Latest adventures

The last two weeks were quite eventful…

First I spent four days in China for the conference in honor of N. Katz’s 71st birthday. I was lucky with jetlag and was able to really enjoy this trip, despite its short length. The talks themselves were quite interesting, even if most of them were rather far from my areas of expertise. I talked about my work with W. Sawin on Kloosterman paths; the slides are now online.

I only had time to participate in one of the excursions, to the Forbidden City,

Forbidden City
Forbidden City

were I took many pictures of Chinese Dragons…

Chinese Dragon
Chinese Dragon

That same evening, with F. Rodriguez Villegas and C. Hall, I explored a small part of the Beijing subway,

Subway map
Subway map

trying to interpret and recognize various Chinese characters, before spending a fair amount of time in a huge bookstore


(where I got some comic books in Chinese for fun).

Upon coming back on Thursday, I first found in my office the two volumes of the letters between Serre and Tate that the SMF has just published, and which I had ordered a few days before taking the plane. Reading the beginning of the first volume was very enjoyable in the train on Friday morning from Zürich to Lausanne, where the traditional Number Theory Days were organized this year. All talks were excellent again — we’re now looking forward to next year’s edition, which will be back in Zürich! And I’ll write later some more comments about the Serre-Tate letters…

And then, from last Monday to Friday, we had in Zürich the conference “Analytic Aspects of Number Theory”, organized by H. Iwaniec, Ph. Michel and myself with the help of FIM. It was great fun, and there were really superb and impressive talks. One interesting experience was the talk by J. Bellaïche : for health reasons, he couldn’t travel to Zürich, but we organized his talk by video (using a software called Scopia), watching it from a teleconference room at ETH. This went rather well.

Proust, my family and Australia

When I was reading Proust, I noted with some amusement the character named simply “Ski” in the first volume of his appearance, a sculptor and amateur musician who is later revealed to be properly called “Viradobetski”, an actual name which was too complicated for the dear Madame Verdurin to try to remember. I just learnt from my better educated brother that

Proust s’est inspiré d’Henri Kowalski né en 1841, fils d’un officier polonais émigré en Bretagne. Il était à la fois compositeur de musique et concertiste.


Proust used as model Henri Kowalski, born in 1841, son of a Polish officer who emigrated to Brittany. He was a composer as well as a concert player.

to quote an authoritative list of Proust characters.

That Henri Kowalski is, it turns out, the son of Nepomus Adam Louis Kowalski, whose brother was Joachim Gabriel Kowalski, one of whose sons was Eugène Joseph Ange Kowalski, one of whose sons was Louis André Marie Joseph Kowalski, the fourth son of whom was my father. This puts me at genealogical distance (at most) six to a character from Proust. (Of course, rumors that Viradobetski was inspired by someone else can be safely discarded).

Wikipedia has a small page on Henri Kowalski, who was quite active and successful as a musician, and a rather impressive traveller. He spent thirteen years in Australia, leaving enough traces to be the subject of public lectures at the university of Melbourne. There are a few of his pieces on Youtube, for instance here. He also wrote a travel book which I now intend to read…

IHÉS summer school online

The IHÉS Summer School on analytic number theory that I co-organized with Philippe Michel ended a few days ago. Even if the weather did not cooperate (rain, scorching heat, gloomy clouds), I think it went very well, although this is of course more for the participants to say…

I certainly learnt things myself, especially in the course of K. Soundararajan, who discussed (among other things) some recent works of his with M. Radziwiƚƚ that I had intended to read, without finding the time…

My own lectures were on trace functions over finite fields. It was the first occasion I’ve had to give more than one talk on this topic, and I used the opportunity to see which ideas could work for a good presentation of the basic ideas to analytic number theorists. I’m quite happy with the outcome, and this will be very useful since I will give courses on the subject during the next two semesters, which should provide at least some amount of notes and drafts for the book that É. Fouvry, Ph. Michel and mysefl are hoping to write.

For those who could not attend the event (which is probably a fair number of people, in view of the fact that an unfortunate independent-scheduling event led to it being simultanenous with the ENFANT/ELEFANT conference organized by L. Pierce and D. Schindler in Bonn), it is quite nice that the whole programme was filmed and is now available on Youtube on the IHÉS channel! (The ordering of the videos is a bit strange, but it is easy to use the descriptions to watch, for instance, all four of Sound’s lectures one after the other).

Chicheley Hall meeting

Just after the end of the semester last week, I went to a short meeting organized by J. Keating, Z. Rudnick and T. Wooley, in the stately English house of Chicheley Hall,


where the Royal Society has a conference center. This was quite a fun occasion, and not only because the curtains had one the most interesting decorative pattern I have seen during years of extensive study:


The talks were only 30 minutes long; because of this and the absence of blackboards, they were all beamer talks, and I’ve uploaded my slides here. They might be useful even for participants in the meeting, since I only had time to cover the first 60% or so of what I had planned, which was a survey of my most recent work with É. Fouvry and Ph. Michel (available here, and which I hope to discuss in more detail in a later post)…

Trace functions, a survey

At last count, my series of works with Étienne Fouvry and Philippe Michel on trace functions and their applications consists of seven research papers or preprints, amounting to a bit more than 200 pages. To these are added a number of works-in-progress or partial notes (some with results we did not need or use and so took out of earlier drafts of our papers, some with worked-out examples or remarks, etc). We have a relatively firm project of writing a monograph account of the whole theory and applications, which we view in part as a way of making accessible some of the deep consequences of the Riemann Hypothesis over finite fields of Deligne, but this is clearly a long-term project. In the meantime, we have written a first short survey, the first draft of which can be found on my web page. This is in fact the written (and slightly expanded) account of a Colloquio de Giorgi that I gave at the

[Scuola Normale Superiore]
Scuola Normale Superiore

Scuola Normale Superiore in Pisa earlier this year, and we have included an unusual representation of the fundamental domain of the modular group acting on the upper half-plane as an homage and acknowledgement of this occasion.