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AMPLE SIGNED

A Study of the Notion of Ampleness in Model Theory and Tits Buildings

Total Cost €

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EC-Contrib. €

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Partnership

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Project "AMPLE" data sheet

The following table provides information about the project.

Coordinator
IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE 

Organization address
address: SOUTH KENSINGTON CAMPUS EXHIBITION ROAD
city: LONDON
postcode: SW7 2AZ
website: http://www.imperial.ac.uk/

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country United Kingdom [UK]
 Total cost 212˙933 €
 EC max contribution 212˙933 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2018
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2019
 Duration (year-month-day) from 2019-09-01   to  2021-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE UK (LONDON) coordinator 212˙933.00

Map

 Project objective

The proposed project AMPLE allocates in the area of mathematical Logic, Model Theory. It aims to develop a full understanding of the notion of ampleness and establish new connections between Model Theory and core mathematics.

Model Theory aims to study and classify mathematical structures according to their THEORIES, that is, the class of all first order logic sentences that are true within them. One of the most important conjectures within Model Theory is Zilber's Trichotomy Conjecture, which suggested a classification of so-called strongly minimal structures - the building bricks of large classes of first order structures. Even though having been refuted quickly after its formulation, this conjecture and its counter example by Hrushovski have shaped the research in model theory and ultimately led Hrushovski to his outstanding proofs of the Mordell-Lang Conjecture, originating in the area of Number Theory.

The notion of AMPLENESS was developed in order to classify the geometries left out in the Trichotomy Conjecture. Even though studied by many after its introduction, there is a plethora of open questions around this notion, witnessing that a thorough understanding is still missing. Answers to these questions have the potential to reshape the view on the classification of first order structures. The ER managed in her PhD thesis to solve one of the main open problems in this area, by combining tools from the field of TITS BUILDINGS, which was developed to classify simple algebraic groups and groups of Lie type.

Together with the project Supervisor, who is a leading expert in the area of ampleness, the ER will establish a full understanding of the notion of ampleness, using its close connections to the theory of Tits Buildings. This project promises new bonds between Model Theory and core mathematics as well as a high applicability to longstanding questions within Model Theory itself. It is thus of high visibility and importance to the community.

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The information about "AMPLE" are provided by the European Opendata Portal: CORDIS opendata.

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