Research

Warning: page under construction

Organization of conferences and workshops

Funding and projects

  • 2022: Sorbonne FSI FASTER, Principal Investigator.
    Tremplin project funded by the Faculty of Science and Engineering of Sorbonne Université, entitled “Fast reconstruction of multivariate algebraic relations”.
  • 2022–2026: ANR&FWF Eagles, Collaborator.
    International collaborative project “Efficient Algorithms for Guessing, inequaLitiEs, and Summation” (recently accepted, details to come).
  • 2020–2023: US Air Force AFOSR, Collaborator. Industrial Project.
  • 2020–2023: ANR De Rerum Natura, Collaborator.
    Collaborative project De Rerum Natura (ANR collaborative research project ANR-19-CE40-0018).
    https://anr.fr/Project-ANR-19-CE40-0018
  • 2019–2024: ANR&FWF ECARP, Collaborator.
    International collaborative project “Efficient certified algorithms for robot motion planning” (ANR-19-CE48-0015 and FWF I 4452-N).
    https://ecarp.lip6.fr/
  • 2017–2018: CNRS-INS2I PEPS JCJC, Principal Investigator.
    Project ARCADIE: fast algorithms and efficient implementations for algebraic computations arising in the decoding of error correcting codes.
    Details on CNRS website.

Software and libraries

  • Recently, I have started to work on development for the msolve library, at first to accelerate the change of monomial order step in multivariate polynomial system solving. This should be integrated in the library sometime in Winter 2023.
  • Co-creator and main developer of the Polynomial Matrix Library (PML, https://github.com/vneiger/pml/), written in C++ and based on the libraries NTL and Flint. PML offers efficient implementations of many algorithms for univariate polynomial matrices over finite fields, with the best-known performance at the time of writing. This library was co-developed with Seung Gyu Hyun and Éric Schost, and described in an article published in ISSAC 2019 proceedings.
  • Contributions to the SageMath open-source mathematics software (https://www.sagemath.org/), in collaboration with Seung Gyu Hyun, Romain Lebreton, and Johan Rosenkilde, aiming at providing a complete set of tools for univariate polynomial matrix computations, with a view towards applications in coding theory and cryptography. The SageMath documentation page at this link describes the tools that have been integrated up to this day.
  • Contributions to the C++ libraries LinBox and FFLAS-FFPACK for efficient implementations of linear algebra operations (https://github.com/linbox-team/).

Supervision of students

Supervision listed below from September 2017 to August 2021 has taken place at Research Institute XLIM, University of Limoges. Supervision listed below from September 2021 on has taken place at LIP6, Sorbonne Université in Paris.

PhD students

  • Nov. 1, 2022–Oct. 31, 2026: PhD student Sriram Gopalakrishnan. International “joint” PhD (co-tutelle), co-directed with Ludovic Perret (Sorbonne Université, France) and Éric Schost (University of Waterloo, Canada), on the topic The algebra of the MinRank problem in post-quantum cryptography: Gröbner bases, complexity, and implementations.
  • Oct. 1, 2019–Sep. 30, 2022: PhD student Maxime Bros. Co-direction (50%) with Philippe Gaborit, on the topic Computation of Algebraic Relations for Multivariate Polynomials to study the Security of Rank-based Cryptosystems. Part of this work, done in collaboration with researchers from Inria Paris and University of Rouen, led to an attack on the security of cryptosystems submitted to the NIST call for post-quantum cryptography standardization.

Master’s students

  • (Planned) Mar. 2023–Aug. 2023: Master student Kevin Tran.
  • (Planned) Mar. 2023–Aug. 2023: Master student Robin Kouba.
  • Feb. 2022–Aug. 2022: Master student Sriram Gopalakrishnan. Co-direction (50%) with Mohab Safey El Din. Thesis title: A Complexity Analysis of the F5 Algorithm in the Case of Generic Input. The internship research work also considered related questions revolving around the MinRank problem in algebraic cryptanalysis. Sriram Gopalakrishnan is now pursuing a PhD degree.
  • Mar. 4–Aug. 30, 2019: Master student Maxime Bros (Université de Limoges), on the complexity of solving polynomial systems related to the security of rank-metric cryptosystems. Co-supervision (80%) with Philippe Gaborit (Université de Limoges). Maxime Bros has defended his PhD on December 8, 2022 and is working as a postdoctoral researcher at National Institute of Standards and Technology, USA.
  • Mar. 10–Aug. 10, 2018: Master student Grace Younes (Université de Versailles Saint-Quentin-en-Yvelines), on the efficient computation of multivariate algebraic relations. Co-supervision (50%) with Simone Naldi (University of Limoges). Grace Younes has obtained a PhD degree from Sorbonne Université and is now an Assistant Professor at Sorbonne University Abu Dhabi, United Arab Emirates.
  • Jan. 2–June 2, 2017: Master student Grigory Solomatov (Technical University of Denmark), on the computation of canonical forms for rectangular polynomial matrices. Co-supervision (50%) with Johan Rosenkilde (Technical University of Denmark). Location: Technical University of Denmark. For his thesis and defense, Grigory Solomatov obtained the maximal grade on the Danish grading scale; this work has led to an article published in the proceedings of ISSAC 2018. Grigory Solomatov has obtained a PhD degree from Technical University of Denmark and is currently a postdoctoral researcher at University of Haifa, Israel.

Other research internships at Master or Bachelor level

  • 2 May – 1 July 2022: Master student Kevin Tran, in first year of Master’s degree, on polynomial system solving and block-Wiedemann techniques (study of fast algorithms and design of an efficient implementation with the Flint library). Kevin Tran is now in his final year of Master’s degree.
  • Sept. 10–Nov. 30, 2018: Bachelor student Seung Gyu Hyun (University of Waterloo, ON, Canada), in the context of a Mitacs Globalink Research Award project about the implementation of efficient algorithms for some families of algebraic relations. Seung Gyu Hyun is now a machine learning engineer at Qualcomm.
  • May 16–July 29, 2016: Master student Vu Thi Xuan (École Normale Supérieure de Lyon), in a three-month research internship on the computation of kernel bases of polynomial matrices. Co-supervision (75%) with Claude-Pierre Jeannerod (Inria). Location: LIP, École Normale Supérieure de Lyon. This work has led to an article published in the proceedings of ISSAC 2017, for which Vu Thi Xuan received the SIGSAM ISSAC Distinguished Student Author Award. Vu Thi Xuan has obtained a joint PhD degree from Sorbonne Université (France) and University of Waterloo (Canada), and is now a postdoctoral researcher at The Arctic University of Norway.

PhD thesis committees

  • Rocco Mora (committee member, 2023, link).
  • Maxime Bros (thesis co-advisor, 2022, link),
  • Isabella Panaccione (guest committee member, 2021, thesis pdf),
  • David Lucas (committee member, 2020, thesis pdf),

Funding and projects during PhD

  • Fall 2015: Mitacs Globalink Research Award (5,000CAD and travel expenses)
    Multivariate polynomial interpolation: efficient algorithms and applications.
    Details on Mitacs website.
  • Fall 2015: Invited PhD Visitor at Fields Institute, Toronto, Canada (2,000CAD)
    For attending the events of the Fields Institute Thematic Program in Computer Algebra.
    Website of the thematic program.
  • Fall 2015 : scholarship of Programme Avenir Lyon — Saint-Étienne (4.5k€)
    Providing support for the international mobility of students (six-month stay at University of Waterloo, Ontario, Canada).
  • Fall 2015 : bourse Explo’RA Doc de la Région Rhône-Alpes (4.2k€).
    Providing support for the international mobility of students (six-month stay at University of Waterloo, Ontario, Canada).
  • Fall 2014 : bourse Explo’RA Doc de la Région Rhône-Alpes (4.2k€).
    Providing support for the international mobility of students (six-month stay at Western University, London, Ontario, Canada).

Research during Bachelor’s, Master’s, and PhD programs:

  • PhD (September 2013 – August 2016)
  • Master’s final internship (February-July, 2012)
  • Master’s, second internship (June-July, 2011)
  • Master’s, first internship (February-May, 2011)
  • Bachelor’s internship (June-July, 2010)