I recently accepted an offer to the Ph.D program in a university. The director of graduate studies contacted me and noted that "you may want to contact Prof. X for any questions regarding your interests in the field". As the title indicated, I want to ask what kind of questions can I ask?
Let me clarify the situation a little bit. I majored in Algebraic Topology and my bachelor dissertation was on this topic, too. But like other fields, Algebraic Topology has many topics to study. Prof. X seems to be interested in my achievement and dissertation (he contacted me before the offer was made). However, I have to say that I do not see the connection between my knowledge and his recent articles. So I really want to ask if he can illustrate his topics. But I am afraid this question could leave a bad impression as this is a matter I can figure out myself (but having someone point it out is nicer).
To sum up,
1) Can I ask him to illustrate his work because I do not see the connection?
2) What are the questions I can and should ask?
Thank you in advance