Paul details a meeting with Peter, James and John in Galatians 2:1-10 (ESV):
Then after fourteen years I went up again to Jerusalem with Barnabas, taking Titus along with me. I went up because of a revelation and set before them (though privately before those who seemed influential) the gospel that I proclaim among the Gentiles, in order to make sure I was not running or had not run in vain. But even Titus, who was with me, was not forced to be circumcised, though he was a Greek. Yet because of false brothers secretly brought in—who slipped in to spy out our freedom that we have in Christ Jesus, so that they might bring us into slavery—to them we did not yield in submission even for a moment, so that the truth of the gospel might be preserved for you. And from those who seemed to be influential (what they were makes no difference to me; God shows no partiality)—those, I say, who seemed influential added nothing to me. On the contrary, when they saw that I had been entrusted with the gospel to the uncircumcised, just as Peter had been entrusted with the gospel to the circumcised (for he who worked through Peter for his apostolic ministry to the circumcised worked also through me for mine to the Gentiles), and when James and Cephas and John, who seemed to be pillars, perceived the grace that was given to me, they gave the right hand of fellowship to Barnabas and me, that we should go to the Gentiles and they to the circumcised. Only, they asked us to remember the poor, the very thing I was eager to do.
Luke also details a meeting of Paul, Barnabas and others from Antioch with the church, apostles and elders in Jerusalem in Acts 15:1-5 (ESV):
But some men came down from Judea and were teaching the brothers, “Unless you are circumcised according to the custom of Moses, you cannot be saved.” And after Paul and Barnabas had no small dissension and debate with them, Paul and Barnabas and some of the others were appointed to go up to Jerusalem to the apostles and the elders about this question. So, being sent on their way by the church, they passed through both Phoenicia and Samaria, describing in detail the conversion of the Gentiles, and brought great joy to all the brothers. When they came to Jerusalem, they were welcomed by the church and the apostles and the elders, and they declared all that God had done with them. But some believers who belonged to the party of the Pharisees rose up and said, “It is necessary to circumcise them and to order them to keep the law of Moses.”
The account in Acts continues in much greater detail including the text of a letter that was produced and circulated to the Gentile churches. While there are many parallels between the two accounts, there are at least two problems with linking them:
Paul says the meeting was private and with only a few influential people (potentially just James, Cephas, and John) whereas Luke makes clear the meeting was public.
The letter to the Galatians makes no mention of the letter from the Jerusalem Council, which would seem to win Paul's case definitively.
If we are to identify the Galatians account with the Jerusalem Council, how are we to address these (and other) objections?
If we say these meetings are separate, which came first and why was the second meeting necessary given the near perfect overlap of the agenda?