At the headquarters of the New York Police Department, in a high-ceilinged, wood-floored room, Erhan Yildirim is speaking to a group of officers. As he lists facts about Islam, they crack their gum and tap their feet. Yildirim is slighter, shorter and snazzier — in a sleek Turkish-made suit — than most of his audience, and he speaks with a Turkish accent to their Brooklynese. Yildirim, as the part-time civilian liaison of the NYPD to Muslims throughout the city, is a man assigned to bridge cultures. “I’m the PR,” says Yildirim, and the PR goes two ways: At once, he is trying to redeem the name of the police department to Muslims and the reputation of Islam to police officers.