High school seniors hoping for an advance nod from Harvard University have swamped it with an unusually large group of 4,245 early applications that represent the most economically and ethnically diverse in the school’s history. Harvard is one of many colleges to be deluged with early applications this year. At Northeastern University, applications to the non-binding early action program are up 14 percent, and Boston University’s binding early decision program has seen a 21 percent rise.