At what point can I call my professor by their first names as an undergraduate research student? I'm currently working closely with a professor on a research project as an undergrad student. I always address her by her last name: Dr.xx. However, this makes me feel distant from her.. I am wondering by which point I could call her by first name? 

Here is some background info:
I got to know her in person by taking a class taught by her and then started working together on this project at the end of last term. We had meetings together for a few times and exchanged a few emails back and forth. She always addressed herself by her first name in the email but I insisted called her Dr.xx to show my respect. However, some of her grad students in the lab are calling her by first name...

Thanks!
Ask her!

Forget about figuring out when you can address her by her first name. Be up front, and ask politely if you can address her by her first name. 

Do not be offended if she declines. 

Naturally, if in conversation she invites you to call her by her first name, then that's pretty clear.