Bourbaki’s death announcement mentions ‘Respectively their father, brother, son, grandson, great-grandson, and grand-cousin’ giving us 5 generations, among which 4 generations of Bourbakis.

Here’s the punchline : a large chunk of the Connes-Marcolli book Noncommutative Geometry, Quantum Fields and Motives can be read as an exploration of the noncommutative boundary to the Langlands program (at least for $GL_1 $ and $GL_2 $ over the rationals $\mathbb{Q} $).

This time we will describe the points of the arithmetic site with Steinitz’ supernatural numbers and adele-classes.

In Bourbaki est mort, CQFD, Pierre Cartier asserts: “Yes, Bourbaki is dead. He was killed by May 68!”

The Leech lattice was, according to wikipedia, ‘originally discovered by Ernst Witt in 1940, but he did not publish his discovery’ and it ‘was later re-discovered in 1965 by John Leech’. However, there is very little evidence to support this claim.

Now that Alain Connes’ talk at the IHES is online, giving hints to prove some of the statements of the arithmetic site, we can continue our story.

From left to right: Jacques Dixmier, Jean Dieudonné, Pierre Samuel, André Weil, Jean Delsarte and Laurent Schwartz on some terrace during the 1951 ‘Ecumenical’ Bourbaki summer-conference in Pelvoux. Where, exactly, was this?

Last week, the IHES shared Pierre Cartier “Les mathématiques de Grothendieck (un survol)” (talk in English though). I don’t know whether this was part of the evening activities of the conference for Maxim Kontsevich 50th birthday (one Groth-activity/conference is quickly becoming the standard…).