Towards a correctly-rounded and fast power function in binary64 arithmetic, 30th IEEE International Symposium on Computer Arithmetic (ARITH 2023), September 5, 2023

CORE-MATH: progress report, FPTalks 2023, July 6, 2023

Déchiffrement d’une lettre de Charles Quint de 1547, Séminaire de Cohésion de la Direction du Numérique, Région Grand Est, May 25. 2023 [in french]

The CORE-MATH Project, GT-eval meeting, February 2, 2023

The CORE-MATH Project, RAIM 2022 : 13èmes Rencontres Arithmétique de l'Informatique Mathématique, November 3, 2022

The CORE-MATH Project, Arith 2022 conference, September 12, 2022. [video]

CORE-MATH: Correctly Rounded Mathematical Functions ... Up to the End User, FPBench Community Meeting, March 3, 2022.

Tout ce que vous avez toujours voulu savoir sur le standard IEEE 754 [in french], Café Calcul, February 10, 2022 [video].

Double Matrix Algorithm, ANR Kleptomaniac, January 19, 2022.

Factoring RSA-250 with PRACE, CaSToRC HPC Seminar Series, November 16, 2021.

CORE-MATH: quand pourra-t-on calculer correctement ?, RAIM 2021 : 12èmes Rencontres Arithmétique de l'Informatique Mathématique, 27-28 May 2021 [in french].

Un logiciel open-source établit un nouveau record de factorisation, invited talk at the Journée Scientifique EXPLOR 2020, Nancy, December 17, 2020 [in french].

Integer factorization: Old and Recent Developments, invited talk at the HistoCrypt conference, Budapest, Hungary, June 15-17, 2020 [conference cancelled due to Covid19].

How Slow is Quadruple Precision?, invited (virtual) talk at the ICERM workshop on Variable Precision in Mathematical and Scientific Computing, Providence, May 6-8, 2020. [video archive]

Introduction à Sage (in french), invited talk at the conference Algorithmics and Programming, Luminy, France, May 6, 2019.

Micro-GMP, presentation at the MPFR / MPC / iRRAM Workshop, Trier, Germany, November 23, 2018.

What if Gauss had had a computer?, invited talk at the topical workshop Celebrating 75 Years of Mathematics of Computation, ICERM, Providence, November 1-3, 2018.

On various ways to split a floating-point number (common work with Claude-Pierre Jeannerod and Jean-Michel Muller), FastRelax workshop, Sophia-Antipolis, France, June 5-7, 2018.

Recent and future developments of GNU MPFR, Dagstuhl workshop on iRRAM, MPFR and MPC, Schloss Dagstuhl, Germany, April 18, 2018.

A tutorial on reliable numerical computation, Dagstuhl seminar "Reliable Computation and Complexity on the Reals", Schloss Dagstuhl, Germany, November 27, 2017.

Optimized Binary64 and Binary128 Arithmetic with GNU MPFR, 24th IEEE Symposium on Computer Arithmetic, London, United Kingdom, July 24, 2017.

Des calculs plus rapides sur 1 et 2 mots-machine dans GNU MPFR, [in french] Journées FastRelax, Paris, France, May 31, 2017.

Multiple Precision: from MP to MPFR, invited talk at the 4th Number Theory Down Under conference, Newcastle, Australia, September 23, 2016.

Better Polynomials for GNFS, invited seminar at the Number Theory Seminar at UNSW, Sydney, Australia, September 21, 2016.

BeDoP: Beyond Double Precision, ANR FastRelax meeting, 27 May 2015, Lyon.

Tiny MPQS, ANR Catrel meeting, 14 January 2015, Palaiseau.

Avec Sage, le Python est dans la boîte !, Enseigner l'informatique en grande École... et en Classes Préparatoires, 14 May 2014, Paris [in french].

Avec Sage, le Python est dans la boîte !, Journée ISN-EPI, Nancy, 17 April 2014, Paris [in french].

L'ordinateur sait-il calculer ? [in french], visite au LORIA de collégiens et lycéens dans le cadre de Maths-en-Jeans, 26 March 2014, Nancy, France.

Advanced Tutorial on Sage at Euroscipy 2013, Bruxelles, August 22, 2013, with accompanying Sage worksheet.

Sélection polynomiale non linéaire pour NFS, ARIC seminar, Lyon, 15 November 2012.

Cryptographie, Lycée Jean de Pange, Sarreguemines, 10 February 2012 [in french].

Random Generation with Philippe Flajolet, talk given at the conference in memory of Philippe Flajolet, Philippe Flajolet and Analytic Combinatorics, 15 December 2011.

Short Division of Long Integers, Caramel seminar, 6 October 2011.

GNU MPFR: back to the future, MaGiX@LiX 2011 Conference, Palaiseau, France, 23 September 2011.

Short Division of Long Integers, 20th IEEE Symposium on Computer Arithmetic (ARITH-20), Tuebingen, Germany, 25 July 2011.

Mathématiques et Cryptographie, colloque Mathématiques et Société organisé par l'Académie Lorraine des Sciences, Nancy, 20 novembre 2010.

Peut-on calculer sur ordinateur ?, exposé aux Leçons de Mathématiques d'Aujourd'hui, Bordeaux, 7 octobre 2010.

Reliable computing with GNU MPFR, Third International Congress on Mathematical Software, Kobe, Japan, September 14, 2010.

An O(M(n) log n) algorithm for the Jacobi symbol, ANTS-IX, Nancy, France, July 20, 2010.

Factorization of a 768-bit RSA modulus, Workshop on Tools for Cryptanalysis 2010, Royal Holloway, University of London, UK, June 22-23, 2010.

Factorisation d'entier : état de l'art, exposé à l'ANSSI, May 31, 2010 [in french].

1.82?, séminaire Caramel, May 28, 2010 [in french].

An Implementation of Orrick's Algorithm, Hadamard Maximal Determinant Workshop, MSI, ANU, Canberra, May 14, 2010.

Calcul flottant, lycée Jeanne d'Arc, 5 March 2010 [in french].

Sage : une alternative libre à Magma, Maple, Mathematica et Matlab, Journée Plume "Les alternatives libres aux outils propriétaires de maths", 4 February 2010, Paris [in french].

An O(M(n) log n) algorithm for the Jacobi symbol, Leiden University, January 20, 2010, Symposium on crypto-related number-theoretic algorithms, . Other photos from Willemien Ekkelkamp's PhD defense: , (credit Herman te Riele).

Arithmétique moderne, cours aux 3èmes Rencontres Arithmétique de l'Informatique Mathématique (RAIM'09), October 28, 2009 [in french].

Modern Computer Arithmetic, MSR Talk Series, Microsoft Research, Redmond, June 12, 2009.

CADO-NFS: An Implementation of The Number Field Sieve, May-June 2009.

Sage: an open-source mathematics software, invited talk at the 2nd public workshop of the SCIEnce Project, École Polytechnique, Palaiseau, France, 19-21 January 2009.

Peut-on faire confiance au calcul flottant ?, exposé à l'Institut de Physique du Globe de Strasbourg, 16 janvier 2009 [in french].

Modular arithmetic, invited talk at the Central European Conference on Cryptography, Graz, Austria, July 2-4, 2008.

Implementation of the inverse square root in MPFR, Dagstuhl seminar "Numerical Validation in Current Hardware Architectures", January 06-11, 2008. This was a hand-written talk, details in the algorithms.tex file from the MPFR distribution.

The MPFR library: well-defined semantics for multiple-precision floating-point numbers, SAGE Days 6 [wiki], Bristol, November 11, 2007 [invited talk].

The Ups and Downs of PARI/GP in the last 20 years , Explicit Methods in Number Theory, Colloquium in honour of Henri Cohen, 15-19 October 2007, Bordeaux [invited talk].

Évaluation des réalisations, séminaire RéseauDev, Paris, 21 mai 2007.

How Fast Can We Multiply Over GF(2)[x]?, Conference on Algorithmic Number Theory, Turku (Finland), May 8-11, 2007 [invited talk]

A GMP-based implementation of Schönhage-Strassen's large integer multiplication algorithm, HDA'07 workshop, Canberra, February 2007, and photos with Richard Brent, Jim White and Joerg Arndt: Jim, Joerg, Paul at the cafe behind the school of art, Paul, Jim, Joerg in front of the school of art, again, and again, Paul, Jim, Richard still in front of the school of art; Paul, Jim, Joerg and Richard in front of the guest room, Prof. Zimmermann, Jim and Richard.

Arithmétique entière, Journées Nationales de Calcul Formel, Luminy, 29 janvier - 2 février 2007 [exposé invité].

Worst cases for sin(BIG), talk at the IEEE 754 revision committee, Apple Cupertino, November 2, 2006. See also the slides of Jean-Michel Muller and Nicolas Brisebarre.

Can we trust floating-point numbers?, ``Computer Mathematics'' session (chair Henk Barendregt), from the ``Grand Challenges of Informatics'' Academia Europaea Informatics Section Symposium, Budapest, September 19-20, 2006 [invited talk]. [videos] [ , photos thanks to Dines Bjorner]

20 Years of ECM, 7th Algorithmic Number Theory Symposium, Berlin, July 23-28, 2006. Here is a photo of Herman te Riele, me, Richard Brent and Alexander Kruppa (left to right) in a Biergarten (courtesy A. Kruppa).

The bit-burst algorithm, Computing by the Numbers: Algorithms, Precision, and Complexity, Workshop in honor of the 60th birthday of Richard Brent, Berlin, July 20-21, 2006.

IEEE 754 Revision, Dagstuhl Seminar 06021, 12 January, 2006.

Fast evaluation of sine and cosine for real argument, Dagstuhl Seminar 06021, 12 January, 2006.

Why transcendentals and arbitrary precision?, IEEE 754 revision committee, Sun Menlo Park, December 15, 2005.

Error bounds on complex floating-point multiplication, Sun Menlo Park, December 14, 2005.

MPFR: une bibliothèque de calcul flottant en précision arbitraire avec arrondi correct [in french], INRIA Rocquencourt, March 16, 2005.

MPFR: a multiple-precision floating-point library with correct rounding, PARI/GP workshop, IHP, Paris, September 15, 2004 [invited talk].

Symbolic Computation: Recent Progress and New Frontiers, invited talk at SCAN'2002, September 2002.

Symbolic computation and computer algebra systems are usually known to be either very slow, or memory expensive. However, some specific symbolic computation problems have received in the last years new algorithmic solutions, which enabled to push further the limits of what is doable within a reasonable amount of time and space. Some noticeable examples are polynomial factorisation, lattice reduction, Groebner basis computation. We will present a few such algorithms, together with a state-of-the-art of what problems computer algebra systems can (or cannot) solve, and for each problem what the current frontiers are.