"Spectral Algorithms Capture Sum-of-Squares on Average"
Tselil Schramm (Harvard)
Monday, November 27, 2017, 2:00 pm
EBU3B, Room 4258
It is well-known that semidefinite programs (such as the Sum-of-Squares or SoS semidefinite programming relaxation) capture spectral arguments. A recent line of work has shown that the reverse is also true for many average-case problems: spectral algorithms are just as powerful as SoS for planted clique, refuting random CSPs, spiked random tensors, and more. In this talk, I will discuss a recent result which shows the equivalence of SoS and spectral algorithms is not a coincidence, and can be shown in a black-box fashion for a broad class of average-case problems.
Based on joint work with Sam Hopkins, Pravesh Kothari, Aaron Potechin, Prasad Raghavendra and David Steurer.