Gianira N. Alfarano

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ABOUT

Since September 2024, I am Chaire de Professeure Junior (tenure-track position) in the Géométrie et Algèbre Effectives team at Rennes University.
I completed my Ph.D. in Mathematics under the supervision Prof. Dr. Joachim Rosenthal at the University of Zurich, on June 2022. Then, I was part of the Mathematical Communication Theory group at TU Eindhoven, led by Prof. Dr. Alberto Ravagnani, from October 2022 to September 2023, and I was a postdoctoral researcher in the Applied Algebra and Information Theory group at University College Dublin (UCD), working in the team of Prof. Dr. Eimear Byrne from October 2023 to August 2024.
My research interests include Algebraic Coding Theory, Finite Fields, Combinatorics, Finite Geometry.

I strongly believe in Federico Ardila-Mantilla's Axioms:

  • Axiom 1. Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
  • Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
  • Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
  • Axiom 4. Every student deserves to be treated with dignity and respect.

List of Co-authors

Aida Abiad, Christof Beierle, Eimear Byrne, Martino Borello, Sebastian Degen, Andrew Fulcher, Relinde Jurrius, Anina Gruica, Takanori Isobe, Karan Khathuria, Altan B. Kılıç, Stefan Kölbl, Gregor Leander, Marine Le Meur, Julia Lieb, Fco. Javier Lobillo Borrero, Giuseppe Marino, Usman Mushrraf, Diego Napp, Alessandro Neri, Rakhi Pratihar, Alberto Ravagnani, Veronica Requena, Joachim Rosenthal, Emina Soljanin, Simran Tinani, Beatrice Toesca, Rocco Trombetti, Antonia Wachter-Zeh, Adrien Vinçotte, Violetta Weger, Ferdinando Zullo.

NEWS

PUBLICATIONS

Journal Papers

  1. G. N. Alfarano, S. Degen. The polytope of all q-rank functions. Accepted for publication in SIAM Journal on Discrete Mathematics (2026)
  2. G. N. Alfarano, R. Jurrius, A. Neri, F. Zullo. Representability of the direct sum of uniform q-matroids. Combinatorial Theory (2026)
  3. G. N. Alfarano, E. Byrne. Recursive properties of the characteristic polynomial of weighted lattices. Advances in Applied Mathematics (2026)
  4. G. N. Alfarano, E. Byrne, A. Fulcher. The Free Product of q-Matroids. The Electronic Journal of Combinatorics (2025)
  5. A. Abiad, G. N. Alfarano, A. Ravagnani. Eigenvalue bounds and alternating rank-metric codes.Journal of Algebra and its Applications (2025)
  6. G. N. Alfarano, J. Rosenthal, B. Toesca. Schubert Subspace Codes. Journal of Algebra and its Applications (2025)
  7. G. N. Alfarano, K. Khathuria, S. Tinani. On Cyclic Matroids and their Applications. Bulletin of the Institute of Combinatorics and its Applications (2024)
  8. G. N. Alfarano, A. Neri, F. Zullo. Maximum Flag-Rank Distance Codes. Journal of Combinatorial Theorey, Series A (2024)
  9. G. N. Alfarano, A. B. Kılıç, A. Ravagnani, E. Soljanin. The Service Rate Region Polytope. SIAM Journal on Applied Algebra and Geometry (2024)
  10. G. N. Alfarano, E. Byrne. The Cyclic Flats of a q-Matroid. Journal of Algebraic Combinatorics (2024)
  11. G. N. Alfarano, M. Borello, A. Neri. Outer Strong Blocking Sets. The Electronic Journal of Combinatorics (2024)
  12. G. N. Alfarano, A. B. Kılıç, A. Ravagnani. Service Aspects of LRC and Batch Codes. IEEE BITS the Information Theory Magazine (2023)
  13. G. N. Alfarano, D. Napp, A. Neri, V. Requena. Weighted Reed-Solomon convolutional codes. Linear and Multilinear Algebra (2022)
  14. G. N. Alfarano, M. Borello, A. Neri, A. Ravagnani. Linear Cutting Blocking Sets and Minimal Codes in the Rank Metric. Journal of Combinatorial Theory, Series A (2022)
  15. G. N. Alfarano, A. Gruica, J. Lieb, J. Rosenthal. Convolutional codes over finite chain rings, MDP codes and their characterization. Advances in Mathematics of Communications (2022)
  16. G. N. Alfarano, F.J. Lobillo, A. Neri, A. Wachter-Zeh. Sum-rank product codes and bounds on the minimum distance. Finite Fields and their Applications (2022)
  17. G. N. Alfarano, M. Borello, A. Neri, A. Ravagnani. Three Combinatorial Perspectives on Minimal Codes. SIAM Journal on Discrete Mathematics (2022)
  18. G. N. Alfarano, J. Lieb, J. Rosenthal. Construction of LDPC convolutional codes via difference triangle sets. Designs, Codes and Cryptography (2021)
  19. G. N. Alfarano, K. Khathuria, V. Weger. A survey on single server private information retrieval in a coding theory perspective. Applicable Algebra in Engineering, Communication and Computing (2021)
  20. G. N. Alfarano, F.J. Lobillo, A. Neri. Roos bound for skew cyclic codes in Hamming and rank metric. Finite Fields and their Applications (2021)
  21. G. N. Alfarano, J. Lieb. On the left primeness of some polynomial matrices with applications to convolutional codes. Journal of Algebra and its Applications (2020)
  22. G. N. Alfarano, M. Borello, A. Neri. A geometric characterization of minimal codes and their asymptotic performance. Advances in Mathematics of Communications (2020)
  23. G. N. Alfarano, C. Beierle, T. Isobe, S. Kölbl, G. Leander. ShiftRows Alternatives for AES-like Ciphers and Optimal Cell Permutations for Midori and Skinny. IACR Transactions on Symmetric Cryptology (2018): 20-47.

Conference Proceedings

  1. G. N. Alfarano, M. Le Meur. Minimal additive codes. Extended Abstract for WCC 2026
  2. G. N. Alfarano, A. Ravagnani, E. Soljanin. Dual-Code Bounds on Multiple Concurrent (Local) Data Recovery. 2022 IEEE International Symposium on Information Theory (ISIT)
  3. G. N. Alfarano, J. Lieb, J. Rosenthal. Construction of Rate (n-1)/n Non-Binary LDPC Convolutional Codes via Difference Triangle Sets. 2020 IEEE International Symposium on Information Theory (ISIT)

Preprints

  1. G. N. Alfarano, R. Pratihar, A. Vinçotte. Code distances of matrix rank-metric codes under Add-and-Remove transformations.arXiv:2610.03460
  2. G. N. Alfarano. Additive codes arising from hypergraphs. arXiv:2609.39680
  3. G. N. Alfarano, G. Marino, A. Neri, R. Trombetti. A proof of the generalized packing-covering conjecture. arXiv:22609.34910
  4. G. N. Alfarano, A. Neri, B. Toesca. Combinatorial constructions of Schubert subspace codes. arXiv:2607.07479
  5. G. N. Alfarano, M. Le Meur. Minimal additive codes and additive strong blocking sets. arXiv:2606.24262
  6. G. N. Alfarano, G. Marino, A. Neri, R. Trombetti. A geometric approach to generalized covering radii of linear codes. arXiv:2606.16669
  7. G. N. Alfarano, U. Mushrraf, F. Zullo. On perfect flag-rank metric codes. arXiv:2606.12934
  8. G. N. Alfarano, M. Borello, A. Neri. The geometry of rank-metric codes. arXiv:2605.19691
  9. G. N. Alfarano, S. Degen. Representability of q-matroids via rank-metric codes. arXiv:2605.15780

Thesis

  1. G. N. Alfarano. Algebraic, Combinatorial and Geometric Aspects of Some Error-Correcting Codes. Ph.D. thesis, University of Zurich, 2022.

PEOPLE

PhD Students
  • Marine Le Meur
    September 2025 - present

Postdoctoral Researchers
  • Rakhi Pratihar
    November 2025 - June 2026
  • Adrien Vinçotte
    January 2026 - present

TEACHING

Fall 2024, Fall 2025, Fall 2026 Algorithmique de base
Teaching assitant
Spring 2022 Student Seminar, MAT011 - Matroid Theory
Fall 2021 MAT005 - Coding Theory
Fall 2020 MAT576 - Finite Fields - Theory and Applications
Spring 2020 MAT512 - Elliptic Curves
Fall 2019 MAT001 - Kryptographie
Spring 2019 MAT005 - Coding theory
Fall 2018 MAT211 - Algebra I
Spring 2018 MAT512 - Elliptic Curves

TALKS

Invited Talks

Plenary talks in conferences are marked with (*)
  • A geometric approach to linear codes with applications to one-weight codes May 2026
    Online seminar, UMI Crittografia e Codici group.
  • A geometric approach to linear codes with applications to one-weight codes April 2026
    Seminar in Grenoble, organized by the group CASC.
    Grenoble, France.
  • (*) Skew-polynomial rings and algebraic coding theory April 2026
    Groebner free methods and their applications.
    Barcelona, Spain.
  • (*) The geometry of one-weight codes March 2026
    Journées Codage et Cryptographie 2026.
    Côte d'Opale, France.
  • (*) Skew-polynomial rings and algebraic coding theory July 2025
    Applications of Computer Algebra (ACA25).
    Heraklion (Crete), Greece.
  • Maximum Flag Rank Distance Codes July 2025
    SIAM Conference on Applied Algebraic Geometry (AG25).
    Special Session: Network Coding.
    University of Wisconsin, USA.
  • The geometry of one-weight codes March 2025
    Dutch-Belgian discrete math seminar.
    Bruxelles, Belgium.
  • The geometry of one-weight linear codes May 2025
    Zurich Seminar in Coding Theory and Cryptography.
  • The service rate region polytope May 2025
    Seminar Discrete Mathematics, Codes and Cryptography - University of Paris 8.
  • The geometry of one-weight linear codes May 2025
    London Symposium on Information Theory.
    Cambridge, UK.
  • Schubert Subspace Codes March 2025
    Algebraic Applications to Coding Theory and Crypto.
    Mexico City.
  • Minimal Codes: The Role of Supports in Coding Theory January 2025
    Barracuda meeting (ANR).
    Bayeux, France.
  • Constant Dimension Subspace Codes in Schubert Varieties July 2024
    2nd AMS-UMI International Joint Meeting.
    Special Session: Algebraic Coding Theory.
    Palermo, Italy.
  • Representability of q-matroid products and linear sets May 2024
    DOCTOR: Delightful Occasion for Combinatorial Talks on Outstanding Research.
    Vrije Universiteit Brussel.
  • Representability of q-matroid products and linear sets May 2024
    Research Seminar.
    Bielefeld University.
  • (*) An Overview on Algebraic Coding Theory May 2024
    Workshop Women in Mathematics.
    Ghent University.
  • An Overview on Minimal Codes and Strong Blocking Sets March 2024
    ACCESS Seminars (online).
  • (*) The Critical Theorem for Rank-Metric Codes February 2024
    OpeRa 2024 - Open Problems on Rank-Metric Codes.
    Università degli Studi della Campania, Luigi Vanvitelli, Caserta, Italy.
  • The Geometry of Minimal Codes January 2024
    Géométrie et algèbre effectives.
    Institut de recherche mathématique de Rennes, France.
  • Rank-metric codes, q-matroids, and independent spaces December 2023
    International Conference on Algebraic Geometry, Coding Theory and Combinatorics - In honour of Sudhir Ghorpade's 60th birthday.
    IIT Hyderabad, India.
  • (*) The Service Rate Region Polytope November 2023
    Colloquium on Coding Theory.
    Ghent University, Belgium.
  • The Geometry of Minimal Codes October 2023
    Algebra and Number Theory Seminars.
    University College Dublin, Ireland.
  • (*) The Geometry of Minimal Codes September 2023
    Annual Conference on Cryptography and Coding Theory - gruppo UMI.
    University of Perugia, Italy.
  • Minimal Codes and Strong Blocking Sets July 2023
    SIAM Conference on Applied Algebraic Geometry (AG23).
    Special Session: Coding Theory and Galois Geometries.
    Eindhoven, The Netherlands.
  • Maximum Flag Rank Distance Codes July 2023
    29th Nordic Congress of Mathematicians with EMS.
    Special Session: Algebraic Coding Theory and Cryptography.
    Aalborg, Denmark.
  • Rank-Metric Codes and q-Matroids April 2023
    University of Groningen, The Netherlands.
  • Matroidal Approach to Coding Theory December 2022
    University of Zurich, Switzerland.
  • Critical Problem for q-Polymatroids December 2022
    University of Paris VIII, France.
  • Critical Problem, q-Polymatroids and Rank-Metric Codes August 2022
    ACA 2022, Session "Algebraic and Geometric Methods in Coding Theory", Istanbul, Turkey.
  • q-Analogues of matroids and codes April 2022
    Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
  • (Linear) cutting blocking sets and minimality of codes October 2021
    Sabancı Algebra Seminar, Turkey.
  • (Linear) cutting blocking sets and their codes September 2021
    PICS, Postgraduate International Coding Theory Seminar.
  • Bounds on the distance of skew cyclic codes September 2021
    Seminar Discrete Mathematics, Codes and Cryptography - University of Paris 8.
  • A geometric interpretation of minimal code May 2021
    De Cifris, Schola Latina Seminars.
  • Minimal linear codes and cutting blocking sets March 2021
    Maths Postgraduate Seminar Series, University College Dublin.
  • The geometry of minimal linear codes March 2021
    eSeminar UGent-VUB.
  • What is...a convolutional code? December 2019
    Zurich Graduate Colloquium, Zurich, Switzerland.
  • σ-Quasicyclic and Projective Convolutional Codes June 2019
    University of Alicante, Alicante, Spain.
  • An introduction to Convolutional Codes June 2018
    Research Seminars, University of Trento, Trento, Italy.

Other Talks

  • Minimal additive codes May 2026
    Combinatorics 2026.
    Naples, Italy.
  • Direct sum of q-matroids and linear sets August 2024
    Workshop on Mostly Matroids 2024, Institute for Basic Science (IBS).
    Daejeon, South Korea.
  • Free product of q-matroids and clubs on the projective line June 2024
    Combinatorics 2024, Carovigno, Italy.
  • Minimal Codes and Strong Blocking Sets July 2023
    International Conference on Finite Fields and Their Applications 2023 (Fq15).
    Paris, France.
  • Weighted Reed-Solomon Convolutional Codes June 2023
    Workshop on Convolutional Codes.
    Zurich, Switzerland.
  • Cyclic Spaces, q-Matroids and Rank-Metric Codes January 2023
    Dutch-Belgian discrete math seminar.
    Ghent University, Ghent, Belgium.
  • q-Matroids and rank-metric codes August 2022
    ACA 2022, Session "q-analogues in combinatorics: matroids, designs and codes", Istanbul, Turkey.
  • The geometry of minimal codes July 2022
    "Contemporary Algebraic and Geometric Techniques in Coding Theory and Cryptography".
    Virtual summer school, Università degli Studi della Campania, Luigi Vanvitelli.
  • Dual-Code Bounds on Multiple Concurrent (Local) Data Recovery June 2022
    IEEE International Symposium on Information Theory (ISIT), Aalto University, Espoo, Finland.
  • q-Matroids and rank-metric codes June 2022
    Combinatorics 2022, Mantua, Italy.
  • Roos-like bound for skew-cyclic codes in Hamming and (sum-)rank metric September 2021
    First Annual Conference: Cryptography and Coding Theory.
  • Construction of Rate (n-1)/n Non-Binary LDPC Convolutional Codes via Difference Triangle Sets June 2020
    IEEE International Symposium on Information Theory (ISIT), Los Angeles, California (virtual conference).
  • New Algebraic Construction of MDP Convolutional Codes December 2019
    Arbeitsgemeinschaft in Codierungstheorie und Kryptographie, University of Neuchatel, Switzerland.

CONTACT

IRMAR, UFR Mathématiques, Université de Rennes Campus de Beaulieu 35042 Rennes Cedex,

Bureau : 617 bâtiment 22

Email: gianira-nicoletta.alfarano(at)univ-rennes.fr

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