I am a member of a large group (academic department) using a central GNU/Linux server. I would like to be able to install web apps like instiki, run version control repositories, and serve content over the web. But the admins won't permit this due to security concerns. Is there a way for them to sandbox me, protecting their servers in case I am hacked? What is the standard solution for a problem like this?
The standard solution to this is virtualization. You create a virtual machine containing your particular configuration and then have it hosted in some server.
There are several different levels of virtualization. XEN HVM and Linux KVM are examples of hypervisor which can run an unmodified instance of a guest operating system. Each instance gets allocated its own memory, the rest of the resources of the computer can be shared.
LXC, OpenVZ and Linux-VServer are more lightweight, extensions of the chroot-based sandboxing approach. The benefit in such case is that all instances can have access to full resources of the machine (if permitted), but all instances share a common appropriately exteded kernel. Even in this case you could have a different Linux distribution instance running on your Debian server.
You can connect to NFS from all of the above virtual machine instances.