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.