My research is broadly in applied mathematics with current research interests at the intersection of matrix completion, compressive sensing, high-dimensional probability and convex optimization. In the theoretical side, my work has used tools from probability to assess the effectiveness of certain convex optimization algorithms. The problems I study originate from consideration of real world applications. As such, they motivate the construction of a mathematical model and the design of algorithms that could handle noisy/incomplete data. A common thread in my research is a theoretical analysis of convex approximations and a principled design of algorithms for possibly large scale problems.
Some of my research topics are:
1. Algorithms for the distance geometry problem with the goal of determining 3D protein structure
2. Fast convex algorithms for the graph matching problem
3. Theoretical analysis of deep learning in certain applications.