The Martian Wikia

Project Elrond is the name of the secret meeting between Annie Montrose, Venkat/Vincent Kapoor, Mitch Henderson, Bruce Ng, Teddy Sanders and Rich Purnell.

It was named by Venkat/Vincent after the Council of Elrond in Lord of the Rings in which they had a secret meeting to make a momentous decision.

Annie was the only one who didn't get the reference (apart from Teddy who wasn't there at the time of the conversation) She then implied that they were nerds who never got laid in high school.

In the meeting, Vincent reveals that astrodynamicist Rich Purnell had figured out a way to get Mark off of Mars by Sol 549, 30 sols before he starved.

The plan which was dubbed 'The Rich Purnell Maneuver' was originally shot down by Teddy but (allegedly) Mitch secretly emailed the maneuver to the Ares III crew and they went against NASA and went through with the plan anyway.