Projects per year
Personal profile
Research interests
I am specialist on Iwasawa Theory and Modular Curves. In particular we are devoloping Iwasawa Theory for function fields of positive characteristic, I am coworking in a joint project with Daniel Macias Castillo (ICMAT, investigador permanente) and also with A.Bandini (Univ.Pisa) and I.Longhi (Univ. Torino).
Moreover I am specialist in the modular curves setting. Here we are developing arithmetic propeties of the quotient classical modular curves (collaborators with D.Tarun (Post-doc in China) and A. Schweizer (KAIST, Korea)).
Moreover I am codirector of a PhD-thesis on projects on smooth plane curves and modularity joint with my colleagues A.El-Guindy and my former PhD-student E. Badr professors at El Cairo or American El Cairo Universities, which also collaborate on twist of curbes of low genus, as a third research project.
My background on Iwasawa theory, related with BSD-conjectures or more general on Tamagawa number conjecture is based in my stay during 1998-2000 with Professor Christopher Deninger team in Muenster, Germany, professor who explained on such conjectures in the ICM 1998 in Berlin.
Some items to mention are as follows:
*Accreditation for Advanced Research, 1st call 2023, from AQU, to apply for Full Professor Position.
*3 positive evaluated periods of 6 years of reseach, the last one granted ends in December 2019. The more important contributions that the applicant did for math community are the paper on 2020 on Iwasawa theory named ``Iwasawa main conjecture for the Carlitz cyclotomic extension and applications" and the 2022 paper on quotient modular curves named ``The automorphism group of the modular curve $X_0^*(N)$ with square-free levels" in the two main lines of my research.
*Reviewer of more than 100 reviews by MathSciNet of AMS, and reviewer of 50 articles in Zentralblatt, and therefore more than 150 reviews of different research articles in Number Theory in the different research bibliography databases written by the applicant .
Moreover, nowadays I am the reviewer choised by AMS for the more than 100 pages paper of the pope in Iwasawa theory Prof.Kazuya Kato (Univ. Chicago) on his recent published paper entitle: ``Conjectures of Sharifi".
*Referee of different articles in 1st and 2nd quartile indexed journals.
*Evaluator for different research commissions outside of Spain, for example the senior teaching excellence of the government of Poland that evaluates professors when presenting research projects and to assign them or not the scholarship requested..
*Co-organizer as scientific or organizational coordinator of different workshops and conferences listed on the Number Theory Web (web of reference for researchers in the research field I am part of):
-Number Theory and Arithmetic Geometry session, within the SCM-RSME-PTM Joint Mathematical Societies Spanish-Polish Congress, Poland, 4-8 September 2023. (scientific committee)
-Workshop on Number Theory STNB, Barcelona last week of January, editions years 2023, 2022, 2020, 2019, 2018, 2017, 2016, 2014, 2010 and 2002. (organizing or scientific committee)
* Speaker in different congress, invited speaker in ``Arithmetic of Modular curves and modular forms" in Busan, 17-19 February 2022, or ``Modular curves and Galois representations" in Zagreb, 18-22 September, 2023.
Education/Academic qualification
Ph. D., Doctor en Matemàtiques, Universitat Autònoma de Barcelona (UAB)
Award Date: 14 Sept 2001
Degree, Matemáticas, Universitat Autònoma de Barcelona (UAB)
Award Date: 20 Jul 1995
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Collaborations and top research areas from the last five years
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VALORACIONES NO ARQUIMEDIANAS EN GEOMETRIA Y TEORIA DE NUMEROS EXPLICITAS
Roe Vellve, J. (Principal Investigator), Masdeu Sabate, M. (Co-Investigador/a Principal), TORRENTS JUSTE, E. (Collaborator), Bars Cortina, F. (Investigator), Nart Vinals, E. (Investigator), Xarles Ribas, F. X. (Investigator) & Novacoski, J. A. (Collaborator)
1/09/21 → 31/08/25
Project: Research Projects and Other Grants
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Métodos efectivos en Geometría Aritmética 2
Roe Vellve, J. (Principal Investigator), Asraan, M. (Collaborator), Farag ., E. E. E. (Collaborator), Gine Vazquez, I. (Collaborator), Bars Cortina, F. (Investigator), Nart Vinals, E. (Investigator) & Xarles Ribas, F. X. (Investigator)
Spanish Ministry of Economy and Competitiveness (MINECO)
30/12/16 → 29/06/21
Project: Research Projects and Other Grants
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Métodos efectivos en geometría aritmética
Roe Vellve, J. (Principal Investigator), Nart Vinals, E. (Co-Investigador/a Principal), Brustenga Moncusi, L. (Collaborator), Gine Vazquez, I. (Collaborator), Bars Cortina, F. (Investigator) & Xarles Ribas, F. X. (Investigator)
Spanish Ministry of Economy and Competitiveness (MINECO)
1/01/14 → 31/12/17
Project: Research Projects and Other Grants
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Métodos combinatorios en geometría aritmética y en geometría algebraica
Nart Vinals, E. (Principal Investigator), Bars Cortina, F. (Investigator), Kock , J. C. (Investigator), Martinez Ramirez, C. (Investigator), Ritzenthaler, C. (Investigator), Roe Vellve, J. (Investigator) & Xarles Ribas, F. X. (Investigator)
Ministerio de Ciencia e Innovación (MICINN)
1/01/10 → 31/12/13
Project: Research Projects and Other Grants
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Mètodes combinatoris en geometria aritmètica
Nart Vinals, E. (Principal Investigator), Kock , J. C. (Researcher on contract), Roe Vellve, J. (Researcher on contract), Bars Cortina, F. (Investigator), Infante Vargas, C. A. (Investigator) & Xarles Ribas, F. X. (Investigator)
Ministerio de Educación y Ciencia (MEC)
1/10/06 → 31/12/09
Project: Research Projects and Other Grants
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The automorphism group of the modular curve $X_0^*(N)$ with square-free levels
Bars Cortina, F., 2021, In: Transactions of the American Mathematical Society. 374Research output: Contribution to journal › Article › Research › peer-review
Open Access1 Downloads (Pure) -
Iwasawa main conjecture for the Carlitz cyclotomic extension and applications
Anglès, B., Bandini, A., Bars, F. & Longhi, I., 1 Jan 2019, In: Mathematische Annalen. p. 1-36Research output: Contribution to journal › Article › Research
6 Citations (Scopus) -
Diophantine stability for curves over finite fields.
Bars Cortina, F. & Lario, J. C., 2025, (Submitted) In: arXiv.org. 18 p.Research output: Contribution to journal › Article › Research › peer-review
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Infinitely many cubic points on X0(N)/⟨wd⟩ with N square-free
Bars Cortina, F. & Dalal, T., 2025, In: Ramanujan Journal. 67, 3Research output: Contribution to journal › Article › Research › peer-review
Open Access -
On the automorphism group of quotient modular curves.
Bars Cortina, F. & Dalal, T., 15 Jun 2025, In: Journal of Algebra. 672, p. 334-378 45 p.Research output: Contribution to journal › Article › Research › peer-review
Open Access1 Downloads (Pure)
Thesis
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Determinació de les corbes $X_0(N)$biel·líptiques
Bars Cortina, F. (Author), Comalada Clara, S. (Director), 26 Sept 1997Student thesis: Final degree project (TFG)
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On the Tamagawa Number Conjecture
Bars Cortina, F. (Author), Xarles Ribas, F.-X. (Director), 12 Sept 2001Student thesis: Doctoral thesis