These three young theater figures are moving into the public eye with confidence and a determination to expand horizons for themselves and their audiences. When Hammaad Chaudry was 19, he moved away from Edinburgh, where he grew up the son of Pakistani immigrants, to attend the University of Surrey, about an hour outside of London. He planned to be a lawyer. But after marching to protest the war in Iraq, Mr. Chaudry grew more interested in political activism — and he found his law studies to be tedious and unfulfilling. He found his voice elsewhere: writing plays. At the end of his first year at university, he joined a writing program at the Royal Court Theater in London geared toward young Muslim writers.