Thibaut Verron

I am currently 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.

#### DONE Publications   english

##### DONE Preprints
• Signature Gröbner bases, bases of syzygies and cofactor reconstruction in the free algebra (2021)
• Signature-based Möller's Algorithm for strong Gröbner bases over PIDs (2019)
M. Francis, T. Verron
• 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
##### DONE Journals
• On Affine Tropical F5 Algorithms (Extended version)
T. Vaccon, T. Verron, K. Yokoyama
Journal of Symbolic Computations, Volume 102, 2021
• 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
• 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
• 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
##### DONE Conference proceedings
• 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
• On FGLM Algorithms With Tate Algebras
X. Caruso, T. Vaccon, T. Verron
International Symposium on Symbolic and Algebraic Computation (ISSAC) 2021
• The generating function of Kreweras walks with interacting boundaries is not algebraic
A. Bostan, M. Kauers, T. Verron
To appear in Formal Power Series and Algebraic Combinatorics (FPSAC) 2021
• 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
• 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
• 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
• 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
• 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
• 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
##### 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
• 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
• Computer Algebra - Fast polynomial arithmetic and factorization (Lecture notes, accessible to Bachelor students)
##### DONE Thesis
• Regularisation of Gröbner basis computations for weighted and determinantal systems, and an application to medical imagery
Defended on 2016/09/26

#### Selected talks (full list here)   english

• 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
• Working with valuations
"Calcul formel" team seminar
XLIM, Université de Limoges, France, 2020/02/27
• Software tutorial: Computing elimination polynomials using interpolation
SFB Statusseminar
Strobl, Austria, 2018/12/04
• Algebraic classification methods for an optimal control problem in medical imagery
Seminar Algebra and Discrete Mathematics
Johannes Kepler University, Linz, Austria, 2017/12/07
• 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

#### Teaching   english

###### Johannes Kepler University, Linz
[368.492] Mathematics for AI 2

2020-2021 Summer semester: all material on Moodle

[368.19n] Algebra (Linear algebra for computer scientists)

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

[368.164] Computer Algebra 2

2018-2019 Winter semester: informations and documents

#### 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.