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…