mac Studio to Dell Monitor

Mac is very fussy about HDMI cables.

HDMI cables you want for HDMI-only Displays (higher resolutions than 720p TV sets) are marked as Certified with an anti-counterfeiting tag and are labeled:

"Premium High Speed HDMI cable" or that + "with Ethernet"  --OR--

"Ultra High Speed HDMI cable" or that + "48G"

Cables with No Certification tags are good for your standard 720p TV set, and not much more.

HDMI was invented for HD TV sets. it works great at its original resolution of 720i or 720p. At higher resolutions, it quickly develops issues that are complex to solve, and the cables and adapters required to solve are NOT intuitive. 

+1 You need to get and use a USB-C to DisplayPort cable between the Mac Studio and that Display.

for example > https://www.amazon.com/Silkland-DisplayPort-Thunderbolt-Compatible-MacBook/dp/B09M38CXZ3/ref=pd_bxgy_img_sccl_2/138-4621538-9473606?

That photo cuts off the part of the back panel where the video input ports are. But I see "U3415Wb" to the far right of the "MODEL NO."

https://dl.dell.com/manuals/all-products/esuprt_display_projector/esuprt_display/dell-u3415w-monitor_user%27s%20guide_en-us.pdf

Going by Page 10 of the manual, when you're looking at the bottom of the monitor, with the screen lying face down, there are several inputs. Left-to-right:

• 3 – HDMI port connector
• 4 – DisplayPort in connector
• 5 – Mini DisplayPort in connector

I would suggest using one of:

• A USB-C to DisplayPort adapter cable, running from one of the Studio's rear-panel USB-C ports to the monitor's DisplayPort in connector.
• A USB-C to Mini DisplayPort adapter cable, running from one of the Studio's rear-panel USB-C ports to the monitor's Mini DisplayPort in connector.
• A HDMI cable, running from the Studio's rear-panel HDMI port to the monitor's HDMI connector

Note: If your Mac Studio has a M1 Max or M2 Max processor, do not connect monitor cables to front-panel USB-C ports. On Studios with the Max chips, the front-panel ports only carry USB – not DisplayPort.

You'll have no problem connecting it. You can use the HDMI port on the monitor with a standard 4k rated HDMI cable to connect it to your Mini's HDMI port. Clean and simple.

Were you able to get the monitor configured with one of the listed options? I own the monitor and am considering a Mac Mini.

Gary at MacMost is a great source for Mac info. He says that HDMI can sometimes be finicky for hooking up a Display. To avoid problems, Gary says use a USB-C to DisplayPort cable.

Just noticed something else on page 12 of the manual.

This monitor has a resolution of 3440 x 1440 pixels. That's a rather odd-ball resolution. It is lower than the UHD 4K (3840 x 2160) pixel resolution that your Studio can support without bringing Thunderbolt into the picture – but still, it's not one of the common ones like 1920 x 1080, 1920 x 1200, 2560 x 1440, or 3840 x 2160.

I don't know if that's going to cause problems in terms of macOS failing to offer the resolution options that you need for that monitor.

The refresh rate (60 Hz) should not be an issue.

3440 x 1440 refers to a display resolution commonly known as UltraWide Quad HD (UWQHD) or 1440p UltraWide.