Whether they can or cannot track you, and to what extent, depends on a lot of factors. Perhaps a separate, but possibly overriding, question should be "do they have reason to?".
If you've purchased the laptop from the University such that it is now your own property, and you are not using any University network resources, then they do not likely have any good reason to track you - and probably aren't. However, if the laptop is on loan from the University or you are using the University's network (via direct connection, VPN, Wi-Fi, or otherwise), the University may still have reason to monitor your usage.
If you accepted the laptop as-is from the University, with their pre-loaded OS and software, and did not wipe the hard drive and re-load the OS yourself, then it is always possible, however likely or not, that they may have some monitoring software on the system which could track your usage. This can be down to the finest detail - keystroke logging, screen capturing, webcam/microphone recording, etc - and without your knowledge. The only way to ensure this is not happening is to wipe the drive and load your own OS.
If you are ever using the University's network resources, they may also be monitoring your traffic. This includes any data you send in the clear over HTTP, FTP, Telnet, etc. as well as the destination or origin of any encrypted traffic such as HTTPS, SSH, etc.. If you are still using the University's standard OS & software load, it's also possible they may have an SSL Proxy configured in your Trusted Root Certificates so that they can read some of your encrypted traffic as well.
The only effective way around network-based monitoring is to use a trusted VPN provider, or a secure anonymizing service such as TOR. Even then, if your VPN/anonymizing service provider relies on SSL certificates and you are still using the University's standard software configuration, this protection may be still stripped via SSL Proxy.
Your best bet, if you don't want the University to be monitoring you, is to use your own trusted hardware that you've configured yourself and stay off their network.