text: In the summer of 2004 , he met and began dating actress Michelle Williams on the set of Brokeback Mountain , and their daughter , Matilda Rose , was born on 28 October 2005 in New York City .
simplified: Ledger was engaged to actress Michelle Williams , whom he met while filming Brokeback Mountain . Their daughter , Matilda Rose , was born on October 28 , 2005 in New York City .