Artificial Intelligence, Numerical Analysis, Combinatorial Optimization

Local graph partitioning algorithms, applications of low-rank SDP solvers, and Statistical Physics

Vertex separators, spectral graph theory, Applications of the Burer-Monteiro framework to solving semidefinite programs

Algorithms, Graphs, Semidefinite Programming and optimization.

Convex Optimization

Optimization, Learning Theory, Design and analysis of algorithms, Approximation algorithm, Online algorithms

Riemannian Optimization, Manifold Learning

First order optimization algorithms interpreted under calculus of variations., Using classical mathematical or physical theory to design scalable algorithms for a broad range of optimization problems.

Theoretical Computer Science, Design of approximation algorithms, Interplay between combinatorics, graph theory, computational complexity, and classical mathematics

Local graph algorithms, Diffusion processes on graphs, Fast approximation algorithms via convex optimization