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Thibaut Verron

About me   english

I was a post-doctoral researcher at the Institute for Algebra at the Johannes Kepler University (Linz, Austria), and the principal investigator of the FWF project P34872 on algorithms for solving certain systems of structured polynomial equations.

My research interest is in effective mathematics, in particular in algebra and geometry. More precisely, I like to describe and develop algorithms to help handle complicated mathematical objects arising in applications.

In this framework, I have been working on algorithms for solving polynomial systems, and in particular on the regularity of the computation of Gröbner bases in different contexts: weighted homogeneous systems which arise for example in cryptography, a classification problem in real algebraic geometry which arose from an optimal control problem, polynomial systems over rings which appear for example in number theory, and systems described by convergent power series from \(p\)-adic geometry.

I studied Mathematics and Computer Science at the École Normale Supérieure in Paris, and I obtained my Masters in Mathematics at the University Paris 11 (Orsay) in 2012. I prepared my PhD thesis in the PolSys team, in the LIP6 (Sorbonne Universités, Paris, France), under the supervision of Jean-Charles Faugère and Mohab Safey El Din. I then spent one year as a post-doc at IRIT (ENSEEIHT, Toulouse, France), working with Joseph Gergaud and Olivier Cots on algebraic techniques for optimal control. I moved to Linz in 2017, and I worked for 4 years with Manuel Kauers on algorithmic combinatorics and computer algebra, in particular algorithmic questions related to D-finite functions and equations.

Publications   english

DONE Preprints
  • Short proofs of ideal membership (2023)
    C. Hofstadler, T. Verron
    LinksLinksLiens: .pdf, arXiv
  • On the computation of Gröbner bases for matrix-weighted homogeneous systems (2022)
    T. Verron
    LinksLinksLiens: .pdf, arXiv, .bib
  • Signature-based Möller's Algorithm for strong Gröbner bases over PIDs (2019)
    M. Francis, T. Verron
    LinksLinksLiens: .pdf, arXiv, .bib, source codecode sourceQuellcode
  • Algebraic-geometric techniques for the feedback classification and robustness of the optimal control of a pair of Bloch equations with application to Magnetic Resonance Imaging (2017)
    B. Bonnard, O. Cots, J.-C. Faugère, A. Jacquemard, J. Rouot, M. Safey El Din, T. Verron
    LinksLinksLiens: .pdf, hal, .bib
DONE Journals
  • Signature Gröbner bases, bases of syzygies and cofactor reconstruction in the free algebra
    C. Hofstadler, T. Verron
    Journal of Symbolic Computation
    LinksLinksLiens: .pdf, arXiv, doi:10.1016/j.jsc.2022.04.001, .bib
  • On Affine Tropical F5 Algorithms (Extended version)
    T. Vaccon, T. Verron, K. Yokoyama
    Journal of Symbolic Computations, Volume 102, 2021
    LinksLinksLiens: .pdf, doi:10.1016/j.jsc.2019.10.012, .bib
  • A Signature-based Algorithm for Computing Gröbner Bases over Principal Ideal Domains
    M. Francis, T. Verron
    Mathematics in Computer Science, Volume 14, Issue 2, 2020
    LinksLinksLiens: .pdf, arXiv, doi:10.1007/s11786-019-00432-5, .bib, source codecode sourceQuellcode
  • Time minimal saturation of a pair of spins and application in Magnetic Resonance Imaging
    B. Bonnard, O. Cots, J. Rouot, T. Verron
    Mathematical Control and Related Fields, Volume 10, Issue 1, 2020
    LinksLinksLiens: hal, doi:10.3934/mcrf.2019029, bib
  • On the complexity of computing Gröbner bases for weighted homogeneous systems
    J.-C. Faugère, M. Safey El Din, T. Verron
    Journal of Symbolic Computations, Volume 76, 2016
    LinksLinksLiens: .pdf, arXiv, doi:10.1016/j.jsc.2015.12.001, .bib
DONE Conference proceedings
  • Signature Gröbner bases in free algebras over rings
    C. Hofstadler, T. Verron
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2023
    LinksLinksLiens: .pdf, arXiv, doi:10.1145/3597066.3597071
  • Universal Analytic Gröbner Bases and Tropical Geometry
    T. Vaccon, T. Verron
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2023
    LinksLinksLiens: .pdf, doi:10.1145/3597066.3597110
  • Transcendence certificates of D-finite functions
    M. Kauers, C. Koutschan, T. Verron
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2023
    LinksLinksLiens: .pdf, arXiv, doi:10.1145/3597066.3597091
  • On Polynomial Ideals and Overconvergence in Tate Algebras
    X. Caruso, T. Vaccon, T. Verron
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2022
    LinksLinksLiens: .pdf, arXiv, doi:10.1145/3476446.3535491, .bib
  • On Two Signature Variants Of Buchberger’s Algorithm Over Principal Ideal Domains
    M. Francis, T. Verron
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2021
    LinksLinksLiens: .pdf, arXiv, doi:10.1145/3452143.3465522, .bib, source codecode sourceQuellcode
  • On FGLM Algorithms With Tate Algebras
    X. Caruso, T. Vaccon, T. Verron
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2021
    LinksLinksLiens: .pdf, arXiv, doi:10.1145/3452143.3465521, slides, .bib
  • The generating function of Kreweras walks with interacting boundaries is not algebraic
    A. Bostan, M. Kauers, T. Verron
    Séminaire Lotharingien de Combinatoire, Issue 85B, 2021, Formal Power Series and Algebraic Combinatorics (FPSAC) 2021
    LinksLinksLiens: .pdf, arXiv, .bib, poster, source codecode sourceQuellcode
  • Signature-based algorithms for Gröbner bases over Tate algebras
    X. Caruso, T. Vaccon, T. Verron
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2020
    Kalamata, Greece (online), 2020/07/20
    LinksLinksLiens: .pdf, arXiv, doi:10.1145/3373207.3404035, .bib, slides, video presentation
  • Integral bases for P-recursive sequences
    S. Chen, L. Du, M. Kauers, T. Verron
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2020
    Kalamata, Greece (online), 2020/07/20
    LinksLinksLiens: .pdf, arXiv, doi:10.1145/3373207.3404004, .bib
  • Gröbner bases over Tate algebras
    X. Caruso, T. Vaccon, T. Verron
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2019
    Beihang University, Beijing, China, 2019/07/15
    LinksLinksLiens: .pdf, arXiv, doi:10.1145/3326229.3326257, .bib, slides
  • On affine tropical F5 algorithms
    T. Vaccon, T. Verron, K. Yokoyama
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2018
    CUNY Graduate Center, New York, USA, 2018/07/18
    LinksLinksLiens: .pdf, arXiv, doi:10.1145/3208976.3209012, .bib
  • Determinantal sets, singularities and application to optimal control in medical imagery
    B. Bonnard, J.-C. Faugère, A. Jacquemard, M. Safey El Din, T. Verron
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2016
    Wilfrid Laurier University, Waterloo, Canada, 2016/07/20
    LinksLinksLiens: .pdf, arXiv, doi:10.1145/2930889.2930916, .bib, slides, source codecode sourceQuellcode
  • On the complexity of computing Gröbner bases for quasi-homogeneous systems
    J.-C. Faugère, M. Safey El Din, T. Verron
    International Symposium on Symbolic and Algebraic Computation (ISSAC) 2013
    Northeastern University, Boston, USA, 2013/06/29
    LinksLinksLiens: .pdf, arXiv, doi:10.1145/2465506.2465943, .bib, slides
DONE Others
  • Why You Should Remove Zeros From Data Before Guessing (Poster presented at ISSAC 2019)
    M. Kauers, T. Verron
    ACM Communications in Computer Algebra, Volume 53, Issue 3, 2019
    LinksLinksLiens: .pdf, doi:10.1145/3377006.3377017, poster
  • Working Notes on the Time Minimal Saturation of a Pair of Spins and Application in Magnetic Resonance Imaging
    B. Bonnard, O. Cots, J. Rouot, T. Verron
    LinksLinksLiens: .pdf, hal, .bib
  • Computer Algebra - Fast polynomial arithmetic and factorization (Lecture notes, accessible to Bachelor students)
    LinksLinksLiens: .pdf
DONE Thesis
  • Regularisation of Gröbner basis computations for weighted and determinantal systems, and an application to medical imagery
    Defended on 2016/09/26
    LinksLinksLiens: .pdf, erratum (last updated on 2019/07/22), .bib, slides

Selected talks (full list here)   english

  • Universal analytic Gröbner bases and tropical geometry
    International Symposium on Symbolic and Algebraic Computation 2023
    Tromsø, Norway, 2023/07/27
    LinksLinksLiens: slides
  • Using signature Gröbner bases to find short ideal representations
    SIAM Conference on Applied Algebraic Geometry
    TU Eindhoven, Eindhoven, The Netherlands, 2023/07/14
    LinksLinksLiens: slides
  • Signature Gröbner bases in the free algebra
    Journées Nationales de Calcul Formel (JNCF 2022)
    CIRM, Luminy (France), 2022/03/03
    LinksLinksLiens: abstract, slides
  • Two signature-based variants of Buchberger’s algorithm for Gröbner bases over principal ideal domains
    "Calcul formel" team seminar
    XLIM, Université de Limoges, France (online), 2021/03/30
    LinksLinksLiens: slides
  • Working with valuations
    "Calcul formel" team seminar
    XLIM, Université de Limoges, France, 2020/02/27
    LinksLinksLiens: slides
  • Software tutorial: Computing elimination polynomials using interpolation
    SFB Statusseminar
    Strobl, Austria, 2018/12/04
    LinksLinksLiens: org worksheet (can be opened as a plain-text file), html
  • Algebraic classification methods for an optimal control problem in medical imagery
    Seminar Algebra and Discrete Mathematics
    Johannes Kepler University, Linz, Austria, 2017/12/07
    LinksLinksLiens: slides
  • Régularité du calcul de bases de Gröbner pour les systèmes homogènes avec poids
    Séminaire Géométrie et algèbre effectives
    IRMAR, Université Rennes 1, Rennes, France, 2017/06/02
    LinksLinksLiens: abstract (in French), slides

Teaching   english

Johannes Kepler University, Linz
[325.01n] Mathematics for physicists 2

2022-2023 Summer semester, exercise sessions in German: all material on Moodle

[368.164] Computer Algebra 2

2018-2019 Winter semester: informations and documents

[368.19n] Algebra for computer scientists

2022-2023 Summer semester, exercise sessions in German: all material on Moodle

2021-2022 Summer semester, exercise sessions in German: all material on Moodle

2019-2020 Summer semester, exercise sessions in English: all material on Moodle

2018-2019 Summer semester, exercise sessions in English: lecture slides and exercise sheets on Moodle

[368.492] Mathematics for AI 2

2020-2021 Summer semester: all material on Moodle

Institut National Polytechnique, Toulouse

(More information on the French version of this page)

Université Pierre et Marie Curie, Paris

(More information on the French version of this page)

Software   english

Tate Algebras

Sage package for working with Tate series over \(\mathbb{Z}_p\) and \(\mathbb{Q}_p\). Class definitions are implemented, as well as algorithms for computing Gröbner bases (Buchberger's algorithm and two signature-based algorithms). Joint development with Xavier Caruso and Tristan Vaccon.

News:
  • 20/07/2020: Presentation of the signature-based algorithms at ISSAC 2020 (slides and video).
  • 20/05/2020: SageMath 9.1 is out, with the signature-based algorithms.
  • 15/07/2019: Presentation of the theory and of Buchberger's algorithm at ISSAC 2019 (slides).
  • 22/12/2018: SageMath 8.5 is out, with the Tate algebra package.
Signature Gröbner bases over PIDs

Magma implementation of signature-enabled versions of Möller's algorithms for computing Gröbner bases for PIDs. The algorithms were presented at ACA 2018 (slides), SIAM AG 2019 (slides) and ISSAC 2021.

Real algebraic classification algorithms for determinantal varieties

Maple implementation of algorithms computing a classification of the real singularities of determinantal varieties. The algorithms were presented at ISSAC 2016 (slides), in the context of an application to contrast optimization in medical imagery. Joint development with Mohab Safey El Din.

Magma-mode

Emacs mode to edit Magma source code. It is built upon the magma-mode written by Luk Bettale. The package can be obtained from github or via melpa.