Quadratic Forms, Rings and Codes

August 31, 2023

Laboratoire de Mathématiques de Lens, Unité de Recherche UR 2462

Organizing committee:   Ahmed Laghribi     André Leroy

This one-day meeting is the second part of the conference "NonCommutative Rings and their Applications, VIII" on ring theory. The meeting will be held in hybrid format and it is supported by the Université d'Artois in the framework of the BQR support (Bonus Qualité Recherche), and the Laboratory of mathematics in Lens, and the program ValoRIS of the Region Hauts-de-France. The aim of this meeting is to gather specialists of quadratic forms, ring theory and coding theory. The hope is to encourage exchange between these areas of research.

We are very happy to announce the speakers of this meeting:

  • 10:00-11:00 Demba Barry   (Université des Sciences, des Techniques et des Technologies de Bamako, Mali)

    • Title:The descent of biquaternion algebras

    • Abstract: Let K/F be a separable quadratic extension and let B be a biquaternion algebra defined over K with trivial corestriction. We associate with B a degree 3 cohomological invariant that determines whether B has a descent to F up to isomorphism. We show the connection between the non-triviality of this invariant and the existence of indecomposable algebras of degree 8 and exponent 2. As applications, we give examples of indecomposable algebras of degree 8 and exponent 2 aver a field of cohomological dimension 3. In characteristic 2, the results of this talk are based on a joint work with A. Chapman and A. Laghribi.

  • 11:10-12:10 Max Dickmann   (IMJ-PRG, Université Paris Cité et Sorbonne Université, France)

    • Title: Special groups and quadratic forms over rings with non-zero-divisor coefficients

    • Abstract: Joint work with F. Miraglia (Univ. de São Paulo) and H. Ribeiro (Univ. de São Paulo) published with the title above in Fundamenta Mathematicae, vol. 258 (2022), pp. 153-209. We present an algebraic theory of diagonal quadratic forms with non- zero-divisor coefficients over preordered (commutative, unitary) rings ?A, T ?, where 2 is invertible and the preorder T satisfies a mild additional requirement, the zero-divisor property. We prove that several major results known to hold in the classical theory of quadratic forms over fields, like the Arason-Pfister Hauptsatz and Pfister's local-global principle, carry over to any class of preordered rings satisfying a property called NT-quadratic faithfulness, a notion central to our results. We prove that this property holds, and hence the above-mentioned results are valid, for many classes of rings frequently met in practice, such as: (i) reduced f-rings and some of their extensions, for which Marshall's signature conjecture and a vast generalization of Sylvester's inertia law are also true; and (ii) reduced partially ordered Noetherian rings and many of their quotients, a result of interest in real algebraic geometry. This paper provides a broad extension of the theory developed in [M. Dickmann and F. Miraglia, Memoirs Amer. Math. Soc. 238 (2015), no. 1128] and of the methods employed therein.

  • 14:00-15:00 Eli Matzri   (Bar-Ilan University, Israel)

    • Title:Computing the correstriction in K_n.

    • Abstract
    • Rosset and Tate showed how to compute the cor in K_2. In this talk I will explain how to extend their method to the case of arbitrary n and give an application for the symbol length question.

  • 15:10-16:10 Steven Dougherty   (University of Scranton, USA)

    • Title:Codes and the MacWilliams Relations

    • Abstract: We shall describe various dualities that give rise to MacWilliams relations for additive codes and we describe consequences of these relations in this setting.

Schedule of the talks:
  1. 10.00-11.00 Demba Barry
  2. 11:10-12:10 Max Dickman
  3. 14:00-15:00 Eli Matzri
  4. 15:10-16:10 Steven Dougherty

    List of participants

    1. Yusuf Alagöz, Siirt University (Turkey).
    2. Lulwah Al-Essa, Imam Abdulrahman bin Faisal University, Dammam (Saudi Arabia).
    3. Dilshad Alghazzawi, King Abdulaziz University, Rabigh (Saudi Arabia).
    4. Shakir Ali, Department of Mathematics Aligarh Muslim University (India).
    5. Meltem Altun Özarslan, Hacettepe University (Turkey).
    6. Maria José Arroyo Paniagua Universidad Autonoma Metropolitana, México (Mexico).
    7. Samir Assuena, Centro Universitário da FEI (Brazil).
    8. Masood Aryapoor, Mälardalen University (Sweeden).
    9. Per Bäck, Mälardalen University (Sweden).
    10. Demba Barry, Sciences University, Bamako (Mali).
    11. Volodymyr Bavula, University of Sheffield (UK).
    12. Nabil Bennenni, USTHB, Alger (Algeria).
    13. Nathan Blacher, University of Sheffield (UK).
    14. Tomasz Brzezinski, Swansea University and University of Bialystok (G.B. and Poland).
    15. Engin Büyükasik, Izmir Institute of Technology (Turkey).
    16. Adam Chapman, Academic College of Tel-Aviv-Yaffo (Israel).
    17. Anna Cichocka, University of Technology (Poland).
    18. Gabriella D’Este, University of Milano (Italy).
    19. Max Dickmann, Sorbonne University, Paris (France).
    20. Steven Dougherty, Scranton University (USA).
    21. André Duarte, Sao Paulo University (Brazil).
    22. Nguyen Viet Dung Ohio University (USA).
    23. Yilmaz Durgun Çukurova University (Turkey).
    24. Michela Ceria, University Politecnico di Bari (Italy).
    25. Fatma Ebrahim, Al-Azhar University, Cairo (Egypt).
    26. Mahdieh Ebrahipour, Vali-e-Asr University of Rafsanjan (Iran).
    27. Susan El-Deken, Helwan University, Cairo (Egypt)
    28. Lhoussain El Fadil, Faculty of Sciences, Sidi Mohamed Ben Abdellah University (Morocco).
    29. Alberto Facchini, University of Padova (Italy).
    30. Raul Ferraz, Sao Paulo University (Brazil).
    31. Walter Ferrer, Dma. Universidad de la República. (Uruguay)
    32. José Gómez Torrecillas, Universidad de Granada (Spain).
    33. Huda Hamdan, Damietta University (Egypt).
    34. Leila Heidari Zadeh, Islamic Azad University, Shoushtar (Iran).
    35. Malgorzata Hryniewicka, Faculty of Mathematics, University of Bialystok (Poland).
    36. Surender Jain, University of OHIO, Athens (USA).
    37. Malgorzata Jastrzebska, Siedlce University (Poland).
    38. Yeliz Kara, Bursa Uludag University(Turkey).
    39. Mahmoud Khaled Ahmed, Elgazeera Higher Institute (Egypt).
    40. Ayten Koc, Gebze Technical University (Turkey).
    41. Emrah Korkmaz, Çukurova University (Turkey).
    42. Ahmed Laghribi, Université d'Artois (France).
    43. André Leroy, Université d'Artois (France).
    44. Sergio Lopez-Permouth, Ohio University, Athens (USA).
    45. Guanglin Ma, Nanjing University of Information Science and Technology (China).
    46. Praveen Manju, Indian Institute of Technology Delhi (India).
    47. Jerzy Matczuk, Warsaw University (Poland).
    48. Eli Matzri, Bar-Ilan University (Israel).
    49. Zeinab Mohamed, South Valley University (Egypt).
    50. Teo Mora, University of Genoa (Italy).
    51. Azam Mozaffarikhah, Ohio University (USA).
    52. Diksha Mukhija, University of Alberta (Canada).
    53. Mehrdad Nasernejad, Université d'Artois (France).
    54. Zahra Nazemian, Graz University (Austria).
    55. Cornelia Ott, Ulm University (Germany).
    56. Murad Ozaydin, University of Oklahoma (USA).
    57. André Perreira, Sao Paulo University (Brazil).
    58. Dmitri Piontkovski, HSE University, Moscow (Russia).
    59. Cesar Polcino Milies, Sao Paulo University (Brazil).
    60. Rakhi Pratihar, Inria Saclay Centre (France).
    61. Louis Rowen, Bar-Ilan University (Israel).
    62. Esengül Saltürk, Istanbul Atlas University (Turkey).
    63. Martha Lizbeth Sandoval, Universidad Autónoma Metropolitana (UAM-I) (Mexico)
    64. Serap Sahinkaya, Tarsus University (Turkey).
    65. Steven, University of Sheffield (UK).
    66. Virgilio Sison, University of the Philippines Los Banos (Philippines).
    67. Daniel Smertnig, Graz University (Austria).
    68. Patrick Solé, I2M (France).
    69. Ashish Srivastava, University of Saint Louis, Missouri (USA).
    70. Steve Szabo, Eastern Kentucky University (USA).
    71. Yaser Toloei, Razi University, Kermanshah (Iran).
    72. Felix Ulmer, University of Rennes (France).
    73. Gulsen Ulucak, Gebze Technical University (Turkey).
    74. Jay Wood, Western Michigan University (USA).
    75. Tulay Yildirim, Karabuk University (Turkey).
    76. Mohamed F. Yousif, The Ohio State University (USA).
    77. Yiqiang Zhou, Memorial University of Newfoundland (Canada).

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