Clustering and community detection
 
Spectral methods
 
Matrix concentration inequalities
 
Large-scale numerical linear algebra
 
Tensor decomposition 
 
Randomized linear algebra 
 
Sparse recovery and compressed sensing
 
Low-rank matrix recovery (convex approaches)
 
Nonconvex matrix factorization
 
Robust principal component analysis
 
Super-resolution and spectral estimation
 
Minimax lower bounds
 
Shallow neural networks