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Thibaut Verron

DONE About me   english

I am currently a post-doc at the Institute for Algebra at the Johannes Kepler University (Linz, Austria), working with Manuel Kauers on algorithmic combinatorics and computer algebra, in particular algorithmic questions related to D-finite functions and 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, before moving to my current position in Linz.

DONE Publications   english

DONE Preprints
  • 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
  • On Affine Tropical F5 Algorithms (Extended version)
    T. Vaccon, T. Verron, K. Yokoyama
    To appear in Journal of Symbolic Computations: special issue on the ISSAC 2018 conference
    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
    To appear in Mathematics in Computer Science: special issue on the ACA 2018 conference
    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-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 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

DONE Selected talks (full list here)   english

DONE Teaching   english

Johannes Kepler University, Linz
[368.19n] Algebra (Linear algebra for computer scientists)

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

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

[368.164] Computer Algebra 2

2018-2019 Winter semester: informations and documents

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)

DONE 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. Möller's weak GB algorithm with signatures was presented at ACA 2018 (slides), and Möller's strong GB algorithm with signatures were presented at SIAM AG 2019 (slides).

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.