Gianira Nicoletta Alfarano
ABOUT
Since September 2024, I am Chair de Professeur 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.
List of Co-authors
Aida Abiad, Christof Beierle, Eimear Byrne, Martino Borello, Andrew Fulcher, Anina Gruica, Takanori Isobe, Karan Khathuria, Altan B. Kılıç, Stefan Kölbl, Gregor Leander, Julia Lieb, Fco. Javier Lobillo Borrero, Diego Napp, Alessandro Neri, Alberto Ravagnani, Veronica Requena, Joachim Rosenthal, Emina Soljanin, Simran Tinani, Beatrice Toesca, Antonia Wachter-Zeh, Violetta Weger, Ferdinando Zullo.
NEWS
- Invited speaker at the session Algebraic Coding Theory, at the 2nd AMS-UMI International Meeting, in July 2024, in Palermo (Italy).
- Invited speaker in the workshop Women in Mathematics , in May 2024, in Ghent (Belgium).
- Invited speaker in the workshop OpeRa, Open Problems in Rank Metric Codes, in February 2024, in Caserta (Italy).
- Invited speaker in the Coding Theory Colloquium, at Ghent University (Belgium) on November 8, 2023.
- Invited speaker at the Annual Congress in Cryptography and Coding Theory, on September 21-22, 2023 in Perugia (Italy).
- I won the Applications of Computer Algebra Early Research Award (ACA-ERA) 2022.
- I won the Best presentation award for my talk The Geometry of Minimal Codes at the Contemporary Algebraic and Geometric Techniques in Coding Theory and Cryptography.
- I organized with Alessandro Neri the invited session Network Coding at the 25th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2022).
- I organized with Michela Ceria and Relinde Jurrius the special session q-analogues in combinatorics: matroids, designs and codes (ACA2022-EIT) at the 27TH International Conference on Applications of Computer Algebra ( ACA2022 ) 15-19 August 2022, Istanbul-Gebze, Turkey.
- Happy to announce the second edition of the ACT Summer School and Coding theory and cryptography- a conference in honor of Joachim Rosenthal's 60th birthday.
- The nice article on Anurag's Math blog talks about our published paper!
PUBLICATIONS
Journal Papers
- G. N. Alfarano, J. Rosenthal, B. Toesca. Schubert Subspace Codes. arXiv:405.20047 to appear in Journal of Algebra and its Applications (2024)
- G. N. Alfarano, K. Khathuria, S. Tinani. On Cyclic Matroids and their Applications. to appear in Bulletin of the Institute of Combinatorics and its Applications (2024)
- G. N. Alfarano, A. Neri, F. Zullo. Maximum Flag-Rank Distance Codes. Journal of Combinatorial Theorey, Series A (2024)
- G. N. Alfarano, A. B. Kılıç, A. Ravagnani, E. Soljanin. The Service Rate Region Polytope. SIAM Journal on Applied Algebra and Geometry (2024)
- G. N. Alfarano, E. Byrne. The Cyclic Flats of a q-Matroid. Journal of Algebraic Combinatorics (2024)
- G. N. Alfarano, M. Borello, A. Neri. Outer Strong Blocking Sets. The Electronic Journal of Combinatorics (2024)
- G. N. Alfarano, A. B. Kılıç, A. Ravagnani. Service Aspects of LRC and Batch Codes. IEEE BITS the Information Theory Magazine (2023)
- G. N. Alfarano, D. Napp, A. Neri, V. Requena. Weighted Reed-Solomon convolutional codes. Linear and Multilinear Algebra (2022)
- 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)
- 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)
- 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)
- G. N. Alfarano, M. Borello, A. Neri, A. Ravagnani. Three Combinatorial Perspectives on Minimal Codes. SIAM Journal on Discrete Mathematics (2022)
- G. N. Alfarano, J. Lieb, J. Rosenthal. Construction of LDPC convolutional codes via difference triangle sets. Designs, Codes and Cryptography (2021)
- 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)
- 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)
- 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)
- G. N. Alfarano, M. Borello, A. Neri. A geometric characterization of minimal codes and their asymptotic performance. Advances in Mathematics of Communications (2020)
- 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
- G. N. Alfarano, A. Ravagnani, E. Soljanin. Dual-Code Bounds on Multiple Concurrent (Local) Data Recovery. 2022 IEEE International Symposium on Information Theory (ISIT)
- 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
- G. N. Alfarano, E. Byrne, A. Fulcher. The Free Product of q-Matroids. arXiv:2412.13025
- G. N. Alfarano, R. Jurrius, A. Neri, F. Zullo. Representability of the direct sum of uniform q-matroids. arXiv:2408.00630
- A. Abiad, G. N. Alfarano, A. Ravagnani. Eigenvalue bounds and alternating rank-metric codes. arXiv: 2405.09254
- G. N. Alfarano, E. Byrne. The Critical Theorem for q-Polymatroids. arXiv: 2305.07567
Thesis
- G. N. Alfarano. Algebraic, Combinatorial and Geometric Aspects of Some Error-Correcting Codes. Ph.D. thesis, University of Zurich, 2022.
TEACHING
| Fall 2024 | Algorithmique de base | I will upload here my (handwritten) lecture notes
Sorting and Complexity Algorithms on graphs Multiplication of polynomials Euclidean division Resultant Multipoint evaluation and interpolation Berlekamp factorization Primality testing |
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 are marked with (*)
- (*) An overview on minimal codes and strong blocking sets. ACCESS Seminars (Online), March 2024.
- (*) The geometry of minimal codes. Géométrie et algèbre effectives, Institut de recherche mathématique de Rennes, France, January 2024.
- Rank-metric codes, $q$-matroids, and independent spaces. International Conference on Algebraic Geometry, Coding Theory and Combinatorics - In honour of Sudhir Ghorpade’s 60th birthday IIT Hyderabad (India), December 2023.
- (*) The service rate region polytope. Coding Theory Colloquium, November 8, 2023, Ghent University.
- (*) The geometry of minimal codes. Algebra and Number Theory Seminar, October 19, 2023, University College Dublin.
- (*) The geometry of minimal codes. Annual conference Cryptography and Coding Theory- gruppo UMI Codici e Crittografia, Perugia (Italy), September 2023.
- (*) Minimal Codes and Strong Blocking Sets. SIAM Conference on Applied Algebraic Geometry (AG23),Special Session Coding Theory and Galois Geometries , Eindhoven, the Netherlands, July 2023.
- (*) Maximum Flag-Rank Distance Codes. 29th Nordic Congress of Mathematicians with EMS, Special Session Algebraic Coding Theory and Cryptography, Aalborg, Denmark, July 2023.
- Minimal Codes and Strong Blocking Sets. International Conference on Finite Fields and their Applications 2023 (Fq15), Paris, France, June 2023.
- Weighted Reed-Solomon Convolutional Codes. Workshop in Convolutional Codes, University of Zurich, Switzerland, June 2023.
- (*) Rank-Metric Codes and q-Matroids. Algebra Seminar, University of Groningen, The Netherlands, April 2023.
- Cyclic Spaces, q-Matroids and Rank-Metric Codes. Dutch-Belgian discrete math seminar Ghent University, Ghent, Belgium, January 2023.
- (*) Matroidal Approach to Coding Theory. Arbeitsgemeinschaft in Codierungstheorie und Kryptographie, University of Zurich, Switzerland, December 2022.
- (*) Critical Problem for q-Polymatroids. Seminar Discrete Mathematics, Codes and Cryptography - University of Paris 8, December 2022.
- (*) Critical Problem, q-Polymatroids and Rank-Metric Codes. Special session Algebraic and Geometric Methods in Coding Theory , at Applications of Computer Algebra (ACA) 2022, Gebze, Turkey, August 2022.
- q-Matroids and Rank-Metric Codes. Special session q-Analogues in combinatorics: matroids, designs and codes , at Applications of Computer Algebra (ACA) 2022, Gebze, Turkey, August 2022.
- The geometry of minimal codes. Contemporary Algebraic and Geometric Techniques in Coding Theory and Cryptography, (virtual summer school), University of Campania, Luigi Vanvitelli, July 2022 ( Best presentation award ).
- Dual-Code Bounds on Multiple Concurrent (Local) Data Recovery. IEEE International Symposium on Information Theory (ISIT), Aalto University, Espoo, Finland, June 2022.
- q-Matroids and rank-metric codes. Combinatorics 2022, Mantua, Italy, June 2022.
- (*) q-Analogues of matroids and codes. Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, April 2022.
- (*) (Linear) cutting blocking sets and minimality of codes. Sabanci Algebra Seminar, University of Sabancy, Turkey, October 2021.
- (*) (Linear) cutting blocking sets and their codes. PICS, Postgraduate International Coding theory Seminar, September 2021.
- Roos-like bound for skew-cyclic codes in Hamming and (sum-)rank metric. First Annnual Conference: Cryptography and Coding Theory, September 2021.
- (*) Bounds on the distance of skew cyclic codes. Seminar Discrete Mathematics, Codes and Cryptography - University of Paris 8, September 2021.
- (*) A geometric interpretation of minimal code. De Cifris, Schola Latina Seminars, May 2021.
- (*) Minimal linear codes and cutting blocking sets. UCD Maths Postgraduate Seminar Series, Dublin, March 2021.
- (*) The geometry of minimal linear codes. eSeminar UGent-VUB, March 2021.
- Construction of Rate (n-1)/n Non-Binary LDPC Convolutional Codes via Difference Triangle Sets. IEEE International Symposium on Information Theory (ISIT), Los Angeles, California, (virtual conference) June 2020.
- (*) What is...a convolutional code? Zurich Graduate Colloquium, Zurich, Switzerland, December 2019 .
- (*) New Algebraic Construction of MDP Convolutional Codes. Arbeitsgemeinschaft in Codierungstheorie und Kryptographie, University of Neuchatel, Switzerland, December 2019.
- (*) σ-Quasicyclic and Projective Convolutional Codes. University of Alicante, Spain, June 2019.
- (*) An introduction to Convolutional Codes, Research Seminars at University of Trento, Italy, June 2018.