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GROUPNIP

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Model theory of groups in NIP theories

The project is in model theory (mathematical logic), with close connections to algebra, especially group theory. Model theory concerns expressibility in logical languages of properties of mathematical structures (e.g. graphs or g... ver más

28/02/2019

UNIVLEEDS

183K€

Presupuesto del proyecto: 183K€

Líder del proyecto

UNIVERSITY OF LEEDS No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Fecha límite participación Sin fecha límite de participación.

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2019-02-28

MSCA-IF-2015-EF: Marie Skłodowska-Curie Individual F...

I+D

Cerrada hace 9 años

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Información adicional privada

No hay información privada compartida para este proyecto. Habla con el coordinador.

1 Participantes

UNIVLEEDS

183.45K€ | Lider

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Duración del proyecto: 35 meses Fecha Inicio: 2016-03-09
Fecha Fin: 2019-02-28

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 183K€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto The project is in model theory (mathematical logic), with close connections to algebra, especially group theory. Model theory concerns expressibility in logical languages of properties of mathematical structures (e.g. graphs or groups). A key notion is that of a `definable set' (generalising algebraic varieties). Model theory identifies `tame' classes of structures/theories such as stable theories, or the much richer class of NIP theories in which definable sets are well-understood, and finds/applies generalisations of geometric notions such as algebraic independence. This project focusses on groups in NIP theories, both as invariants and as definable objects. The three research Workpackages (with specific objectives) concern (1) Applying methods from the recently-developed `Polish structures' to problems of topological dynamics of type spaces in NIP theories, (2) finding methods to compute homology groups (which measure `n-amalgamation') of generically stable types in NIP theories, and characterising the homology groups for algebraically closed valued fields, (3) examining the fine structure of NIP profinite groups, viewed in a 2-sorted language with open subgroups uniformly definable. The Fellow, Dobrowolski, will receive training through research in the model theory groups in Leeds and (on a 3-month secondment) in Lyon. There will be knowledge transfer to Dobrowolski of expertise in model theory, group theory, and topological dynamics in Leeds and Lyon, and Dobrowolski will transfer to Leeds and Lyon the understanding he has built up in Wroclaw and Seoul, on Polish structures and homology groups of first order theories. He will be supervised by Macpherson in Leeds and Wagner in Lyon, but also interact with the large model theory groups in both centres. He will receive complementary training in Leeds on a range of professional academic skills, including outreach, and will take advantage of opportunities for outreach activities in Leeds related to his research.

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