There are three papers that operate and each of them have a crest item they will give out if you answer some questions for them.

Each item gives you an achievement for co-operation.

On Karnak the Ul'dah GM appeared
Sunday, 1 January
12:30PM (GMT+0)
9:30PM (JST)

There are other threads for battles etc so this is no different. Please post your sightings so we can all work out when they will be showing up.