- Bogdanov's note on the limits of gap amplification in Dinur's proof; and Jutla's alternate implementation of one of Dinur's steps. (If we used Charanjit's argument in the lecture than this option might not be available.)
- Raz' counter-example to a strong version of the parallel repetition (PR) theorem
- Fiege, Kindler, and O'Donnell.'s work on the connection between PR and foam
- Anup Rao's first paper on PR
- Venkatesan Guruswami, Daniel Lewin, Madhu Sudan, and Luca Trevisan. A tight characterization of NP with 3-query PCPs. FOCS 1998. ($NP = PCP[O(log n), 3]$ with perfect completeness and soundness $1/2+\epsilon$, for any $\epsilon$)
- Lectures 11 (section 2 onwards) and 12 and 13 from Venkat and Ryan's course. (Two/three students can present these in sequel.)
- Ben-Sasson and Sudan, Short PCPs with polylog query complexity

- Uriel Feige, A Threshold of ln n for Approximating Set Cover (JACM 1998, STOC 1996)
- Johan Hastad's classic work Some optimal inapproximability results, (STOC 97, JACM 2001)

- Khot, On the power of unique 2-prover 1-round games, STOC 2002.
- Khot/Kindler/Mossel/O'Donnell, Optimal inapproximability results for MAX-CUT and other two-variable CSPs?, FOCS 2004.
- Mossel, E. O'Donnell, R. Oleszkiewicz, Noise stability of functions with low influences: Invariance and optimality.
- Subhash Khot, Guest column: inapproximability results via Long Code based PCPs, ACM SIGACT News, v.36 n.2, June 2005

- Howard J. Karloff, Uri Zwick: A 7/8-Approximation Algorithm for MAX 3SAT? FOCS 1997: 406-415. ($P = PCP[O(log n), 3]$ with completeness $1$ and soundness $1/2$)
- J. Håstad, Clique is Hard to Approximate within n to the power 1-epsilon, Acta Mathematica, Vol 182, 1999, pp 105-142. (Another classic paper; uses amortized free bit complexity; should be presented)
- Irit Dinur, Shmuel Safra: The importance of being biased. STOC 2002: 33-42 (Best NP-hardness of approximating Vertex Cover, 1.36, some one must present this paper, please!)
- Uriel Feige, Joe Kilian: Zero Knowledge and the Chromatic Number. J. Comput. Syst. Sci. 57(2): 187-199 (1998). Also, CCC 96. (Best NP-hardness of approximating Chormatic number.)
- Hardness of approximating the min distance of linear codes
- Dumer, Micciancio, Sudan, Hardness of approximating the minimum distance of linear codes, FOCS 1999, also IEEE Transactions on Information Theory, 49(1):22-37 (Jan. 2003).
- Cheng and Wan, A Deterministic Reduction for the Gap Minimum Distance Problem, STOC 2009 (Hardness of approximating the distance of a linear code - the result is better than the Dumer-Micciancio-Sudan result, so it is better to present this paper)
- Venkatesan Guruswami, Prasad Raghavendra, Hardness of Solving Sparse Overdetermined Linear Systems: A 3-Query PCP over Integers, ECCC TR09-020. (A generalization of Hastad's 3-bit PCP.)
- Chuzhoy et al, On the approximability of some network design problems, SODA 2007
- R. O'Donnell, Y. Wu, Conditional hardness for satisfiable 3-CSPs, STOC 2009
- Guruswami et al, Hardness of learning half-spaces with noise, FOCS 2006
- Matthew Andrews, Lisa Zhang: Logarithmic hardness of the undirected edge-disjoint paths problem. J. ACM 53(5): 745-761 (2006)
- Matthew Andrews, Julia Chuzhoy, Sanjeev Khanna, Lisa Zhang: Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion. FOCS 2005: 226-244

- Prasad Raghavendra, Optimal Algorithms and Inapproximability Results for Every CSP?, STOC 2008 (Co-winner of the Best Paper award and winner of the Best Student Paper award)
- Gowers uniformity, influence of variables, and PCPs, STOC 2006
- Conditional hardness for approximate coloring, STOC 2006
- On the hardness of approximating multicut and sparsest cut, CCC 2005
- Khot & Regev,Vertex cover might be hard to approximate to within 2-ε, JCSS 2008, FOCS 2002. (Optimal UGC-hardness of vertex cover)

- Eric Blais, Testing juntas nearly optimally, STOC 2009