noncommutative Fourier transform

At the
noncommutative algebra program in MSRI 1999/2000, Mikhail Kapranov gave
an intriguing talk Noncommutative neighborhoods and noncommutative Fourier transform
and over the years I’ve watched the video of this talk a number
of times. The first part of the talk is about his work on Noncommutative geometry
based on commutator expansions and as I’ve once worked through it
this part didn’t present problems. On the other hand, I’ve never
understood much from the second part of the talk which claims to relate
these noncommutative formal neighborhoods to _noncommutative Fourier
transforms_. The string coffee table has a post Kapranov
and Getzler on Higher Stuff linking to two recent talks by Kapranov
on noncommutative Fourier transforms at the Streetfest. Marni
Sheppeard made handwritten notes available. I definitely should find the time
to get through them and have another go at the Kapranov-video…