Philippe Michel and myself are organizing a Winter School in January 2019 on the topic of trace functions and their applications to analytic number theory. There is a very basic web page for the moment. Most importantly, the application form, which will be setup by the conference center where the school will be held, is not yet available.

The setting is the CSF (Congressi Stefano Franscini), which is a conference center of ETH located in Ticino (so this will be a good occasion to practice italian). The school is intended essentially for current PhD students, together with a smaller number of recent PhDs ; the total number of participants should be around 50. There will be five minicourses, given by T. Browning, Ph. Michel, L. Pierce, W. Sawin and myself. A more detailed programme will appear in due course…

It’s not every day that I have three upcoming conferences to announce which I co-organize. In chronological order:

June 1 and 2, 2018, Ph. Habegger, Ph. Michel and myself are organizing the 14th edition of the “Number Theory Days”. It will be in Basel, for the first time — from then on, it will rotate between Basel, Lausanne and Zürich.

The respective web pages have more information (and in the last two cases, these will be updated when the FIM webpage is created; this will contain the registration form, as well as the web page to request funding for junior participants).

Subsidiary question: Which book is Bill Duke holding in the picture? Any correct answer (without cheating) gives right to one drink of your choice.

This afternoon, while chatting with Will Sawin, between addressing rather technical points of ongoing projects, we observed that although we’ve seen seminar talks shared between two speakers, it was never with simultaneous speakers. It was just a step to jump from there to the idea that someone should write an Opera about a mathematical seminar talk, which — as opera does — would allow a duet, or trio, or quartet, or quintet, or sextet, of simultaneous speakers, including maybe some from the audience, or the chairperson trying to control the situation.

Unfortunately, I don’t know music, but if I were twenty years old, I’d be very tempted to write “Seminar”, the definitive opera about a math talk. At least, I can think of a libretto and try to write it (which language? I think French is best here, although the title should then be “Séminaire” or “L’exposé” in that case; which topic? good question — of course it would have to be a real talk; which style?)

In any case, I can safely predict a triumph in enlightened circles.

I participated last week to the wonderful Ventotene 2017 Conference, a worthy continuation of Ventotene 2015. Reaching the island required this time even more of the stamina that the conference website recommends, since the weather was rough enough that the faster hydrofoil boat did not run (stranding about 30 of the participants in Formia on Sunday evening), while even the rather bigger one behaved more like a large scale roller-coaster than most people would wish.

After arriving at the island, Monday was still a bit unpleasant (it was much more for those who were unlucky to be exposed when one of the few short but very violent rain showers fell…), but the remaining of the time was beautiful. On the way back, I had to stop in Rome for a night, and tasted the most delicious ragù bianco di coniglio that one can imagine.

I’m already looking forward to the next conference…

One of my great pleasures in life is to walk leisurely down from my office about 30 minutes before the train (to Paris, or Göttingen, or Basel, or what you will) starts, browse a few minutes in one of the second-hand bookstores on the way, and get on the train with some wonderfully surprising book, known or not.

A few months ago, I found “Condorcet journaliste, 1790-1794”,

which one cannot call a well-known book. It is the printed version of the 1929 thesis (at the École des Hautes Études Sociales) of Hélène Delsaux, and its main goal is to survey and discuss in detail all the journal articles that Condorcet, that particularly likable character of the French revolution (about the only one to be happily married, one of the very few in favor of a Republic from the outset, and — amid much ridicule — a supporter of vote for women), wrote during those years.

Condorcet was also known at the time as a mathematician; hence this remarkable quote from the book in question:

Il est généralement admis que rien ne dessèche le coeur comme l’étude approfondie des mathématiques…

or in a rough translation

It is a truth universally acknowledged that nothing shrivels the heart more than the deep study of mathematics… [Ed. Note: what about real estate?]

This book cost me seven Francs. More recently, my trip to the bookstore was crowned by the acquisition of a reprint of R. Dedekind’s “Stetigkeit und irrationale Zahlen” and “Was sind und was sollen die Zahlen” (five Francs)

and of a first edition (Teubner Verlag, Leipzig, 1907) of Minkowski’s “Diophantische Approximationen”

for the princely sum of thirty-eight Francs.

The content of Minkowski’s book is not at all what the title might suggest. There are roughly two parts, one concerned with the geometry of numbers, and the second with algebraic number theory. In both cases, the emphasis is on dimensions 2 and (indeed, especially) 3, so cubic fields are at the forefront of the discussion in the second part. This leads to a much greater number of pictures (there are 82) than a typical textbook of algebraic number theory would have today. Here are two examples,

and here is Minkowski’s description of the Minkowski functional (or gauge) of a convex set: