What is noncommutative geometry?

I’m giving an introductory seminar talk this afternoon to let new graduate students know about the noncommutative geometry research group at Penn State and what it is we do.  My plan is to begin with a short “elevator speech” about NCG (a few minutes) and then follow it up with four ten-minute vignettes of “Things we talk about a lot”

• Hilbert space
• K-theory
• Curvature
• Expanders

and at least to indicate the existence of all of the $$(4 \times 3)/2 = 6$$ connections among these concepts as well.  Here is a link to a scanned version of my notes for the talk.