Thank you all for your replies...
Tell me also this please - I have used the word "could" at the beginning of my sentence. Is this correct? Maybe I should have used "would" instead? What is the difference?
You are right, you should be using "would"
The difference is that
could asks the question, is the professor capable of doing this. Obviously the answer is yes, he/she is capable.
Using
would means is the professor willing to do this. Again, obviously, it is up to the professor to decide whether or not to do this. You are asking if he/she is willing to do it.
Good for you for catching the difference.
I am not a teacher.