DE: Let me first say: welcome to our department! What type of mathematics are you interested in?

HZ: My research lies in geometric combinatorics. I am interested in polytopes, one of favorite discrete objects studied by ancient Greeks.

DE: Do you have a favorite open problem?

HZ: Günter Ziegler (now president of FU Berlin) proposed the following open problem: Consider a 4-dimensional polytope. Denote by f_i the number of its i-dimensional faces (for example, f_0 is the number of vertices) and define the fatness as the ratio (f_1+f_2)/(f_0+f_3).
Question: Is fatness bounded? The current record for the upper bound is around 9. No improvement has been made in the last 20 years.

DE: What types of courses are you most excited to teach?

HZ: I would love to teach anything related to combinatorics or discrete geometry. Linear algebra is also a fun course to teach; I probably already have taught it too many times.

DE: What have you liked the most about Hawai’i so far?

HZ: The mountains here are impressive. Dazzling in the morning sun and fading in the gray evening mist, they afford a myriad of scenes.

DE: Can you tell us something about yourself that might be surprising?

HZ: I can think of two things.
1. I failed two prelim exams in the first year of the PhD program; at that time I was very focused on writing a Kung-fu novel (which is, of course, not an excuse).
2. I did not plan to be a mathematician. In high school I thought it would be cool to become a reporter for National Geographic, and so I planned on studying archaeology or geology or journalism in college. My dream did not come true… Is it good or bad?