Is there a way to trigger an email to the user when there is a project task assigned to them?
Here is the link of adding tasks to a project
Working with Tasks
As you can see, there is an entry which says Assign To: Assuming I pick a user or a role which is in turn mapped to a user. Can i trigger an email when a task is assigned with in a project?
Check PROJECT APPROVAL WORKFLOW
Update it to add send email task. You may have to create a custom email workflow step and add it the workflow:
Adobe Experience Manager Help | Creating custom AEM workflow steps that send email messages
Send Template'd E-mail