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The Model Theory of Groups

Obiettivo

The topic of the project is to develop new connections between model theory (a subfield of mathematical logic) and algebra, involving applications to group theory. We propose to work on some questions regarding groups definable in various important first order structures: o-minimal, without the independence property (NIP) and algebraically closed valued fields (ACVF) and others. Especially, we are interested in model-theoretic connected components of such groups. The quotient of the group by one of its model-theoretic components connected with `logic topology' is a quasi-compact topological group, and can be seen as a canonical set-theoretical invariant of first order theory of a given group. We plan to investigate in this context groups of Lie type (e.g. Chevalley groups), finitely generated nilpotent groups and algebraic groups over valued fields. We aim also to initiate a systematic study of the model theory of affine buildings, and of associated groups of automorphisms. We intend to combine classical Lie theory, results about covering numbers of Chevalley groups and some applicant's achievements. Working on affine buildings we use the classification of Bruhat-Tits buildings. The solutions to our conjectures and questions give us a results of new kind not only in model theory but in algebraic group theory and in additive combinatorics.

Invito a presentare proposte

FP7-PEOPLE-2009-IEF
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Coordinatore

UNIVERSITY OF LEEDS
Contributo UE
€ 173 903,20
Indirizzo
WOODHOUSE LANE
LS2 9JT Leeds
Regno Unito

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Regione
Yorkshire and the Humber West Yorkshire Leeds
Tipo di attività
Higher or Secondary Education Establishments
Contatto amministrativo
Dugald Macpherson (Prof.)
Collegamenti
Costo totale
Nessun dato