Portrait of Patricia Medina

Welcome! I am an Assistant Professor in the Department of Mathematics at CUNY—New York City College of Technology (City Tech), with a temporary appointment at the CUNY Graduate Center. My work develops mathematical approaches to machine learning, with emphasis on feature engineering, representation learning, and applications to LiDAR/3D point clouds and remote sensing data. I also work in applied functional analysis (Banach space methods), numerical analysis, and the mathematical treatment of PDEs that model physical phenomena.

For more details, see my CV (PDF) .

I enjoy collaborating with undergraduate students on research. Below is a video featuring student research projects (Summer 2020).

I also maintain a teaching blog with short summaries and reflections: Patricia's Teaching Blog.

Research Areas

Selected themes

  • PDE modeling and numerical analysis: mathematical treatment and simulation of physical phenomena in porous media and geoscience applications (e.g., methane hydrates and adsorption models).
  • Mathematical frameworks for machine learning: feature engineering and dimensionality reduction motivated by measure theory and functional analysis, with applications to LiDAR/3D point clouds and remote sensing data.

Projects

Selected topics

LiDAR / 3D Point Clouds

Classification and representation learning for multi-class 3D point clouds, with emphasis on mathematically motivated feature engineering and dimensionality reduction.

Feature Engineering and Dimensionality Reduction

Designing descriptors inspired by measure theory and functional analysis (e.g., dyadic neighborhoods, product-coefficient-type features) to improve learning performance and interpretability.

PDE Modeling in Porous Media

Mathematical modeling and numerical simulation of physical phenomena in porous media, including multi-component transport and phase-transition processes.

Methane Hydrates and Adsorption

Mathematical treatment, analysis, and computation for hydrate formation and adsorption models, including stability and reduced numerical models.