NOTE: For some videos of board talks, the video shows a black screen with just audio.
To fix this, you need to switch to the 2nd view, which appears as two arrows in the bottom right side of the video.
Shachar Lovett:
From Sunflowers to Thresholds [lecture notes]
- Lecture 1: Sunflower conjecture [video]
- Lecture 2: Improved bound for the sunflower conjecture, spread lemma [video]
- Lecture 3: Threshold phenomena and the Kahn-Kalai conjecture [video]
- Lecture 4: Monotone circuit lower bounds [video]
Bhavik Mehta:
For part of the theorem proving track of the course, I will give an introduction to the Lean theorem prover. As such, and to work on the exercises, you should bring a laptop and try to install Lean in advance. Installation instructions can be found here: https://leanprover-community.github.io/get_started.html. If you are struggling with this, then we will have some time during the week to iron out some installation problems. There are also alternative ways to try and work with Lean on your laptop without installing it, so don’t worry too much if after a few attempts it still doesn’t seem to work.
If you would like to get started early, I recommend trying the Natural Number Game: https://adam.math.hhu.de/#/g/leanprover-community/NNG4. I won’t be following this, but the ideas there will still be relevant, and it’s fun to try nonetheless.
- Lecture 1: Introduction to theorem proving [video]
- Lecture 2: Introduction to Lean [video]
- Lecture 3: Reading and writing Lean proofs [video]
- Lecture 4: Complex Lean proofs [video]
Github link: https://github.com/b-mehta/epfl-comb
Raghu Meka:
- Lecture 1: 3-term AP problem. Behrend’s construction. Application to NoF protocols. Corners problem and equivalence to NoF [video]
- Lecture 2: Finite fields and the polynomial method. Other notable examples of the polynomial method (just pointers). Structure vs randomness approach overview [video]
- Lecture 3: The weak-rate proof over finite fields. Spreadness and obtaining better rates for finite fields using analytic proofs. Spectral positivity. [slides] [video]
- Lecture 4: Analytic proof: Sifting. Decoupling inequality (statement), spread regularity lemma, application to detecting triangles. Summary. [video]