@antoinechambertloir@mathstodon.xyz avatar

antoinechambertloir

@antoinechambertloir@mathstodon.xyz
  • Apprentice mathematician (Professor at Université Paris Cité),
    interested in algebraic geometry, number theory and (more recently) proof formalization
  • Apprentice musician (drums, tabla, cajon; previously Diderock; a rarely meeting jazz trio/quartet).
  • Apprentice progressist.

In love with math, jazz, indian music and poetry. ⏚

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antoinechambertloir, to random French
@antoinechambertloir@mathstodon.xyz avatar

Déficit public: "Ce n'était pas prévisible", estime Jean-René Cazeneuve (député Renaissance, rapporteur général de la Commission des Finances)

Déficit public encore: "Il faudra s'attaquer au statut de la fonction publique", estime Éric Ciotti (président des Républicains)

(insérer émoji fourche, hallebardes, guillotine, Hitchcock…)

antoinechambertloir, to random French
@antoinechambertloir@mathstodon.xyz avatar

C'est cool la messagerie ENT du lyée qui se fait hacker, quand les élèves ont perdu l'habitude d'avoir un cahier de textes et que tout est sur une appli indisponible parce que l'ENT est bloqué tout le week-end…
À part ça, on peut porter plainte pour défaut de prudence, insuffisance de moyens, quand une application web obligatoire de l'Éducation nationale met des jeunes en contact avec des contenus violents ?

krazykitty, to random French
@krazykitty@mamot.fr avatar

Eh bien ce concert autour de Gérard Caussé, supposé mettre en valeur l'alto, était un très beau plaidoyer pour la retraite. Il a été un grand altiste (il est toujours très grand (pardon (en même temps à côté de Renaud Capuçon))), il a bien mérité de passer ses journées à lire le journal et promener son petit chien maintenant.

antoinechambertloir,
@antoinechambertloir@mathstodon.xyz avatar

@krazykitty @MatsuBasho
Ça arrive...
C'est en entendant des concerts de jazz qui s'étaient annoncés prodigieux (McCoy Tyner...) que j'ai accepté que la musique vivante ne pouvait pas être parfaite.
Et peut être qu'elle ne doit pas l'être.
Cela dit, c'est frustrant.

johncarlosbaez, (edited ) to random
@johncarlosbaez@mathstodon.xyz avatar

There are a lot of deep conjectures about L-functions. For example, there’s the Langlands program. And the Riemann Hypothesis counts too, because the Riemann zeta function is the grand-daddy of all L-functions! But there’s also a million-dollar prize for proving another conjecture about L-functions. It's called the Birch-Swinnerton and Dyer Conjecture, and it's about L-functions of elliptic curves.

So if you want to learn about this stuff, you may try to learn the definition of an L-function of an elliptic curve. And if you go someplace like Wikipedia, you'll immediately hit an obstacle: the definition is very complicated.

In fact it's so complicated that I figured there's no way this can be the real definition. I started simplifying it a bit here:

https://golem.ph.utexas.edu/category/2024/03/counting_points_on_elliptic_cu.html

But I guessed I could simplify it a lot more.

(1/3)

antoinechambertloir,
@antoinechambertloir@mathstodon.xyz avatar

@johncarlosbaez There is a serious difficulty in your definition, that if you have an elliptic curve E over Q,
E(Z), E(Z/nZ) do not make sense a priori.
In fact, a great deal of work is needed to explain what this means, independently of the initial equation (which can have denominators). This can be done by hand for elliptic curves, see Tate's formulaire (written by Deligne, in the Antwerp volumes on modular forms), or abstractly, invoking the “Néron” model (which, for elliptic curves, predates Néron, of course).

But of course, you recovered the initial work of Hasse and Weil, who defined the zeta function of a system of equations (=scheme of finite type) over Z, and, in the case of elliptic curves, took out the zeta factors.

What is miraculous is that these delicate factors are exactly the ones which will furnish a nice functional equation, L(s)<->L(2-s).

In the 60s, Serre worked a lot to guess how to define correctly the zeta function of a variety over Q, especially the bad factors, when guessing a good system of equations over Z is hopeless, in terms of the Galois representations associated with the variety.

antoinechambertloir,
@antoinechambertloir@mathstodon.xyz avatar

@johncarlosbaez But there are no elliptic curves over Z, at least in the accepted terminology.
By definition, elliptic curves over a ring behave like families of elliptic curves, it has to be proper and smooth (in the terminology of differentiable manifolds, a submersion with compact fibers).
(And even, Jean-Marc Fontaine showed that there are no abelian varieties over Z.)

I believe Hasse's work where some “Hasse-Weil” zeta function appears is that one. (Apparently, he had suggested the question to Pierre Humbert.) He couldn't have the definition you propose:

“Eine entsprechende Analogisierung der Reihendefinition der Zetafunktion von K
erscheint nicht möglich, weil man in K zwar eine eindeutige Primdivisorzerlegung, nicht
aber auch eine eindeutige Punktzerlegung hat.”

but once schemes were there, it was possible to exhibit what Hasse wanted.

https://sci-hub.st/https://doi.org/10.1515/9783110835007.450

antoinechambertloir,
@antoinechambertloir@mathstodon.xyz avatar

@macbro @johncarlosbaez Even that is not enough. You can modify the curve over Z in a fairly large number of ways, this will totally change the zeta function, it will lose the functional equation, etc. but it should not.

ciredutempsEsme, to random French
@ciredutempsEsme@mamot.fr avatar

Est ce que vos enfants ont le droit de se tromper ? De se planter ?
Êtes vous prêts à cette éventualité ?

antoinechambertloir,
@antoinechambertloir@mathstodon.xyz avatar

@scudery @ciredutempsEsme Il y a un roman poignant de Doris Lessing sur la question, Le cinquième enfant…

antoinechambertloir, to random French
@antoinechambertloir@mathstodon.xyz avatar

Capes d'allemand pour n⁰2. Send hugs.

YVioujard, to random French
@YVioujard@piaille.fr avatar

Eh bien, je commence à en avoir lu un paquet, des ouvrages sur le HPI, c'est assez systématiquement la foire au n'importe quoi. Celui-là par contre, il vaut vraiment le coup. Il revient sur de nombreux "mythes" absurdes de manière très claire, rationnelle, sourcée et bien expliquée. Je vous le conseille chaudement. Il est sorti cette année, en janvier.

antoinechambertloir,
@antoinechambertloir@mathstodon.xyz avatar

@YVioujard @scudery @ciredutempsEsme ... Et surtout affecter d'urgence les soldats US mobilisés pendant la première guerre mondiale.
Autrement dit, dune mesure imparfaite mise en œuvre dans un but conjoncturel et précis, faire une notion « scientifique » de l'intelligence .

LegalizeBrain, (edited ) to random French
@LegalizeBrain@mastodon.zaclys.com avatar

deleted_by_author

    •
    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar

    @LegalizeBrain
    Qu'est-ce qui t'empêche de passer à OS X 10.12 ou plus ? (J'ai un MacBookPro 2015, Max OS 10.12.7.)

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar

    @LegalizeBrain Ah, 2012, pas 2018 !

    antoinechambertloir, to random French
    @antoinechambertloir@mathstodon.xyz avatar

    Il y a au moins deux mots de 5 lettres qui commencent par « mer » et j'ai reçu un mail ce matin, auquel j'aurais pu répondre aussi par l'un que par l'autre. Avec un point d'exclamation.

    antoinechambertloir, to random French
    @antoinechambertloir@mathstodon.xyz avatar

    This is so 2024…

    highergeometer, to random
    @highergeometer@mathstodon.xyz avatar

    YES! The French journal Comptes Rendus Mathématique is now Diamond Open Access, not published by Elsevier any more!

    https://comptes-rendus.academie-sciences.fr/mathematique/

    That's going on my list of potential journals to publish in, now....

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar

    @highergeometer I am an editor of that journal (I am actually quitting the board), and that was one of the first things I wrote to colleagues I contacted to referee one paper!
    The new journal accepts not only short announcement notes, but also longer papers (not too long, though), more or less of any kind, especially if they would be hard to publish in other journals.

    antoinechambertloir, to jazz French
    @antoinechambertloir@mathstodon.xyz avatar

    There was a guy named Maxwell,
    who was born on that day, 100 years ago,
    even if his birth certificate doesn't say so.
    His second name was Lemuel.
    Whatever — everybody calls him Max.
    Let's embark for a 100 days celebration
    with Max Roach, here on Mastodon.
    You know what to do? — Follow the hashtag…

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar
    1. Dance Griot

    Let's continue to listen to that album with Anthony Braxton ! Tonight's tune is quite different, you'll see. Roach starts by a short introduction, in which one recognizes classic “roachian” drum patterns (that ta-dada-dadum, ta-dada-dadum, ta-dada-dum…) but he does not fall into them and Braxton starts improvising in an almost bebop style, with a classic bebop drum accompaniment by Roach — a systematic swing pattern on the ride cymbal, and a syncopated counterpoint on the snare drum and the bass drum. At some point, Braxton steps back, the two play more rhythmically than melodically, and Roach ends the track by a solo part.

    https://www.youtube.com/watch?v=5l5MpIPyE2s

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar
    1. Epistrophy

    This is a composition by Thelonious Monk, revisited by the percussion collective M'Boom in 1979. Quite a challenge when most of the instruments they play are anharmonic. Thanks to Joe Chambers on the vibraphone, and Fred King and Freddie Waits on marimba, we have a melody, but I would like to send a big up to the timpani guys (Warren Smith and Omar Clay) who play with the tension of the skin and produce wonderful effects (the kind of woo-woo tabla players are fond of).
    Kenyatta Abdur-Rahman is on bells and Ray Mantilla on triangle.

    https://www.youtube.com/watch?v=vdgoPgbp9VU

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar
    1. U-Jaa-Ma

    After their 1976 studio recording, Max Roach and Archie Shepp toured in several festivals.
    Tonight's track is taken from a 1979 concert in Austria that was published under the title The Long March. The album contains solo pieces, either by Max Roach or by Archie Shepp, and duet pieces. “The Long March” is one of them, but it is… long, and not really easy listening. This one, “U-Jaa-Ma”, is a composition of Archie Shepp that starts with a powerful syncopated riff using only beats 4 and 1.

    The word Ujamaa is Swahili for “fraternity”. According to Wikipedia, it was also the name of a socialist ideology that formed the basis of anti-colonial activist Julius Nyerere's social and economic development policies in Tanzania after it gained independence from Britain in 1961.
    On the recording of a 1975 concert (in Massy, close to my living place), Shepp translates this word as “Unity”.

    You'll hear what these two musical forces can build out of this political project of “unity” and “fraternity”.

    https://www.youtube.com/watch?v=XzfdktgaoRU

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar
    1. South Africa Goddamn

    From the same album as yesterday, another duet tune featuring Max Roach and Archie Shepp, bringing a definitely different atmosphere.

    The tune starts with the drums only. At some point Shepp enters and brings in a melancholic melody, that sometimes turns into sad shrieks, which Roach sustains with an infectious groove that superposes a rapid flow of non-resonant sixteenth notes using rim shots, a regular hi-hat on beats 2 and 4, and (basically) quarter notes on tom-toms in descending pitches on beats 1, 2 and 3. When Shepp finishes his chorus and lets Roach plays solo, he continues playing the same groove only varying the intensity of the sound, a part I found really beautiful.

    There is rage, of course, but there is hope.

    https://www.youtube.com/watch?v=P9xK0dEQ2H8

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar
    1. China's Waltz

    Let's listen to Max Roach quartet, still with Odean Pope on flute, Calvin Hill on bass, and Cecil Bridgewater on trumpet.
    Taken from the 1979 album Pictures in a Frame, this is a simple waltz, which the musicians play with simplicity. The melody is played by the trumpet, with a beautiful second voice on the flute, and a third one on bass.

    https://www.youtube.com/watch?v=yjtbNrTir5I

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar
    1. Ode From Black Picture Show

    It's a solo piece, by Max Roach only.
    A piece he composed and sings and plays at the piano.

    The lyrics are taken from an anonymous nursery rhyme, “There was a man of double deed”, which seems to be simultaneously well known and mysterious — nothing makes sense, except for our final death…

    Roach turns it into a torchy lament.

    https://www.youtube.com/watch?v=gJQ5b1o5dRI

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar
    1. The Martyr, Pt 1.

    This is a very long track, more than 30 minutes, composed by Max Roach, recorded in quartet in 1977.
    Reggie Workman at the bass starts with a great riff and Billy Harper (tenor sax) and Cecil Bridgewater (trumpet) share the joy of improvising on this melody, while Roach pushes the band with a forceful energy.
    After 8 minutes, the mood changes for a bass chorus that lasts 7 minutes, with rare interventions by the trumpet. The drum chorus that follows a second exposition of the theme is full of energy, yet melodic. As often with this quartet, the sax chorus escapes (so it seems, at least) the melody which it recalls occasionally. A new drum chorus in a different style, using drum rolls to provide long sounds, and toms to infer melodies. The rhythmic structure of the theme can be felt all along, and it's as if Roach is never bored, nor tired of playing this incredible melody. A last bar, a rim shot, and the musicians give a final version of the theme.

    https://www.youtube.com/watch?v=6V53wnyPgfc

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar
    1. Six Bits Blues

    The same album as yesterday, The Loadstar, features this beautiful, heart-rending, slow blues, also composed by Roach, which is so slow that the triplet decomposition of the beat gives a 3/4 feel. As for yesterday, the musicians take the opportunity of playing the tune live to expand it to a long 20 minute piece, so I felt more natural, and maybe more indulging to you, to suggest the 1981 version, in Chattahoochee Red, which lasts only 4 minutes. (Of course, that means you'll be deprived of a beautiful bass chorus.)

    https://www.youtube.com/watch?v=8WQR512n3eQ

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar
    1. The Dream / It's Time

    The album Chattahoochee Red contains pieces of all kinds, and the one that opens the volume is a drum improvisation by Max Roach on top or Martin Luther King Jr's 1963 speech at the Lincoln memorial, “I Have A Dream”.

    After the final “Free At Last”, the quartet goes on with Max Roach's composition “It's Time”.

    Is there anything more to say?

    https://www.youtube.com/watch?v=JxneNQUMcCc

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar
    1. Symbols

    A free improvisation duet with Connie Crothers, on piano, recorded in NYC, 1982.

    Born in 1941, Connie Crothers was an American pianist, a student of Lennie Tristano. She recorded a twentieth of albums in the years 1980 up to her death in 2016.

    Of course, since this is free improvisation, there's no apparent melody, no systematic groove. Despite Roach's constant engagement in avant-garde music, it seems he didn't involve in that musical form except for that recording. I find interesting that he doesn't impose his traditional licks, but simply tries to cooperate with Crothers. Discovering that album as I prepare this post, I'll definitely spend some time listening to her music.

    https://www.youtube.com/watch?v=kntGMbEUi2c

    antoinechambertloir,
    @antoinechambertloir@mathstodon.xyz avatar
    1. Ruby My Dear

    A Thelonious Monk ballad, here played by Max Roach Quartet, from the 1983 In the light album.

    Anyway, it is essentially Cecil Bridgewater (trumpet) that we hear, with a light drumming on brushes and, especially when the chorus starts, a bass line by Calvin Hill, and to conclude, a second line on saxophone by Odean Pope.

    That's a very humble and melancholic version. Ruby was Monk's first love.

    https://www.youtube.com/watch?v=bQLTuJXyo7s

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