# Talks

*Click on a title to see the slides.*

**Positivity of Linear Recurrent Sequences via Invariant Cones**, a talk at the Joint Conference De Rerum Natura & Functional Equations and Interactions, Anglet, June 2024. An earlier version was given at the Bellairs Workshop on Algorithmic Aspects of Dynamical Systems, Barbados, May 2023. Corresponding Maple demonstration pdf.**Computation of Sums and Integrals by Reduction-Based Creative Telescoping**, a talk at the differential seminar, Paris, December 2023. Corresponding Maple demonstration pdf.**Minimization of Differential Equations and Algebraic Values of E-Functions**, a talk at the Atelier E-fonctions, G-fonctions et périods, Paris, January 2023. Corresponding Maple demonstration pdf.**Absolute Root Separation**, a talk an Oberwolfach meeting on Enumerative Combinatorics, December 2022. An earlier version was given at at the journées du GDR EFI, June 2021 and an even earlier one at our seminar, Lyon, March 2020. Corresponding Maple demonstration pdf.**Walks in Cones and Tight Enclosures of Laplacian Eigenvalues**, a talk at Lattice Paths, Combinatorics and Interactions, June 2021. A 2h-long version was previously given at the working group*Transcendance et Combinatoire*, May 2021. An earlier and shorter version was given at our workshop on Fast and Reliable Approximation, Lyon, May 2019.**Certified Numerics in the Asymptotics of Rational Function Coefficients**, at the Nuscap days in Toulouse, June 2022. An earlier version was given at the joint Polsys-Specfun seminar in June 2021.**Generalized Hermite Reduction, Creative Telescoping and Definite Integration of D-Finite Function**, a talk at Applications of Computer Algebra in Santiago de Compostella, June 2018. An earlier version was given at the FastRelax Days in Sophia-Antipolis.**Algorithmic Tools for the Asymptotics of Linear Recurrences**, a talk at our seminar, March 2018. An earlier version was given at the Workshop on Computer Algebra in Combinatorics at the ESI in Vienna, November 2017.**Recursive Combinatorial Structures: Enumeration, Probabilistic Analysis and Random Generation**, a 3h-long tutorial at STACS’2018, February 2018. Corresponding software demonstration maple format,pdf.**On (Effective) Analytic Combinatorics**, a talk at the Séminaire Algorithmes organized by Claire Mathieu at the Collège de France, December 2017. Corresponding software demonstration.**Algorithmic Tools for the Asymptotics of Diagonals**, a talk longer than the previous one and more focused on diagonals, at the meeting on Lattice walks at the Interface of Algebra, Analysis and Combinatorics in Banff, Canada, September 2017. This is a minor update of an invited talk entitled Diagonals: Combinatorics, Asymptotics and Computer Algebra, given at the Analysis of Algorithms conference, Princeton, June 2017.**Linear Differential Equations as a Data-Structure**, a talk at the conference on Foundations of Computational Mathematics. The slides contain pictures of colleagues who were in the audience and to whom I could redirect questions. Barcelona, July 2017.**Combinatorial Newton Iteration with Michèle**, a talk at the workshop for Michèle Soria’s emeritus title, Paris, May 2017.**Symbolic-Numeric Tools for Multivariate Analytic Combinatorics**, a talk at the FastRelax Meeting, Toulouse, May 2016.**An Introduction to Analytic Combinatorics**, a presentation at the Meeting in Discrete Structures of the LIP, Lyon, Dec. 2015.**An Introduction to Recent Algorithms Behind the DDMF**, a talk that followed a presentation of the DDMF by Frédéric Chyzak at the International Symposium on Orthogonal Polynomials, Special Functions & Applications, NIST, Maryland, June 2015.**Linear differential equations and recurrences as a data-structure**, a 2h-long talk in the very nice atmosphere of the famous Leçons de Mathématiques et d’Informatique d’Aujourd’hui, Bordeaux, May 2015.**Introduction to D-finiteness and creative telescoping**, a talk at the workshop on Approximation and Combinatorics in Luminy, with a focus on results on bounds, algebraic series and approximation results in the sense of this semester of CIRM dedicated to Artin approximation, April 2015.-
**Multiple Binomial Sums**, an overview on creative telescoping together with a presentation of our new summation algorithm, with a small demo, presented at Foundations of Computational Mathematics in Montevideo, December 2014. A more focused and technical talk on the same subject at our AriC seminar, March 2014. A shorter version was given at the workshop Journées Holonomes in Grenoble, February 2014 and at the meeting on Enumerative Combinatorics in Oberwolfach, March 2014. -
**Algorithmic Variations on Linear Differential Equations**is a very flexible title for a survey talk on various recent results. This version was presented at the very nice MBM2014 day organized at Labri (Bordeaux) when Mireille Bousquet-Mélou was awarded the silver medal of the CNRS, in October 2014. An earlier variant of this talk (with a different selection of topics) was given at the Séminaire de Combinatoire et Théorie des Nombres at Institut Camille Jordan, December 2012. It was itself a variant of a previous version at IHES for their workshop on Differential Equations and Galois Theory, Bures-sur-Yvette, October 2011. -
**Reliable numerical evaluation of special functions. Algorithms and experiments**, a talk at the Challenges in 21st Century Experimental Mathematical Computation of ICERM, July 2014. A longer version, but more preliminary, was given at the nice meeting of the MAC team in Banyuls, June 2014. -
**Implicit Species at the Basis of Analytic Combinatorics**. A talk at the conference AofA 2013 in Menorca, May 2013. -
**An introduction to species theory**. A talk at the seminar of the team PLUME in ENS-Lyon. May 2013. -
**Newton Iteration, Computer Algebra and Combinatorics**. A talk at the day celebrating the opening of the library of the University of Versailles named after Philippe Flajolet, May 2013. This is an improved version (with more focus) of a previous talk at the Journées d’Informatique Fondamentale de Paris Diderot, April 2013. An earlier version was given on the occasion of Pierre Nicodème’s retirement in Villetaneuse, February 2013. -
**Un peu de calcul formel pour l’analyse**. Talk at the day for newcomers in the LIP, January 2013. -
**Automatic Proofs of Identities**(with a version in video). A talk at the Séminaire de Combinatoire Philippe Flajolet at the IHP, Paris, May 2011. I also gave it the following month at the Séminaire du Labri in Bordeaux. A very close version was presented at Computational and Analytical Mathematics Conference in honour of Jonathan Borwein’s 60th birthday, Vancouver, May 2011. This is the one for which there is this video. An earlier variant of this talk was also presented at the seminar of the Key Laboratory of Mathematics Mechanization of the Chinese Academy of Sciences (Beijing, November 2010) and at the seminar of the laboratoire d’informatique Gaspard Monge of the University of Marne-la-Vallée. December 2010. An older version called Automatic Proofs of Identities: Beyond A=B was an invited talk at FPSAC 2009, Linz, July 2009. This was itself an improved version of a talk at the LIP Seminar. April 2009 and another one at the Journées de Combinatoire de Bordeaux. February 2009. -
**Newton Iteration for Combinatorial Systems and Applications**, a talk given at the Colloquium de l’Institut de Mathématiques de Bordeaux, June 2012. An earlier version was given at the Discrete Math Seminars at Simon Fraser University, May 2011. A version tailored to the audience of Alea 2011 was given at the meeting in Luminy in March 2011. -
**The Dynamic Dictionary of Mathematical Functions**. A presentation of the DDMF at an invited talk at the Conferences on Intelligent Computer Mathematics. Paris, July 2010. A slightly shorter version at the International Congress on Mathematical Software. Kobe, September 2010. An earlier one was presented at the Joint Institutes Workshop of the joint Inria-Microsoft Research Centre. April 2010. An older version presenting the state of DDMF in 2009 was given at the Forum 2009 of the joint Inria-Microsoft Research Centre. January 2009. -
**Newton Iteration: From Numerics to Combinatorics, and Back**, an invited talk at ANALCO10, Austin, Texas, January 2010. -
**Automatic Analysis of Combinatorial Structures, Old and New**. A talk on the same topic as the next one, but for a different audience. This was for Philippe Flajolet’s 60th birthday. December 2008. -
**Combinatorial Newton Iteration and Efficient Random Generation**. A talk at the Conference Gecko/Tera08 for Marc Giusti’s 60th birthday. See also the corresponding article. November 2008. -
**Composition of Power Series, Change of Basis and Orthogonal Polynomials**(handout version). A talk at the Algorithms Seminar, based on both our issac article and later report, June 2008. -
**Gfun: 15 years later**. A 45 minutes talk at the Workshop on Combinatorics and Statistical Physics of the Erwin Schrödinger International Institute for Mathematical Physics, Vienna, May 2008. A shorter version had been given at the Joint Mathematics Meeting of the AMS and the MAA at New Orleans, January 2007. -
**Asymptotic Analysis for the Analysis of Algorithms**with its Maple examples. A minicourse at the 2008 International Conference on the Analysis of Algorithms. April 2008. -
**Differential Equations for Algebraic Functions**. A talk at the Algorithms Seminar, based on our issac article. June 2007. -
**D-finiteness**. A 4-hour course at the Ecole Jeunes Chercheurs en Informatique Mathématique with Alin Bostan and Frédéric Chyzak. March 2007. -
**Fast Computation of Power Series Solutions of Systems of Differential Equations**. This is the talk given at SODA 2007 corresponding to our paper with A. Bostan, F. Chyzak, F. Ollivier, E. Schost and A. Sedoglavic. January 2007. -
**On the Complexity of Gröbner Basis Computation for Regular and Semi-Regular Systems**A talk at the workshop Algorithms in Algebraic Geometry of the IMA, September 2006. I had given an earlier version of this talk at the 10th seminar on Analysis of Algorithms, Berkeley 2004. -
**Automatic Proofs of Special Functions or Combinatorial Identities**A presentation for professors in the*classes préparatoires*in the journées informatiques X-UPS, Palaiseau, May 2006. -
**Fast compact solutions of linear differential and difference equations**A talk at the Waterloo Workshop on Computer Algebra for Sergei Abramov’s 60th birthday, Waterloo, April 2006. -
**D-finiteness: Algorithms and Applications**, an invited talk at ISSAC 2005, Beijing, July 2005. -
**Polynomial and Rational Solutions of Linear Differential or Difference Equations**A talk at the Algorithms Seminar in May 2005. -
**Analytic Combinatorics of Connected Graphs**(in French). A talk that I gave at UQAM (Montreal), at the Algorithms Seminar, at the Alea’04 meeting (in English), and at the “Séminaire Physique Mathématique et Géométrie” in Paris. **Introduction to D-finite series**A series of two talks I gave at the ALEA’03 meeting.

Before that, I was using old-fashioned transparencies.