The S2719DC has HDMI 2.0 and USB-C inputs. What output connector types are available on your GTX 1080? It should have at least one HDMI output, in which case you should be able to connect your HDMI cable to that. Otherwise, if your 1080 has a DisplayPort output, you MIGHT be able to use a USB-C to DisplayPort cable, but those are meant to connect a USB-C port on a laptop to a DisplayPort input on a display, and I don't know if it will work in the other direction as would be needed here.
Regular DVI would not allow the display to work at its maximum resolution (and there's no point in a DVI-I to VGA adapter anyway because the display doesn't have DVI or VGA), and HDMI to VGA would not be useful either because VGA would not work at the display's maximum resolution and would look bad anyway because it is an analog signal. You also can't use those types of adapters to send a VGA signal into an HDMI input; you can only send an HDMI signal into a VGA input if the conversion is done within the cable/adapter.
So again, look at the connector types available on the 1080. I believe all recent NVIDIA cards have at least 1 HDMI output, but if not, let us know what's available.