I've started working for a company that demand I use a wired ethernet connection while working for them. I work from home, and they're based in a foreign country, so they're not likely to be sneaking around my house watching me while I work. My question is whether they can tell from their end if I'm using a wired or wireless connection from my laptop to my router.
There is no simple way for them to determine categorically if you are using a wireless connection, but it is possible to infer it.
the bottom line is that WIFI almost always has higher and more variable latency and more limited bandwidth then a wired connection - and use of a wireless connection can be inferred - but probably not proven - by looking at these characteristics - Some ways they may be able to do it -
If they are looking closely, they MAY be able to detect you are using wireless - particularly if you are using a VPN from your desktop. It could be possible to infer the use of wireless by looking at latency characteristics across your VPN and comparing those with latency characteristics to your router.
A very determined system administrator might also be able to make inferences by looking at web logs and seeing how your response times differ from the norm for your geographic location, and how variable they are - as WIFI connections are often quite variable. It would be difficult to use this method to conclusively prove anything though.