Proof, the 2001 Tony Award and Pulitzer Prize-winning play by David Auburn about a father and daughter who have more similarities than they might realize, begins its Broadway run at the Booth Theatre on March 31. The official opening is set for April 16, with the limited engagement scheduled to run through July 19. Hamilton Tony winner Thomas Kail directs the first-ever New York revival, which stars Ayo Edebiri a…