Research

Research Areas

My research focuses on Mathematical Foundations of Generative Models, with particular interest in Optimal Transport, Topological Data Analysis, and the problem of learning Data Manifolds. 

I have also worked on Graph Neural Networks, particularly with applications on Bioinformatics.

Ongoing Projects...

1. Wasserstein Push-forward Generative Models: convergence guarantees via Least Squares analysis

2. Extracting Geometry out of Diffusion Language Models

3. Topological Data Analysis and Diffusion Models

4. Complexity of Neural Networks and Generative Models via Pfaffian functions