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TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20310309T030000 RDATE:20311102T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20320314T030000 RDATE:20321107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20330313T030000 RDATE:20331106T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20340312T030000 RDATE:20341105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT UID:ad5cdc055dd8c5aaed1078eef72dfbf8 CATEGORIES:Pre-Defense CREATED:20190823T084029 SUMMARY:Hardness of Approximation and PCPs. LOCATION:CoRE A (301) DESCRIPTION;ENCODING=QUOTED-PRINTABLE:
The famous PCP (probabilistically checkable proof) theorem states that o
ne can verify a proof by reading the proof at a very few locations such tha
t if the proof is correct, then the verifier always accept the proof where
as the verifier rejects the incorrect proof with high probability. The PCP
theorem has applications in proving hardness of approximation results for m
any optimization problems. This thesis is centered around proving hardness
results as well as studying the components in the proof of the PCP theorem.
A low degree test is one of the important components in proving
the PCP theorem. In this talk, I will talk about a recent result about a l
ow degree test. Our main result is a new combinatorial proof for a low degr
ee test that comes closer to the soundness limit, as it works for all epsil
on ≥ poly(d)/|F|^{1/2} , where d is the degree. This should be compared to
the previously best soundness value of epsilon ≥ poly(m, d)/ |F|^{1/8}. Our
soundness limit improves upon the dependence on the field size and does no
t depend on the dimension of the ambient space. Our proof is combinatorial
and direct: unlike the previous proofs, it proceeds in one shot and does no
t require induction on the dimension of the ambient space.