. >> additional support has been provided by rosalynn p. walterbernard and irene swartz, sue and edgar walken heim iii, the cheryl and phillip mills team family, judy and josh west on, and by contributions to your pbs station from viewers like you. thank you. >>> welcome to the program, everyone. i'm christiane amanpour in hanoi where a summit between the united states and north korea came to an abrupt end today without an agreement on denuclearization. already there are conflicting accounts from both sides as to what actually happened behind closed doors. president trump says that while he still hopes for further progress in this process, the talks broke down over sanctions relief. >> basically, they wanted the sanctions lifted in their entirety. and we couldn't do that. they were willing to denuke a large portion of the areas that we wanted but we couldn't give up all of the sanctions for that. >> the president says that he's unwilling to trade full sanctions relief for partial denuclearization. so that is why he walked but flying home to washin