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...
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Información proyecto MODGROUP
Líder del proyecto
UNIVERSITY OF LEEDS
No se ha especificado una descripción o un objeto social para esta compañía.
TRL
4-5
Presupuesto del proyecto
174K€
Fecha límite de participación
Sin fecha límite de participación.
Descripción del proyecto
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.