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- EU Research Framework Programme
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- International Research Projects Office
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- Higher Education Institute
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- Gran Vía de Colón, 48, 2nd floor
Professor Pedro A. García Sánchez, from the Department of Algebra at the University of Granada, welcomes postdoctoral candidates interested in applying for a Marie Skłodowska-Curie Postdoctoral Fellowship (MSCA-PF) in 2022 at this University. Please note that applicants must comply with the Mobility Rule (for more information about the 2022 call, please consult: http://sl.ugr.es/0cmA).
Brief description of the institution:
The University of Granada (UGR) was founded in 1531 and is one of the largest and most important universities in Spain. With over 60,000 undergraduate and postgraduate students and 6,000 members of staff, the UGR offers over 70 undergraduate degrees, 100 master’s degrees (9 of which are international double degrees) and 28 doctoral programmes via its 127 departments and 22 centers. Accordingly, the UGR offers one of the most extensive and diverse ranges of higher education programmes in Spain.
The UGR has been awarded with the "Human Resources Excellence in Research (HRS4R)", which reflects the institution’s commitment to continuously improving its human resource policies in line with the European Charter for Researchers and the Code of Conduct for the Recruitment of Researchers. The UGR is also internationally renowned for its excellence in diverse research fields and ranked among the top Spanish universities in a variety of ranking criteria, such as national R&D projects, fellowships awarded, publications, and international funding.
The UGR is one of the few Spanish Universities listed in the Shanghai Top 500 ranking - Academic Ranking of World Universities (ARWU). The 2021 edition of the ARWU places the UGR in 201-300th position in the world and as the second highest ranked university in Spain (http://sl.ugr.es/0cmF), reaffirming its position as an institution at the forefront of national and international research. The UGR stands out in the specialties of Library & Information Science (position 36); Food Science & Technology (39) and Hospitality & Tourism Management (51-75), according to the latest edition of this prestigious ranking by specialties (http://sl.ugr.es/0bSp). A little lower in the ranking, the UGR also stands out in Mathematics (76-100) and Mining & Mineral Engineering (76-100).
Additionally, the UGR has 7 researchers who are at the top of the Highly Cited Researchers (HCR) list (http://sl.ugr.es/0cmD), most of these related to the area of Computer Science. It is also well recognized for its web presence (http://sl.ugr.es/0a6i), being positioned at 54th place in the top 200 Universities in Europe.
Internationally, the University of Granada is firmly committed to its participation in the calls of the Framework Programme of the European Union. For the duration of the last two Framework Programmes, the UGR has obtained for FP7 a total of 67 projects, with total funding of 18.029 million euros, and for H2020, 119 projects with a total funding of around 29.233 million euros.
Brief description of the Centre/Research Group:
Our group works on commutative monoids. These include affine and numerical semigroups. The main interests of our group can be extracted from the web page of the Monoids and Applications Network (http://www.ugr.es/~semigrupos/MyA/index-en.html).
Both numerical and affine semigroups arose in a natural way in the study of nonnegative integer solutions of linear Diophantine equations. Later, numerical semigroups gained interest for researchers in commutative algebra and algebraic geometry thanks to the concept of value semigroup associated to an algebraic curve, which allows fundamental properties of the curve to be derived from arithmetic operations in the semigroup.
Factorization in terms of irreducible elements in integral domains has been also a source of interest in the study of commutative monoids. New families of monoids arise related to rings that have been long studied in the literature.
The study of the properties of algebraic-geometry codes in terms of the Weierstrass semigroup associated with one point of a curve pushed forward even more the research on the properties of the Weierstrass semigroups, which translate to given features in the code.
Applications to combinatorial configurations of lines and points, as well as the connection between certain families of numerical semigroups and cyclotomic polynomials, provided even more motivation for the investigation of commutative monoids.
The researcher will work mainly in applications of commutative monoids. These applications will be the study of nonunique factorization invariants, applications of monoids to coding theory, and if the candidate has some basic programming skills, maintenance and enhancement of the GAP package numericalsgps (see https://www.gap-system.org/Packages/numericalsgps.html and https://gap-packages.github.io/numericalsgps/).
There are several nonunique factorization invariants that measure how far a monoid is from being factorial (unique factorizations) or half-factorial (all factorizations have the same length). This is an abstraction of the well-known concept of unique factorization domain. Our research group has produced several algorithms for the computation, and thus study, of some of these invariants: Delta sets, catenary degrees, elasticity, tame degree, omega primality. Apart from the potential calculation of invariants, there are other interesting problems related to this study, such as realization problems: finding monoids with prescribed invariants.
In the last decades numerical semigroups became a tool to measure properties of one-point algebro-geometric codes. We have produced a series of papers computing Feng-Rao distances and numbers, which give upper bounds for the number of errors that such codes may correct. These distances have been calculated only for some specific families of numerical semigroups.
A tool to produce batteries of examples is essential in many cases in research, since it may help to understand whether a conjecture holds, or to depict the behaviour of some invariants. To this end we developed the GAP package numericalsgps. This package was accepted in 2015, but we keep adding new functionalities and improvements.
- Mathematics (MAT)
For a correct evaluation of your candidature, please send the documents below to Professor Pedro A. García Sánchez (firstname.lastname@example.org):
- Letter of recommendation (optional)