Hi Danielle,
Thanks for reaching out to us! I’ll help you here…
Unfortunately there are no shortcodes to embed the community submit an event form or the list events the user has created 🙁
This feature was suggested a while ago in The Events Calendar user voice page, please do up vote it and you can also comment on thy you think this an important feature: Shortcode for Community Events.
Maybe the membership plugin has a code to insert in a given template or a way to call the auth form via code?
Sorry not to have a better answer for this,
Best,
Nico