It would be fairly simple to use a redirect to take people from example.com to example.com/events (and there are lots of plugins that could help with this) – that’s exactly what we do on our WP Shindig demo site.
If you want to actually make the root path at example.com the main calendar page that’s slightly more involved and there are numerous things you may need to consider, depending on how deep you need the customization to be. For that sort of change you’d have to figure things out for yourself 🙂