I had this problem with my 1080 and just solved it yesterday. You'll need to install using integrated graphics, install nvidia drivers, then switch back to the 1080.
First, make the live USB for Ubuntu. Go into your BIOS settings, and enable both iGPU and the GPU. Plug in your monitor to the HDMI port on the motherboard, and install Ubuntu as normal. After installation, boot Ubuntu and install the nvidia-367 drivers. Once that's done, you can plug your motherboard back into the the GPU and use Ubuntu.
Here's the PPA you need for nvidia-367: https://launchpad.net/~graphics-drivers/+archive/ubuntu/ppa
One problem I haven't solved is that the monitor turns off while Ubuntu is loading. It turns back on at the login screen. Not sure why :/