How to write a personal statement for a "PhD orientation program" (in mathematics)? I'm about to apply for a short "visiting and orientation program" at a large prestigious university where I may be interested in applying for graduate school. 


  This program lasts a couple of weeks and consists of 
  
  
  several courses that present the research done by every research group in the math department;
  meetings with the faculty members and current students. 
  


For the admission, I'm required to submit a statement of purpose. 

Now, the scope of statements of purpose written for graduate admission is quite clear: they need to show research potential and experience in an area of interest. 

However, I'm confused about what makes a good candidate for a PhD "visiting and orientation program". 


  That is, what kind of information, qualification, and motivations may admission committees be looking for in a candidate for such a program?
I speculate as I do not know the faculty and their philosophy. 
To my own experiences (PhD 20 years ago, and had some DBA students on my own before I went back to industry), I would suggest you differentiate between research potential and experience against "visiting and orientation". For an orientation program, ...


I would expect people to be open to all directions of learning, in our own as well as in different areas.  
The ability to network, 
ability for out-of-the box thinking, 
ability for telling ideas but also listening. 


Think about onion rings around the exploration of your topics.

How do you show those abilities? Examples from your life?