Topics

1. Learning DNF in time 2^{O(n^{1/3})} by A. Klivans and R. Servedio.
2. Learning DNF from random walks by N. Bshouty, E. Mossel, R. O'Donnell, R. Servedio. These slides could be helpful.
3. Agnostically Learning Halfspaces by A. Kalai, R. Klivans, Y. Mansour, R. Servedio.
4. Fooling Gaussian PTFs via Local Hyperconcentration by R. O'Donnell, R. Servedio and L.-Y. Tan. — here is the recorded talk.
5. The Gaussian Surface Area and Noise Sensitivity of Degree-d Polynomial Threshold Functions, by D. Kane. Using the invariance principle one could obtain bounds (with worse constants) on the Hamming cube too. See this paper.
6. Pseudorandom Generators from the Second Fourier Level and Applications to AC0 with Parity Gates by E. Chattopadhyay, P. Hatami, S. Lovett, A. Tal.
7. Oracle Separation of BQP and PH by R. Raz, A. Tal. — here is the recording of the talk on this paper.
8. Explicit, Almost Optimal, Epsilon-Balanced Codes, by A. Ta-Shma. — first I suggest watching these video lectures (Part I and Part II).
9. Noise stability of functions with low influences: invariance and optimality by E. Mossel, R. O'Donnell, K. Oleszkiewicz.
10. Distributional and L-q norm inequalities for polynomials over convex bodies in R-n by A. Carbery, J. Wright.
11. Learning low-degree functions from a logarithmic number of random queries by A. Eskenazis, P. Ivanisvili. — the bound in n is actually sharp by this result.
12. The Correct Exponent for the Gotsman-Linial Conjecture by D. Kane. — here is a recorded talk on techniques in this paper. And here are the slides. — formally Gotsman-Linial conjecture as stated is false, see this paper; however, the most important inequality AS(f) ≤ C d sqrt(n) can hold.
13. A Structure Theorem for Poorly Anticoncentrated Gaussian Chaoses and Applications to the Study of Polynomial Threshold Functions by D. Kane. — perhaps watching this talk could help to read the paper.
14. Towards a Proof of the Fourier-Entropy Conjecture?, by E. Kelman, G. Kindler, N. Lifshitz, D. Minzer, M. Safra. — here is a recording of the talk on the paper.
15. On rank vs. communication complexity, by Noam Nisan and Avi Wigderson.
16. A structure theorem for Boolean functions with small total influences, Hamed Hatami.
17. Pseudorandom generators hard for k-DNF resolution and polynomial calculus resolution, by Alexander A. Razborov.