional data analysis and single-cell trajectory inference
• Graph Signal Processing: Heat and wave dynamics on graphs for molecular structure prediction
• Neural Representation Learning: Geometric and topological deep learning for brain activity analysis

Mathematics

My mathematical background informs my ML research. I have worked on:

Key Areas:

• Differential Geometry: Geometric flows, exponential maps for time-varying vector fields
• Functional Analysis: Nonlinear spectral theory and fixed-point theory
• Differential Equations: Boundary value problems with integral conditions

See my publications for the full list of research outputs.