I have the same monitor and run a 580 gtx.
If you use HDMI you get 1080p max resolution as others have said -- I've never been able to get a higher res using HDMI. I have my PS3 connected via that.
My computer via DL DVI and my mac through its display port both at 2560x1600. It just gives you all the options which is one reason we paid so much for one.