PCP research proposal Hi I am taking an undergraduate taking a course in Probabilistic checkable Proofs. I will greatly appreciate if you can suggest some good research ideas and pertaining reading for someone who is just getting started. Thanks!
Here are some recent papers on PCPs with small query complexity that I found interesting:


arxiv.org/pdf/1305.1979
eccc.hpi-web.de/report/2013/179/download
wisdom.weizmann.ac.il/~dinuri/mypapers/DH.pdf   
eccc.weizmann.ac.il/report/2015/085   
cs.utexas.edu/~danama/papers/par-rep/final3.pdf   
cs.utexas.edu/~danama/papers/par-rep-limit/paper.pdf   
eccc.hpi-web.de/report/2016/160


Also, this paper is somewhat older, but it is interesting and can help understanding the context to some of the previous papers. In addition, if I may recommend a paper of my own, I think this paper contains open problems that might be useful.