Research
Exploring the intersection of optimization, machine learning, and applied mathematics to solve complex problems in signal processing and data analysis.
Distance Geometry
Developing algorithms to reconstruct geometric configurations from partial distance information. This area combines optimization theory with geometric intuition to solve embedding problems.
Applications
Matrix Completion
Investigating methods to recover missing entries in matrices from partial observations, with applications to recommendation systems and image processing.
Applications
Compressive Sensing
Developing theoretical foundations and practical algorithms for signal reconstruction from far fewer samples than traditional methods require.
Applications
Dictionary Learning
Creating adaptive representations for data by learning overcomplete dictionaries that capture the underlying structure of signals and images.
Applications
Optimization Theory
Developing efficient algorithms for non-convex optimization problems with applications to machine learning and signal processing.
Applications
Gas Dynamics
Mathematical modeling and numerical simulation of shock waves and fluid flow phenomena, with applications to aerospace and engineering systems.
Applications
Current Funding
Developing new theoretical and computational approaches for solving distance geometry problems with applications to protein folding and sensor network localization. View Award Details