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 |