MODGROUP
The Model Theory of Groups
| Coordinatore | UNIVERSITY OF LEEDS
Organization address
address: WOODHOUSE LANE contact info |
| Nazionalità Coordinatore | United Kingdom [UK] |
| Totale costo | 173˙903 € |
| EC contributo | 173˙903 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-2009-IEF |
| Funding Scheme | MC-IEF |
| Anno di inizio | 2010 |
| Periodo (anno-mese-giorno) | 2010-10-01 - 2012-09-30 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
UNIVERSITY OF LEEDS
Organization address
address: WOODHOUSE LANE contact info |
UK (LEEDS) | coordinator | 173˙903.20 |
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Obiettivo del progetto (Objective)
'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.'