Rémi Imbach

E-mail: remi.imbach(at)laposte.net

Short bio

I am currently a research engineer in the MoCo research team at IRMA (Institute for Advanced Mathematical Research), University of Strasbourg.

From may 2021 to october 2023 I was a research engineer in the GAMBLE research team at INRIA (National Institute for Research in Computer Science and Control).

From May 2018 to September 2020 I was assistant professor (without tenure) at Courant Institute of Mathematical Sciences, New York University.

From June 2017 to March 2018 I was part of the AGAG (Algebra, Geometry and Computer Algebra) group as Scientific Assistant at Technische Universität Kaiserslautern, department of Mathematics.

From November 2014 to October 2016 I held a post-doctoral position in the VEGAS (Effective Geometric Algorithms for Surfaces and Visibility) research team at INRIA.

I was previously PhD student, then A.T.E.R (teaching & research position), in the IGG (Computer Graphics and Geometry) team of the ICube laboratory, Université de Strasbourg.

My research specialities are: certified root/solution clustering, symbolic numeric algorithms, computational algebraic geometry and certified geometric computation.

Please find here a detailed CV in French.
Software

2023 pwpoly is now released as a C library and soon available as a package for python and in Maple 2024. It implements our fast root finding algorithm described in [IM23].

2023 befft , a C library for radix-2 fft in double precision with bounded error is available

2023 Our implementation of the complex root approximation algorithm of [Moroz21] is now available througth the fsolve command (and RootFinding:-Isolate , HR method) in Maple 2023.

Aug. 2019 Ccluster.jl now implements the root clustering algorithm for triangular algebraic systems of [IPY19].

June 2018 Ccluster is an implementation of a neer optimal complex root clustering algorithm (see [BSS+16]). It is available either as a stand-alone program, or in the package Ccluster.jl for the programming language Julia

March 2016 subdivision_solver is a solver for square systems of polynomial equations using exhaustive search in an initial bounded real domain given as a box (i.e. a vector of intervals). It is specifically designed to handle systems of large dense polynomials and uses adaptive multi-precision arithmetic to stay robust to hard cases. subdivision_solver is proposed as a package for the mathematical software SageMath .

[IM23] Rémi Imbach and Guillaume Moroz. Fast evaluation and root finding for polynomials with floating-point coefficients. In Proceedings of the 48th International Symposium on Symbolic and Algebraic Computation, ISSAC ’23, page 325-334, New York, NY, USA, 2023. Association for Computing Machinery. [ bib | http ]
[Moroz21] Guillaume Moroz. New data structure for univariate polynomial approximation and applications to root isolation, numerical multipoint evaluation, and other problems. 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS) [ DOI ]
[BSS+16] Ruben Becker, Michael Sagraloff, Vikram Sharma, Juan Xu and Chee Yap. Complexity Analysis of Root Clustering for a Complex Polynomial. Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '16 [ DOI ]
List of publications

International Journals
[IPY21] Rémi Imbach, Marc Pouget, and Chee Yap. Clustering complex zeros of triangular systems of polynomials. Mathematics in Computer Science, 15(2):271--292, 2021. [ bib | http ]
[IMP18] Rémi Imbach, Guillaume Moroz, and Marc Pouget. Reliable location with respect to the projection of a smooth space curve. Reliable Computing, 26:13 -- 55, 2018. [ bib | http ]
[IMP17] Rémi Imbach, Guillaume Moroz, and Marc Pouget. A certified numerical algorithm for the topology of resultant and discriminant curves. Journal of Symbolic Computation, 80, Part 2:285 -- 306, 2017. [ bib | DOI | http ]
[IMS17] Rémi Imbach, Pascal Mathis, and Pascal Schreck. A robust and efficient method for solving point distance problems by homotopy. Mathematical Programming: Series A and B, 163(1-2):115--144, 2017. [ bib | http ]
[ISM14] Rémi Imbach, Pascal Schreck, and Pascal Mathis. Leading a continuation method by geometry for solving geometric constraints. Computer-Aided Design, 46:138--147, 2014. [ bib | .pdf ]
International Conferences proceedings
[IM23] Rémi Imbach and Guillaume Moroz. Fast evaluation and root finding for polynomials with floating-point coefficients. In Proceedings of the 48th International Symposium on Symbolic and Algebraic Computation, ISSAC ’23, page 325-334, New York, NY, USA, 2023. Association for Computing Machinery. [ bib | http ]
[IP22] Rémi Imbach and Victor Y Pan. Accelerated subdivision for clustering roots of polynomials given by evaluation oracles. In Computer Algebra in Scientific Computing: 24th International Workshop, CASC 2022, Gebze, Turkey, August 22--26, 2022, Proceedings, pages 143--164. Springer, 2022. [ bib | preprint  ]
[IP21] Rémi Imbach and Victor Y Pan. Root radii and subdivision for polynomial root-finding. In Computer Algebra in Scientific Computing: 23rd International Workshop, CASC 2021, Sochi, Russia, September 13--17, 2021, Proceedings 23, pages 136--156. Springer, 2021. [ bib | preprint ]
[IP20] Rémi Imbach and Victor Y. Pan. New progress in univariate polynomial root finding. In Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, ISSAC ’20, page 249–256, New York, NY, USA, 2020. Association for Computing Machinery. [ bib | DOI | http ]
[IP19] Rémi Imbach and Victor Y. Pan. New practical advances in polynomial root clustering. In Daniel Slamanig, Elias Tsigaridas, and Zafeirakis Zafeirakopoulos, editors, Mathematical Aspects of Computer and Information Sciences, pages 122--137, Cham, 2020. Springer International Publishing. [ bib ]
[IPY+19a] Rémi Imbach, Victor Y. Pan, Chee Yap, Ilias S. Kotsireas, and Vitaly Zaderman. Root-finding with implicit deflation. In Matthew England, Wolfram Koepf, Timur M. Sadykov, Werner M. Seiler, and Evgenii V. Vorozhtsov, editors, Computer Algebra in Scientific Computing, pages 236--245, Cham, 2019. Springer International Publishing. [ bib | http ]
[IPY18] Rémi Imbach, Victor Y. Pan, and Chee Yap. Implementation of a near-optimal complex root clustering algorithm. In James H. Davenport, Manuel Kauers, George Labahn, and Josef Urban, editors, Mathematical Software -- ICMS 2018, pages 235--244, Cham, 2018. Springer International Publishing. [ bib | DOI | http ]
[IMP16] Rémi Imbach, Guillaume Moroz, and Marc Pouget. Numeric and Certified Isolation of the Singularities of the Projection of a Smooth Space Curve. In Ilias S. Kotsireas, Siegfried M. Rump, and Chee K. Yap, editors, Mathematical Aspects of Computer and Information Sciences: 6th International Conference, MACIS 2015, Berlin, Germany, November 11-13, 2015, Revised Selected Papers, pages 78--92, Cham, 2016. Springer International Publishing. [ bib | DOI | http ]
[MSI12] Pascal Mathis, Pascal Schreck, and Rémi Imbach. Decomposition of geometrical constraint systems with reparameterization. In Proceedings of the 27th Annual ACM Symposium on Applied Computing, pages 102--108. ACM, 2012. [ bib | http ]
[IMS11] Rémi Imbach, Pascal Mathis, and Pascal Schreck. Tracking method for reparametrized geometrical constraint systems. In 2011 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, pages 31--38. IEEE, 2011. [ bib | .pdf ]
Technical Report
[Imb16] Rémi Imbach. A Subdivision Solver for Systems of Large Dense Polynomials. Technical Report RT-0476, INRIA Nancy, March 2016. [ bib | http | .pdf ]
French Workshop proceedings
[IMP15] Rémi Imbach, Guillaume Moroz, and Marc Pouget. A certified numerical approach to describe the topology of projected curves. In Journées de l'Association Française d'Informatique Graphique, 2015. [ bib | .pdf ]
[IMS12] Rémi Imbach, Pascal Mathis, and Pascal Schreck. Une approche par décomposition et reparamétrisation de systèmes de contraintes géométriques. In Journées du Groupe de Travail en Modélisation Géométrique, 2012. [ bib | .pdf ]
PhD Thesis
[Imb13] Rémi Imbach. Résolution de contraintes géométriques en guidant une méthode homotopique par la géométrie. PhD thesis, Université de Strasbourg, 2013. [ bib | .pdf ]
Selected communications

Seminars
Jan. 2021 Complex Roots Clustering.
Joint Joint PolSys SpecFun Seminar, Sciences Sorbonne Université, Paris [ http | pdf ]
Nov. 2019 Practical Advances in Complex Root Clustering.
Joint CUNY Graduate Center-Courant Seminar in Symbolic-Numeric Computing, Courant Institute of Mathematical Sciences, New York [ http | pdf ]
Jan. 2019 Complex Roots/Solutions Clustering Algorithms.
OGRE team seminar, Nantes, France
May 2018 Numerical and certified computation of the topology of projected curves.
Joint CUNY Graduate Center-Courant Seminar in Symbolic-Numeric Computing, CUNY Graduate Center, New York [ http  | pdf ]
Jul. 2017 Certified numerical tools for computing the topology of projected curves.
Algebra, Geometry und Computer Algebra seminars, Technische Universit\"at Kaiserslautern Germany [ http  ]
Sep. 2016 Certified numerical tools for computing the topology of projected curves.
AriC seminar, Lyon, France [ http  | pdf ]
International Conferences
Jul. 2023 Fast evaluation and root finding for polynomials with floating-point coefficients. ISSAC '23 (International Symposium on Symbolic and Algebraic Computation), Tromso, Norway. [.pdf ]
Jul. 2020 New progress in univariate polynomial root finding. ISSAC '20 (International Symposium on Symbolic and Algebraic Computation), Online. [.pdf ]
Aug. 2019 Clustering Complex Zeros of Triangular Systems of Polynomials. CASC 2019 (Computer Algebra in Scientific Computing), Moscow, Russia. [.pdf ]
July 2018 Implementation of a near-optimal complex root clustering algorithm . ICMS 2018 (International Congress of Mathematical Software), Notre-Dame, USA. [.pdf ]
June 2016 Interval tools for computing the topology of projected curves. SWIM 2016 (Summer Workshop on Interval Methods) Lyon, France [.pdf ]
Nov. 2015 Numeric and Certified Isolation of the Singularities of the Projection of a Smooth Space Curve. MACIS 2015 (Sixth International Conference on Mathematical Aspects of Computer and Information Sciences), Berlin, Germany [.pdf ]
Nov. 2013 Leading a continuation method by geometry for solving geometric constraints. GD/SPM 13 (Geometric and Physical Modeling), Denver, Colorado, USA [.pdf ]
Sept. 2011 Tracking method for reparametrized geometrical constraint systems. SYNASC 11 (Symposium on Symbolic and Numeric Algorithms for Scientific Computing), Timisoara, Roumanie
National Workshops
Nov. 2015 A Certified Numerical Approach to Describe the Topology of Projected Curves. Journées de l'Association Française d'Informatique Graphique 2015, Lyon [.pdf ]
Oct. 2015 Numeric certified algorithm for computing the topology of projections of real spatial curves. Journées Informatique et Géométrie 2015, ESIEE Parie, Marne-la-Vallée [.pdf ]
Jun. 2014 Une méthode de continuation guidée par la géométrie pour résoudre des systémes de contraintes géométriques. INRIA Nancy - Grand Est, France [.pdf ]
Mar. 2012 Une approche par décomposition et reparamétrisation de systèmes de contraintes géométriques. Journées du Groupe de Travail en Modélisation Géométrique, Strasbourg, France
PHD Defense
Oct. 2013 Résolution de contraintes géométriques en guidant une méthode homotopique par la géométrie. Université de Strasbourg, France [.pdf ]
Some of the documents proposed here contains animations that can only be, as far as I know, visualized with latest versions of a well-known pdf viewer. You can contact me to obtain a version without animations.

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