TF: Juspreet Singh Sandhu (jus065@g.harvard.edu)

Lectures: Tuesdays and Thursdays 3:45pm-5:00pm

Location: SEC 1.402

Office hours:

Chin: Mondays and Thursday 1-2pm @ SEC LL1.201, or by appointment

Juspreet: Tuesdays 1-2pm @ SEC 3.317 (Theory lounge)

Canvas: Link

Discussion: Ed

Homework submisson: HotCRP

Follow this Google calendar for the most updated schedule.

- 09/17/2022 - Course announcements are now on Ed. Please send me an email so that I can add you to the platform.

50% - 1 Project

10% - Peer-grading

Number | Date | Topics | Notes | References |
---|---|---|---|---|

1 | 9/6 | Introduction, Fourier expansion | Ed | Chapters 1.1, 1.2, 1.3 |

2 | 9/8 | Basic identities, Linearity testing | Ed | Chapters 1.4 + Theorem 1.27, 1.6 |

3 | 9/13 | Linearity testing, Social choice theory | Ed | Chapters 2.1 |

4 | 9/15 | Influence | Ed | Chapters 2.2 |

5 | 9/20 | Total Influence, Sensitivity, Noise Stability | Ed | Chapters 2.3, 2.4 |

6 | 9/22 | Low-degree functions | Ed | Chapters 3.1, 3.2 |

7 | 9/27 | Learning low-degree functions | Ed | Chapters 3.4, 3.3, 3.5 |

8 | 9/29 | Goldreich-Levin theorem, Kushilevitz-Mansour algorithm | Ed | Chapters 3.5, 4.1 |

9 | 10/4 | Random restrictions, Switching Lemma | Chapters 4.3, 4.4 | |

10 | 10/6 | Switching Lemma | Ed | |

11 | 10/11 | Multi-Switching Lemma | Ed | |

12 | 10/13 | Multi-Switching Lemma, Low-degree concentration of DNF | Ed | Chapter 4.4 |

13 | 10/18 | Low-degree concentration of AC0 | Ed | Chapter 4.5 |

14 | 10/25 | Bonami's lemma | Ed | Chapter 9.1 |

15 | 10/27 | Hypercontractivity, Small-set expansion | Ed | Chapters 9.2, 9.5 |

16 | 11/1 | Level-k inequality, FKN theorem | Ed | Chapters 9.1, 9.5 |

17 | 11/3 | KKL theorem | Ed | Chapters 9.6 |

18 | 11/8 | PRGs, k-wise independence | Ed | |

19 | 11/10 | bounded independence plus noise | Ed | |

20 | 11/15 | Polarizing random walk | Ed | |

21 | 11/17 | Polarizing random walk, Fourier growth | Ed |

You are allowed to discuss homework questions with others in the class, only

- Homework 1 (due
~~Sept 30~~Oct 5) - Homework 2 (due
~~Oct 21~~Oct 31) - Homework 3 (due Dec 2)

The topics are open-ended. You should cover some new material on the topic that is not in Ryan O'Donnell's book. Here are some suggestions:

- survey a research area and focus on how the analysis of Boolean functions is used;
- learn about a technical lemma in a paper, present it in the simplest way as possible;
- attack a research problem. If you succeed, congratulations, write a paper and present it. If not, summarize your attempts. A list of open problems can be found here.

- Basics
- - Influence, Sensitivity
- Learning
- - Low-degree algorithm
- - Goldreich-Levin theorem
- Circuits
- - Random restrictions
- - Switching Lemmas
- Hypercontractivity
- - Low-degree functions
- - Isoperimetric inequalities
- - Junta theorems
- Pseudorandomness
- - Bounded independence, small-bias space
- - Bounded independence plus noise
- - Fractional pseudorandom generators
- Monotone functions
- - Sunflower lemma
- - Threshold phenomena