Around these parts, we call it the Supreme Court's BFC, or Big [Fall] Conference. Others call it the "long" conference. We're sure the clerks have their own nicknames for annual stack of around 2,000 petitions.
This year's BFC falls on Monday, September 29, and when it gets here, the justices and their clerks will have their work cut out for them, with thousands of petitions seeking SCOTUS review. Nearly all of those petitions, of course, will be denied, but each petition has to be reviewed by both the cert. pool (eight justices' combined clerks, who divide and conquer) and Justice Samuel Alito's independent team of clerks.
Let's trace the steps of these petitions: