Category: Mathematics

GANT Winter School draft schedule

The first draft of a schedule for the GANT Winter School, co-organized by Ph. Michel and myself from Jan. 18 to 28, 2011, at the Bernoulli Center of EPF Lausanne (or, as we like to say here in Zürich, ETH Lausanne) is now available. For the moment, it is found on Google Calendar to accomodate possible tweaks, but a downloadable PDF will also be produced soon for offline convenience. The names of the courses can easily be correlated with those on the updated poster; for convenience, here is the list (in chronological order of appearance during the school):

  • “Automorphic forms” — “Modular forms, automorphics forms and automorphic representations”, E. Lapid and Ph. Michel
  • “Sieve methods” — “Sieve methods”, É. Fouvry and myself
  • “Growth and expansion in groups” — “Sum-product phenomena, expansion in groups and applications”, H. Helfgott and P. Varjú
  • “Sato-Tate”: “La conjecture de Sato-Tate” — J.-P. Serre
  • “Spectral and ergodic methods” — “Point counting on homogeneous varieties: spectral and ergodic-theoretic methods”, M. Einsiedler and S. Mozes
  • “Point counting on algebraic varieties” — “Point counting on algebraic varieties and analytic number theory”, T. Browning and R. de la Bretèche

We will also provide abstracts of the courses fairly soon…

(By the way, does anyone know which — if any — URL incantation can force the calendar link to open on the correct date in 5-day-week-display mode?)

Bourbaki report update

I have uploaded a corrected version of my Bourbaki report on sieve in expansion (in particular, after hesitating, I have chosen the title “Sieve in expansion” instead of “Sieve and expansion”). And I have pretty much cornered the market for French surveys on sieve and expanders by translating the report in French (Crible en expansion) ; this is the version that will appear in Astérisque in a year or so. (Of course, both will remain available from my web page also).

As before, corrections, linguistic or mathematical, are welcome — I still have about a month before submitting the text for the final version, and there will be a proof stage later on.

And I will be happy to give away translation rights to any other language, including Espéranto (and Klingon)…

The literary potential of author names

In an age where literary originality is hard to come by, shouldn’t more attention be paid to the great potential of author’s names as literary device? In mathematics, we can enjoy the delightful papers of Nicolas & Sárközy (for instance, this one). Theoretical physicists probably still chuckle when reading the paper of Alpher, Bethe and Gamow (though the story goes that Alpher was pretty upset when Gamow decided to add Bethe as a co-author, purely for euphonical reasons…)

Do you know any other examples?

(As for myself, I am sorry that the traditions of mathematical publication make it highly unlikely that a Stanley — Kowalski paper will ever appear.)

Paleography

On my page of notes and unpublished writings I’ve just added a very old preprint of Ph. Michel and me, after realizing yesterday that I wanted to point out something in it (that was never actually published) to a student, but that I couldn’t locate the TeX file for it anywhere. Fortunately, Philippe had a better-organized archive…

Here, “old” means that it goes back to 1997, which is a time when I used OzTeX on a Mac with 24 megabytes of memory and a 400 megabytes hard drive to typeset this file (and my PhD thesis). And old also means that the TeX file is in LateX 2.09 format… (I was actually surprised that the modern LaTeX 2e was still able to compile it with no difficulty whatsoever).

But when it comes to antiquated computer technology and old writings, my proudest exhibit is my very first publication:

This goes back to January 1986, and is the complete listing of a wonderful piece of computer software, published in the French periodical Hebdogiciel. Back in those days (when I suspect that some of my readers were not yet born), the typical storage equipment for a “personal computer” was a standard K7 tape, or a single 3 inch (non)floppy drive. Computer networks for personal use did not really exist, and there were a few dozen mutually incompatible computer brands, each of which sold with basically no software except a Basic programming language. In Hebdogiciel, every week, one listing was printed (and readers were supposed to type it if they wanted to use those programs…) for each of the most popular brands. (In my case, Amstrad; I was the proud owner of the renowned CPC 664). All these programs were sent by other readers like me.

Amusingly, if I remember right, Hebdogiciel would actually pay the authors of their programs (I think the amount paid was measured by the number of lines, hence a tendency — maybe laudable — for authors to incorporate wide expanses of beautifully delineated comments in their programs…)

More exponential sums

Here’s an update on the front of exponential sums…

(1) The conference I co-organized at FIM on exponential sums over finite fields

ended about two weeks ago. It was quite nice (at least from my point of view…). As usual here, the excellent organization made it possible to enjoy the mathematics with no extra issues to take care of. Most talks were on blackboard but, with authorization, here are the files for those that were on beamer (I think I may miss one or two, which I will add later):

(2) The second part of my class on exponential sums (cohomological methods) continues. I only barely started the lecture notes I was planning to write, the first few weeks of the semester having been simply too busy. As a result, although they are available and will be updated regularly from now on, they are quite incomplete. Most damagingly, the beginning material (introduction and motivation for going towards describing algebraic exponential sums using traces of Frobenius on suitable “Galois” representations of fundamental groups) is mostly missing for the moment. Still, the end parts of Chapter III are written and the contents, from Chapter IV onwards, will hopefully be kept in sync with the class, and no further gaps will appear. Since Chapter IV will start introducing the Grothendieck-Lefschetz trace formula, the étale cohomology groups, and then go on towards the formalism of weights and Deligne’s general version of the Riemann Hypothesis, this might still be of interest even before I find the time (next semester, probably) for filling up the gaps.

My plan next year, when (and if) this second part is done nicely enough, will be to put it together with the first part of the class (on elementary methods) to produce a proper book on exponential sums over finite fields. I’ll be happy to receive even before any feedback on the way the text shapes up, especially from the point of view of people in analytic number theory or in other fields where exponential sums are applied.