Swizz Beatz and Alicia Keys met downtown Monday after performing blocks from each other uptown. After Beatz delivered a song composed for the Knicks at the Beacon Theater, he threw a 50th birthday party for a friend at the Meatpacking District restaurant Catch. The producer and 25 friends then headed up to Catch Roof, while Beatz’s wife arrived downstairs for a late dinner following her Lincoln Center concert. Keys then joined her hubby on the roof, and the two hopped into a DJ booth to spin songs, including Keys’ single, “New Day.”