2017 SOS Seminar lecture notes:

These are powerpoint slides corresponding to the whiteboard lectures I gave for a sum of squares seminar in fall 2017.

Lecture 1: Introduction to the Sum of Squares Hierarchy
Lecture 2: Linear Programming and Duality
Lecture 3: Semidefinite Programming
Lecture 4: Goemans-Williamson
Lecture 5: SOS Proofs and the Motzkin Polynomial
Lecture 6: Linear Programming and Sparsest Cut
Lecture 7: Arora-Rao-Vazirani
Lecture 8: SOS Lower Bound for 3-XOR
Lecture 9: SOS Lower Bound for Knapsack
Lecture 10: Gap Reductions and SOS
Lecture 11: Graph Matrices
Lecture 12: SOS Lower Bounds for Planted Clique Part I
Lecture 13: SOS Lower Bounds for Planted Clique Part II
Lecture 14: Planted Sparse Vector
Lecture 15: Exact Tensor Completion
Lecture 16: Subexponential Time Algorithm for Unique Games and Small Set Expansion