Sony has begun sending out invites for their E3 press conference, and the invitations reveal that the conference will be held on Monday, June 9th at 6 PM.
Below are other press conferences that have also been confirmed so far:
EA: Monday, June 9th at 12:00 PM PST
Nintendo Direct: Tuesday, June 10th at 9:00 AM PST
Microsoft: Monday, June 9th at 9:30 AM PST
E3 runs from June 10th to June 12th.