Objective The project is in model theory (mathematical logic), which concerns the expressibility in logical languages of properties of mathematical structures (e.g. graphs, groups, rings). Model theory aims to identify borders between `tame' and `wild' objects in mathematics, and to pin down abstract notions of independence and dimension and understand the geometry of `definable sets' in a structure, often with wide-ranging applications. This project focusses on classes of finite structures (e.g. the class of all finite fields), and on the `ultraproduct' construction which converts a class of finite structures to an infinite `pseudofinite' structure' which inherits properties of the class and is amenable to model-theoretic methods, with applications for the finite structures. Key objectives include:(i) proving a trichotomy for pseudofinite geometries -- they should be `trivial', `group-like', or `field-like'; (ii) developing current concepts from abstract model theory for pseudofinite structures;(iii) identifying first order properties of pseudofinite groups, and constraints on their possible quotients;(iv) finding links between the model-theoretic `independence theorem', Gowers' notion of `quasi-random groups', and the Szemeredi regularity theorem in graph theory. (v) model theory of finite ordered structures, and links to finite model theory.To support his future academic research career, the Fellow, Garcia, will receive training through research in the model theory groups in Leeds and (through a secondment) Lyon. There will be knowledge transfer to Garcia of expertise in model-theoretic algebra of Leeds and Lyon, and Garcia will also build knowledge of finite model theory and its computer science applications. He will receive complementary training in many research skills (including outreach), and will transfer to Leeds expertise he has gained in the excellent model theory groups in Berkeley and Bogota, while deepening EU-Colombia mathematics links. Fields of science natural sciencesmathematicspure mathematicsdiscrete mathematicsmathematical logicnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicsgraph theorynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatoricsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Topic(s) MSCA-IF-2014-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF) Call for proposal H2020-MSCA-IF-2014 See other projects for this call Funding Scheme MSCA-IF-EF-ST - Standard EF Coordinator UNIVERSITY OF LEEDS Net EU contribution € 183 454,80 Address Woodhouse lane LS2 9JT Leeds GB See on map Region Yorkshire and the Humber West Yorkshire Leeds Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
