What's new in Fourier Analysis?

Insofar as a lot of the stuff we do in class is from the olden days (the '90s, let's say), you might be wondering what's going on in Fourier Analysis of Boolean Functions currently. Here are some highlights from the recent top conferences. I would like to emphasize that there are lots of other good recent papers on the topic!

• STOC '06: Gowers Uniformity, Influence of Variables, and PCPs by Alex Samorodnitsky and Luca Trevisan. Topic: Hardness of Approximation and pure Fourier Analysis.
  
  
• FOCS 2005: Nonembeddability theorems via Fourier analysis by Subhash Khot and Assaf Naor. Topic: Metric Spaces.
  
  
• GAFA journal 2007: Boolean functions with small spectral norm by Ben Green and Tom Sanders. Topic: Classical Analysis. (Mentioned in class today.)
  
  
• COLT 2006: Improved lower bounds for learning intersections of halfspaces by Adam Klivans and Sasha Sherstov. Topic: Learning Theory.
  
  
• FOCS 2005: On non-approximability for quadratic programs by Sanjeev Arora, Eli Berger, Elad Hazan, Guy Kindler, and Muli Safra. Topic: Hardness of Approximation.
  
  
• FOCS 2005: On Delsarte's Linear Programming Bounds for Binary Codes by Michael Navon and Alex Samorodnitsky. Topic: Coding Theory.
  
  
  
• FOCS 2005: Lower bounds for the noisy broadcast problem by Navin Goyal, Guy Kindler, and Mike Saks. Topic: Distributed Networks.
  
  
• Complexity 2005: On the hardness of approximating Multicut and Sparsest-Cut by Shuchi Chawla (of CMU), Robi Krauthgamer, Ravi Kumar, Yuval Rabani, and D. Sivakumar. Topic: Hardness of Approximation.
  
  
• Improving on a Complexity 2005 paper: Learning symmetric k-juntas in time $n^{o\left(k\right)}$ by Mihail Kolountzakis, Evangelos Markakis, and Aranyak Mehta. Topic: Number Theory and Learning Theory.
  

The first few papers in the list may be particularly readable for people taking the class.