Algebraic curves and codes

• Grant number: 23/08271-5
• Support Opportunities: Scholarships abroad - Research
• Start date: March 01, 2024
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Saeed Tafazolian
• Grantee: Saeed Tafazolian
• Host Investigator: Jaap Top
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: University of Groningen, Netherlands

Abstract

The aim of this project is to study algebraic curves defined over anfield of positive characteristic. This is including to study curves over finite fields with many rational points, i.e., to construct maximal curves using fiber products of curves, to construct supersingular curves using class field theory, to study algebraic geometric codes on algebraic curves and also to study the automorphism groups of certain curves. Indeed I intend to work, with Prof. Jaap Top, and finish papers on the above topics from the field of algebraic curves, both extending the successful joint results we published in 2019 and in 2023. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

TAFAZOLIAN, SAEED; TOP, JAAP. On certain maximal hyperelliptic curves related to Chebyshev polynomials (vol 203, pg 276, 2019). JOURNAL OF NUMBER THEORY, v. 269, p. 2-pg., 2024-11-30. (23/08271-5)

TAFAZOLIAN, SAEED. The generalized Suzuki curve. FINITE FIELDS AND THEIR APPLICATIONS, v. 100, p. 8-pg., 2024-10-11. (23/08271-5)

DIAS, GUILHERME; TAFAZOLIAN, SAEED; TOP, JAAP. On certain maximal curves related to Chebyshev polynomials. FINITE FIELDS AND THEIR APPLICATIONS, v. 101, p. 21-pg., 2024-10-23. (23/08271-5)