In the display’s manual, on page 11, there’s a list of supported HDMI “standard” resolutions:
480p, 480i, 576p, 720p, 1080p, 576i, 1080i
Further down, on page 12, where they state it’s HDMI 1.4, there’s an important footnote (emphasis mine):
Does not support HDMI 1.4 optional specification, includes HDMI Ethernet Channel (HEC), Audio Return Channel (ARC), standard for 3D format and resolutions, standard for 2K and 4K digital cinema resolution.
So, unfortunately, it can’t do anything higher than 1080p via HDMI.
An active HDMI-to-Displayport converter may be available, though finding them will be very hard because the other way (DisplayPort → HDMI) is in much higher demand. It’ll probably be about $100.
Update: While researching further, I didn’t find anything. So it seems that no such adapter is available or even announced. I found a single HDMI→DP adapter, which is limited to 1080p.
A few people had success in experimenting with custom display timings at a reduced refresh rate and got an earlier Dell model (U2711) to display 1440p at 50 Hz via HDMI, see here (last posts). Whether this is possible largely depends on your GPU and its drivers.