I was last week in Verbania, Italy, for the conference in honor of the 150th anniversary of the Riemann Hypothesis, which was also the inaugural activity of the new RISM (*Riemann International School of Mathematics*). It was a very pleasant occasion. Already during the Sunday afternoon presentation (open to a general audience), there was a beautiful historical lecture by R. Narasimhan, who explained in particular that “monodromy” was invented by Riemann, in a course on hypergeometric functions which barely escaped being forgotten: only three students attended it, two of whom dropped after a few lectures, and the last one publicly stated (years later) that he hadn’t understood a word of what Riemann was saying, but had stayed because his father (or maybe someone else: I have forgotten this detail) had told him that Riemann was the new man in mathematics, and that he should follow his lectures… Which he did, taking faithful notes — though he did so in a special type of shorthand which almost made them useless a few years later when time came to transcribe them.

The main lectures were especially pleasant (for me at least) in areas of geometry which I am not usually involved with: learning the current state of the art in an interesting field of mathematics can be quite a bit more enlightening if it comes from two or three hours of lectures coming from real experts (especially if there are opportunities to discuss any question afterwards). So I particularly liked the short course by J-P. Demailly, the one by J. Cheeger, and the two lectures by C. Voisin, who explained very clearly the current knowledge of both the topological constraints for Kähler varieties (what is apparently called the “Kodaira problem”), and what is currently the best that is understood about the notorious Hodge conjecture.

The slides of many lectures can be found on a page of the conference web site, and others will be posted soon (including mine; the beamer presentation can already be downloaded here).

The conference was all the more enjoyable due to the very pleasant setting by the shore of the Lago Maggiore, and although the weather was not uniformly good, the best day was Wednesday, when the excursion to the Borromean Islands was organized. The quality of the organization can be seen from the rather fancy notebook that was given to participants at the beginning:

Acc. to Arnoldin “Kelper’s second law and the topology of Abelian integrals” in Kvant Selecta, the use of the idea of monodromy dates back to Newton’s proof of the non-algebraicity of the volume function of plane “ovals” inPrincipia, book 1, lemma 28.…so that explains the link at http://www.monodromy.com