Purchased domain: joinmyconference.com in 2007. trademarked myconference in 2010 by someone else. they claim infringement Do I have to cease & desist?

If they did not have use of the trademark prior to your registration of your domain in 2007, you do not have to stop using your domain and could possibly even seek to have their registration canceled. It is a more complicated question if their use goes back to, e.g., 2006, and they only registered it in 2010.