Abstract. The title, minus the last 5 words, completely describes what I want to share with you while we are in Montpellier. I'll tell you that Drinfel'd associators are the solutions of the homomorphic expansion problem for u-knots (really, knotted trivalent graphs), that Kashiwara-Vergne-Alekseev-Torossian series are the same for w-knots, that the two are related because u- and w- knots are related, and that there are strong indications that "v-knots" are likewise related to the Etingof-Kazhdan theory of quantization of Lie bialgebras, though some gaps remain and significant ideas are probably still missing. Kontsevich's quantization of Poisson structures seems like it could be similar, but I am completely clueless as for how to put it under the same roof.
Montpellier Handout: m1.html, m2.html, m.pdf.
Further Handouts: Bonn-0908, Luminy-1004, Copenhagen-081009, Dancso on Furusho, Oporto-0407.
All Handouts in one big file: booklet.pdf.
Other Lecturers' Videos. Alekseev's Talk 1, Alekseev's Talk 2, Enriquez' Talk, Torossian's Talk, Furusho's Talk, Calaque's Talk.
Blackboard Shots for Burgunder's "Les idempotents de Lie
et la conjecture de Kashiwara-Vergne":
1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
(sorry, my video camera run out of battery)
Pictures. Image Gallery: Places: Montpellier, June 2010.
All source files: m.zip.