Software engineer
Ingénieur logiciel
Software-Entwickler
Mindbreeze GmbH
Mindbreeze GmbH
Mindbreeze GmbH
Linz,
Austria
Autriche
Österreich
CV CV (en anglais) Lebenslauf (auf Englisch)
Stackexchange profile Profil sur Stackexchange Profil auf Stackexchange
About me english
I am currently a software engineer at Mindbreeze in Linz, Austria.
Before that, 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.
The focus of my research was 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
- Signature-based Möller's Algorithm for strong Gröbner bases over PIDs (2019)
- 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)
DONE Journals
- On the computation of Gröbner bases for matrix-weighted homogeneous systemsT. Verron
Journal of Symbolic Computation, Volume 125, 2024
LinksLinksLiens: .pdf, arXiv, doi:10.1016/j.jsc.2024.102327, .bib - Short proofs of ideal membershipC. Hofstadler, T. Verron
Journal of Symbolic Computation, Volume 125, 2024
LinksLinksLiens: .pdf, arXiv, doi:10.1016/j.jsc.2024.102325, .bib - Signature Gröbner bases, bases of syzygies and cofactor reconstruction in the free algebraC. Hofstadler, T. Verron
Journal of Symbolic Computation, Volume 113, 2022
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 DomainsM. 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 ImagingB. 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 systemsJ.-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 ringsC. 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 GeometryT. Vaccon, T. Verron
International Symposium on Symbolic and Algebraic Computation (ISSAC) 2023
LinksLinksLiens: .pdf, doi:10.1145/3597066.3597110 - Transcendence certificates of D-finite functionsM. 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 AlgebrasX. 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 DomainsM. 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 AlgebrasX. 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 algebraicA. 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 algebrasX. 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 sequencesS. 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 algebrasX. 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 algorithmsT. 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 imageryB. 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 systemsJ.-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 - Computer Algebra - Fast polynomial arithmetic and factorization (Lecture notes, accessible to Bachelor students)
Selected talks (full list here) english
- Universal analytic Gröbner bases and tropical geometryInternational Symposium on Symbolic and Algebraic Computation 2023
Tromsø, Norway, 2023/07/27
LinksLinksLiens: slides - Using signature Gröbner bases to find short ideal representationsSIAM Conference on Applied Algebraic Geometry
TU Eindhoven, Eindhoven, The Netherlands, 2023/07/14
LinksLinksLiens: slides - Signature Gröbner bases in the free algebraJournées 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
- Software tutorial: Computing elimination polynomials using interpolationSFB 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 imagerySeminar 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 poidsSéminaire Géométrie et algèbre effectives
IRMAR, Université Rennes 1, Rennes, France, 2017/06/02
LinksLinksLiens: abstract (in French), slides
Teaching english
Johannes Kepler University, Linz
2022-2023 Summer semester, exercise sessions in German: all material on Moodle
2018-2019 Winter semester: informations and documents
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
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.
- 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.
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.