I would ask Carol Dweck to autograph my copy of her book, mindset.

Beyond that, I might ask about research and application:
1) Research.
Mindset (copyright 2006) was based on research. I might ask if there is new research spawned by her book, and what the central questions are. On the other hand, I might ask if research has been completed since mindset was published which might re-emphasize certain points in mindset... call other earlier research into question... refine any points... etc.
2) Application.
In the ongoing nature/nurture discussion, mindset relates to nurture. Are there specific schools which have implemented a policy of encouraging growth mindset, and what do the results show? Similarly, is there reader mail which indicates that families have dedicated themselves to a growth mindset, and achieved positive results (anecdotal evidence)?

Other posters upthread have shared some recent threads with lively discussion of mindset. Another such thread is Gifted girls.

Regarding Carol Dweck speaking, there are several youtube videos, including Teaching a Growth Mindset.

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Our head honcho is an avowed "Dweckian". I want to understand why.
Stories on pp63-67 may help explain this? Possibly these stories indicate that adopting a growth mindset may help close any achievement gap and/or excellence gap, in a positive way (without capping the growth of the top performers). Also pp196-202. ETA: Another post discusses that a possible gap in mindset may result in capping growth of students at the top.