Awhile back, someone was asking for this, and I gave them some "starter" code that was almost right. I've gone back and packaged this as an official add-on to the Events Calendar mod. You can find it here.
From the readme:

This add-on requires the Events Calendar MOD by Red1 (found at SnitzBitz). It adds advanced search functionality for the Events Calendar. You can search by Topic, Event, or both, and events are differentiated from normal topics with an "Event" label.

Enjoy.<