How to write a sincere reply to a very positive reply from a professor? My roomie has recently been applying for PhD programmes. He's particularly interested in the one led by prof X, so the other day he sent an email presenting his research experiences and showing his interest in prof X's research. He got a very positive reply from prof X today:


  Hi XXX, Yes I am planning to accept PhD students this year. I strongly encourage you to apply... please indicate theory as your interest and/or mention my name as faculty of interest in your application. 


This sounds like great news. So my roomie decides to reply and tell X he's really enthusiastic about applying to this programme. But neither of us has any idea what would be an appropriate way to do this. Would simply writing like "thanks for your help prof X I will definitely apply!" be too short and not show enough enthusiasm? Could anybody give some advice?
Thank you for your reply, Professor X. I am happy to hear that you're interested in taking on a PhD student for next year, I will definitely be putting in an application for the position. I look forward to hearing more about the project in the future. Regards, me.


You don't need to throw them a parade, but take a little more time to email them something other than just, 


  Thanks a bunch!