Your local sys-admin can track your browsing history if they can get you to install a certificate on your (or their machine) - in which case they can man-in-the-middle your connection.
If you have your own device and are sure they don't have a certificate, the best they can do is get a feel for what sites you are going to by looking at the IP address of the sites and the traffic profile (ie lots of traffic could imply downloading of videos), and IP addresses of big sites normally have reverse lookup. They can also use DNS records to find the DNS you requested if you are using their DNS servers which is likely.
If the sysadmin does not have access to your machine to install the cert or local software, they can't use the network to see what page(ie folder) you are going to in the site as this is encrypted (This information is sent in the header of your request, which happens after SSL is negotiated).
Source: I am a system administrator who handles sites with HTTPS and from time-to-time manually do HTTP / HTTPS requests to check corner cases.