The final project in the course will involve reading a research-level paper and either summarizing it or giving a short presentation, depending on the amount of students that will take the course for credit. This may include linking out to related open research directions and making some progress along them.

Papers for Final Project

  1. Inductive proof Majority is Stablest 
  2. AND Testing 
  3. Hypercontractivity on the symmetric group  
  4. Gaussian Noise Sensitivity and Fourier Tails   
  5. Gaussian Bounds for Noise Correlation of Functions   
  6. Testing Juntas   
  7. Degree vs. Approximate Degree and Quantum Implications of Huang’s Sensitivity Theorem   
  8. Polynomial bounds for decoupling, with applications   
  9. Local Chernoff    
  10. Towards a Proof of the Fourier–Entropy Conjecture?   
  11. Quadratic Goldreich-Levin Theorems   
  12. Reed-Muller Codes Achieve Capacity on Erasure Channels   
  13. Noise sensitivity on the p-biased hypercube   
  14. XOR Lemmas for Resilient Functions Against Polynomials   
  15. Decision list compression by mild random restrictions   
  16. Biasing Boolean Functions and Collective Coin-Flipping Protocols over Arbitrary Product Distributions   
  17. On the structure of subsets of the discrete cube with small edge boundary   
  18. On the Fourier tails of bounded functions over the discrete cube   
  19. A Hypercontractive Inequality for Matrix-Valued Functions with Applications to Quantum Computing and LDCs  
  20. Reverse hypercontractivity and applications   
  21. Decision trees and influences    
  22. Fourier entropy for classes of functions    
  23. Group mixing   
  24. Pseudorandom Generators for Read-Once Branching Programs, in any Order   
  25. Fooling Gaussian PTFs via Local Hyperconcentration   
  26. The Correct Exponent for the Gotsman-Linial Conjecture   
  27. Improved lower bounds for embeddings into L1   
  28. Concentration on the Boolean hypercube via pathwise stochastic analysis   
  29. Second-order bounds on correlations between increasing families

Course Info

As Taught In
Spring 2021
Learning Resource Types
Lecture Notes
Problem Sets