Can this monitor run 144hz with HDMI?

Solution
DisplayPort can handle higher bandwidth than HDMI for use of high refresh rates but need to be careful with the cable you buy though. Just make sure the cable you buy is HBR2 standard and you will be fine. http://www.displayport.org/cables/how-to-choose-a-displayport-cable-and-not-get-a-bad-one/



Display port is definitely the ideal choice, the quality is crisp and the response time on the monitor feels great.
 
DisplayPort can handle higher bandwidth than HDMI for use of high refresh rates but need to be careful with the cable you buy though. Just make sure the cable you buy is HBR2 standard and you will be fine. http://www.displayport.org/cables/how-to-choose-a-displayport-cable-and-not-get-a-bad-one/

 
Solution
Despite what you may read, there is no such thing as a DisplayPort 1.1 cable and DisplayPort 1.2 cable. A standard DisplayPort cable, including the so-call DisplayPort 1.1 cables, will work for any DisplayPort configuration including the new capabilities enabled by DisplayPort 1.2, including 4K and multi-stream capabilities. All standard DisplayPort cables support RBR, HBR (High Bit Rate), and HBR2 (High Bit Rate 2), which can support 4K at 60Hz, or up to four 1080p displays using multi-stream.