Dessin par Hélène
Michel Waldschmidt

Interview for the seminar Geometry, Arithmetic and Differential Equations of Periods (GADEPs), Rio de Janeiro, Friday, October 9, 2020. The video is available on You Tube.

AMS 2021 Bertrand Russell Prize.
    The prize honors research or service contributions of mathematicians or related professionals to promoting good in the world and recognizes the various ways that mathematics furthers human values.

Interview par le CIMPA le 9 décembre 2020 à Nice.

Michel Waldschmidt, Limourien mathématicien - Limours Magazine 165 Juin 2021 p.20.

Run for GRAID
    La Commission pour les Pays en Développement de l'Union Mathématique Internationale a créé le programme GRAID (Graduate Assistantships in Developing Countries). Son objectif est de permettre à des étudiants de pays défavorisés de poursuivre leurs études et de préparer un master ou une thèse en mathématiques dans leur pays, grâce à un soutien financier minimal. Les dons sont à adresser au CIMPA (Centre International de Mathématiques Pures et Appliquées), association reconnue d'utilisé publique, ce qui permet aux contribuables français de bénéficier d'une déduction fiscale pour leurs dons - voir le site du CIMPA Donation à GRAID (Graduate Research Assistantships In Developing countries)
    Run for GRAID contribue au financement, mes dernières courses en juillet et août 2021 en font partie. Voir mon compte facebook, les sites Run For Graid et Angel Pineda Running for GRAID.
    Concert Solidaire à Limours, La Scène, samedi 20 novembre 2021 à 20h30. Au profit de trois associations dont Run For Graid.
    Voir aussi la vidéo de présentation.

Call for applications for GRAID: The Math Programs site is ready for submissions. Application Deadline: March 15, 2022.

Project Support Program 2022: Call for Applications
    This program supports higher education and capacity building projects as well as local initiatives in mathematics and mathematical education, be they international, regional or local initiatives in developing countries (IMU definition).
    Research projects are not eligible.
    The projects should start between July 1, 2022 and June 30, 2023.
    The maximum amount to be awarded to each application is 10000 €. Exact amounts will depend on the mathematical quality and impact and on budget constraints.
    The deadline for applications is January 31, 2022.
    Only online submitted applications are eligible.
    For more information, please visit here: https://www.mathunion.org/cdc/grants/project-support-program

Agenda

Archives from January 2009 till now.

Prochaînement - Coming soon

January 31 - February 02, 2022, Online conference «DAYS of TRANSCENDENCE» in occasion of Professor Yuri Nesterenko's 75th birthday.
    Tuesday, February 1, 2022, 11:45-12:15 UTC+3: On sets of linear forms of maximal complexity, joint work with Michael Kaminski and Igor E. Shparlinski.

Jeudi 3 février 2022, Séminaire de théorie des nombres de Nancy-Metz
    14:30 - 15:30 exposé: Ensembles de formes linéaires de complexité maximale d'après un travail en commun avec Michael Kaminski et Igor E. Shparlinski.

February 13-21, 2022. Lahore (Pakistan)
    University of the Punjab, Department of Mathematics - National Mathematical Society of Pakistan. PU-NMS International Schools Series for Students and Faculty.
    From Monday, February 14, 2022 to Friday, February 18, 2022, 11:30 am – 1:00 pm. Five courses on Interpolation formulae for analytic functions.
    Tuesday, February 15, 2022, 4.00 pm - 5.30 pm. Lecture on the topic: Mathematics for Computer Science. Towards exact rounding of the elementary functions, an application of Diophantine Approximation to Scientific computing and validated numerics.
    Thursday, January 17, 2022, 4:00 pm – 5:30 pm Lecture on Linear recurrence sequences.
    Saturday, February 20, 2022, 12:30 pm – 2:00 pm, Department of Mathematics, Government College Women University Faisalabad . Lecture: Is the Euler constant a rational number, an algebraic irrational number or else a transcendental number?

March 6 - 15 , 2022, N'Djaména (Tchad)
    Université de N'Djaména, Faculté des Sciences Exactes et Appliquées, Département de Mathématiques.

April 9, 2022. Monthly talks of the Iranian Mathematical Society.

April 17-23, 2022. Mathematisches Forschungsinsitut Oberwolfach (Germany)
    Workshop Diophantische Approximationen

May 16-21, 2022, Marina di San Gregorio, Patù (Lecce), Italy
    CDM 210 Leuca2022 - Celebrating Claude Levesque's, Damien Roy's and Michel Waldschmidt's birthdays.

May 23-25, 2022, Università di Pisa (Italy)
    La grandezza dei punti piccoli, Celebrating Francesco Amoroso's 60th birthday.

Dimanche 5 juin 2022, Ultra Trail Tour de Nancy, 46 km, 1420 D+.

Mardi 7 juin 2022, exposé au Séminaire différentiel, centre de recherche Inria de Saclay.

12 - 24 juin 2022, Institut de Mathématiques et de Sciences Physiques (IMSP), Dangbo, Benin.
    École de recherche du CIMPA : Algèbre, arithmétique et applications. Cours: Approximation diophantienne.

August 22 - September 3, 2022 (dates to be confirmed). African Institute for Mathematical Sciences (AIMS), M'Bour, Senegal
    CIMPA Research School on cryptography, theoretical and computational aspects of number theory.
    Course: Elementary approach to elliptic curves.

Research papers (submitted) - Articles de recherche (soumis)

Lidstone Interpolation (I). One variable. Proceedings of the 87th Annual Conference of the Indian Mathematical Society, December 2021. To be published in the February 2022 issue of The Mathematics Student.

Lidstone Interpolation (II). Two variables. Submitted to the Asian-European Journal of Mathematics.

Lidstone Interpolation (III). Several variables.

With Michael Kaminski and Igor E. Shparlinski,
    On sets of linear forms of maximal complexity, 12p.
    arXiv: 2110.04657 [cs.CC].

Research papers (recently published) - Articles de recherche (viennent de paraître)

On entire functions of several variables with derivatives of even order taking integer values.
    Journal of Ramanujan Society of Mathematics and Mathematical Sciences (JRSMAMS), Vol. 9, No. 1, December 2021, 95-104.     arXiv: 2112.02529 [math.CV].

On transcendental entire functions with infinitely many derivatives taking integer values at two points. Southeast Asian Bulletin of Mathematics, Vol.45(3) (2021), 379-408.
    arXiv: 1912.00173 [math.NT].

On transcendental entire functions with infinitely many derivatives taking integer values at several points. Moscow Journal of Combinatorics and Number Theory, 9-4 (2020), 371-388. DOI 10.2140/moscow.2020.9.371 (Zbl) (MR)
    arXiv: 1912.00174 [math.NT].

Avec Etienne Fouvry,
    Sur la représentation des entiers par des formes cyclotomiques de grand degré. Bull. Soc. Math. France, 148 2 (2020), 253-282. DOI 10.24033/bsmf.2805.
    arXiv: 1909.01892 [math.NT]. (Zbl) (MR)

With Etienne Fouvry and Claude Levesque,
    Representation of integers by cyclotomic binary forms. Acta Arithmetica, 184.1 (2018), 67 - 86. DOI 10.4064/aa171012-24-12 (Zbl) (MR).
    arXiv: 712.09019 [math.NT].
    Online Encyclopedia of Integer Sequences:
       OEIS A296095 Integers represented by cyclotomic binary forms.
       OEIS A293654 Integers not represented by cyclotomic binary forms.
       OEIS A299214 Number of representations of integers by cyclotomic binary forms.
       OEIS A301429 Decimal expansion of an analog of the Landau-Ramanujan constant for Loeschian numbers.
       OEIS A301430 Decimal expansion of an analog of the Landau-Ramanujan constant for Loeschian numbers which are sums of two squares.

Recent surveys - articles de synthèse récents

Le théorème des six exponentielles restreint à l'irrationalité. Revue de la filière mathématiques RMS, avril 2021, 131ème année, N.3, 2020-2021, 26-33.
    English translation: Six Exponentials Theorem - Irrationality. 9 pages. To appear in Resonance.

Integer-valued functions, Hurwitz functions and related topics: A survey. Number Theory. Proceedings of the Journées Arithmétiques, 2019, XXXI, held at Istanbul University. Edited by Kağan Kurşungöz and Ayberk Zeytin, De Gruyter Proceedings in Mathematics, De Gruyter 2022, pp. 61-82.
    arXiv:2002.01223 [math.NT]

Third kind elliptic integrals and transcendance (3 pages). Appendix to the paper Third kind elliptic integrals and 1-motives by Cristiana Bertolin. Journal of Pure and Applied Algebra, Volume 224, Issue 10, October 2020, 106396, 1-28. DOI 10.1016/j.jpaa.2020.106396
    arXiv:1905.07247 [math.NT]

Thue Diophantine equations - a survey.
    Class Groups of Number Fields and Related Topics, ed. Kalyan Chakraborty, Azizul Hoque and Prem Prakash Pandey, p. 25-41 . Springer Nature Singapore Pte Ltd., 2020.
    Proceedings of the International Conference ICCGNFRT-2017, HRI Allahabad, September 2017. DOI 10.1007/978-981-15-1514-9_3 (Zbl)

With Razvan Barbulescu. Poster summarizing The abc conjecture and some of its consequences. Archives HAL-01626155 version 3.

Lectures - Courses - Conferences - Videos

Les fichiers pdf ou ppt de mes exposés récents ou plus anciens sont téléchargeables.
You can download the pdf or ppt files of my recent or not so recent lectures and talks.

In English

Transcendental Number Theory: recent results and open problems.
        pdf file 5.7 Mo, 99p.
        update 2022

Lidstone interpolation Four courses at The Institute of Mathematical Sciences (IMSc).
          Lecture 1: Friday, December 10 2021 15:30 - 16:45  link to the video
          Lecture 2: Saturday, December 11 2021 15:30 - 16:45  link to the video
          Lecture 3: Monday, December 13 2021 11:30 - 12:45  link to the video
          Lecture 4: Tuesday, December 14 2021 15:30 - 16:45  link to the video
          Slides on Lidstone interpolation -   update 2021.

History of Indo-French Scientific Partnership
    Indo-French Cooperation in Mathematics. 14,2 Mo., 67p.
        update 2021

Schanuel's Conjecture: algebraic independence of transcendental numbers.
        pdf file 21.5 Mo, 68 p.
        update 2021

Irrationality and transcendence of values of special functions.
        pdf 11.2 Mo, 112p.
        update 2021

Online course CIMPA on Interpolation.
       pdf files: course 1, 1.6 Mo, 48 pages, course 2, 406 Ko, 49 pages, course 3, 934 Ko, 50 pages, course 4, 1.6 Mo, 65 pages.
       Link to the videos on You Tube (December 2020)
       Exercices Sheet 1CorrectionsSheet 2CorrectionsSheet 3CorrectionsSheet 4Corrections
        update 2021

Some variants of Seshadri's constant. slides pdf 14.4 Mo, 104p. Link to the video (October 12, 2020).
        update 2020

An introduction to the theory of finite fields (pdf: 82 pages).
        update 2020

Linear recurrence sequences.
    Part I, examples. Link to the video, September 21, 2020.
    Part II, the theory. Link to the video, September 28, 2020.
        update 2020

On the Brahmagupta-Fermat-Pell Equation.
        print pdf: 2.3 Mo, 86 p.
        The video (July 23, 2020) is available on You Tube.
        update 2020

The square root of 2, the Golden ratio and the Fibonacci sequence.     print pdf 4.5 Mo, 89p.
        The video (July 20, 2020) is available on YouTube
        update 2020

Srinivasa Ramanujan His life and his work.
        pdf slides, Link to a video (December 16, 2020). Link to another video on You Tube (Dec. 29, 2020).
        update 2020

Integer valued entire functions.     screen pdf 2.3 Mo, 171p.     print pdf 1.1 Mo, 17p.
       see also the Online course CIMPA on Interpolation. pdf file: course 4, 1.6 Mo, 65 pages. Link to the video on You Tube (December 15, 2020).
        update 2020

Lidstone series, generalisations and arithmetic applications.
        screen pdf 764 Ko, 131p.   print pdf 792 Ko, 15p.
       see also the Online course CIMPA on Interpolation. pdf files: course 2, 406 Ko, 49 pages, course 3, 934 Ko, 50 pages, Link to the videos on You Tube (Dec. 2020)
       update 2020

Two invariants related to two conjectures due to Nagata.
        slides pdf 14.4 Mo, 104p. Link to the video (October 12, 2020).
        update 2020

Representation of integers by cyclotomic binary forms. 43p., 3.6 Mo. Number Theory Web Seminar, Tuesday, May 12, 2020.
    Link to recording and slides
        update 2020

Introduction to Galois Theory
        screen pdf: 4,2 Mo, 85 p.   print pdf: 1,1 Mo, 15 p.
        update 2019

Some of the most famous open problems in number theory.
        screen pdf: 5.8 Mo, 214 p.   print pdf: 1.8 Mo, 28 p.
        update 2019

Continued fractions: introduction and applications.
        screen pdf: 3.7 Mo, 147 p.   print pdf: 1.1 Mo, 20 p.
        update 2019
  See also
        Continued fractions (unpublished manuscript, 46 pages).

The unity of mathematics - examples from transcendental number theory.
        pdf file, screen version: 4.1 Mo, 147p.   pdf file, print version: 1.4 Mo, 20p.
        Video on YouTube of the first and third courses (October 2018).
        update 2018

On the Landau-Ramanujan constant pdf file, screen version: 3.4 Mo, 130 p.   pdf file, print version: 1.1 Mo, 18 p.
        update 2018

An elementary introduction to error correcting codes.
        powerpoint file (161 p., 4.3 Mo)   pdf file (44 p., 5.5 Mo).
        update 2018

An elementary introduction to cryptography.
        powerpoint file (95 p., 3.6 Mo)   pdf file (24 p., 6.2 Mo).
        update 2018

Is the Euler constant a rational number, an algebraic irrational number or else a transcendental number?
        pdf file, screen version: 3.4 Mo, 126 p.   pdf file, print version: 1.3 Mo, 22 p.
        update 2017

On the abc conjecture and some of its consequences.
        screen pdf: 5.5 Mo, 195 p.   print pdf: 2.1 Mo, 30 p.
        update 2017

On the Markoff equation x^2+y^2+z^2=3xyz;
        screen pdf 4.6 Mo, 171 p.   print pdf 4.8 Mo, 22 p.
        update 2016

Diophantine equations and Diophantine approximations
        screen pdf: 3.2 Mo, 161 p.   print pdf: 1.9 Mo, 23 p.
        update 2016
  See also
Families of Diophantine equations.
        screen pdf 1.9 Mo, 99p.   print pdf 1.3 Mo, 15p.
        update 2016

Diophantine approximation with applications to dynamical systems.
        screen pdf: 1.2 Mo, 119 p.   print pdf: 1.2 Mo, 14 p.
        update 2016

Multiple zeta values.
        screen pdf: 2.3 Mo, 151 p.   print pdf: 2.3 Mo, 19 p.
        update 2014

Diophantine equations and Diophantine approximation
        screen pdf: 1.3 Mo, 96 p.   print pdf: 1.3 Mo, 16 p.
        update 2012

En français

Le Podcast de la culture mathématique: Trajectoires #18: Nombres Transcendants (23 septembre 2019).

Les débuts de la théorie des nombres transcendants.
        fichier pdf, version écran: 4,2 Mo, 52 pages     fichier pdf, version à imprimer: 3,2 Mo, 11 pages
        mise à jour 2019

Introduction à la cryptographie.
        fichier powerpoint, 3,4 Mo, 89 pages   fichier pdf, version à imprimer, 6,2 Mo, 23 pages.
        mise à jour 2018

introduction aux codes correcteurs d’erreurs
        fichier ppt, 4 Mo, 164 p.   fichier pdf, version à imprimer: 5,9 Mo, 41p.
        mise à jour 2018

L'équation de Brahmagupta - Pell - Fermat.
        fichier pdf, version écran: 3,3 Mo, 193 p.   fichier pdf, version à imprimer: 3,3 Mo, 21 p.
        mise à jour 2017

Sur l’équation de Markoff x^2+y^2+z^2=3xyz.
        fichier pdf, version écran 4,9 Mo, 221 p.   fichier pdf, version à imprimer 5 Mo, 27 p.
        mise à jour 2016

La conjecture abc
        fichier pdf, version écran 19,4 Mo, 152 p.   fichier pdf, version à imprimer 19,6 Mo, 25 p.
        mise à jour 2016

Fractions continues, introduction et applications
        fichier pdf, version écran: 3,7 Mo, 145 p.     fichier pdf, version à imprimer: 3,7 Mo, 20 p.
        mise à jour 2016

Problèmes ouverts en théorie des nombres.
        fichier pdf, version écran: 4,4 Mo, 203 p.     fichier pdf, version à imprimer: 4,4 Mo, 27 p.
        mise à jour 2015

La constante d'Euler est-elle un nombre rationnel, un nombre algébrique irrationnel ou bien un nombre transcendant?
        fichier pdf, version écran: 4,5 Mo, 128 p.     fichier pdf, version à imprimer: 4,5 Mo, 22 p.
        mise à jour 2014

Nombres transcendants: résultats récents et problèmes ouverts
        fichier pdf, version écran 4,4 Mo, 142 p.   fichier pdf, version à imprimer 3,9 Mo, 15 p.
        mise à jour 2009

Valeurs zêta multiples, d'Euler à nos jours.
        fichier pdf, version écran 2,2 Mo, 236 p.   fichier pdf, version à imprimer 1,1 Mo, 26 p.
        mise à jour 2008