My current research is on various topics in computational complexity theory, information theory and discrete mathematics. A unifying theme in my work is the interaction between amortization, symmetry and approximation. Among the topics that I am particularly interested in are: fast matrix multiplication, Shannon capacity of graphs/hypergraphs, asymptotic spectra theory, direct sum theorems and Ramsey type problems. I use methods from diverse fields, including representation theory, algebraic geometry, quantum information theory, polynomial optimization.