Details of Grant 

EPSRC Reference:	GR/R57263/01
Title:	Model Theory Of Analytical and Pseudo-analytic structures.
Principal Investigator:	Zilber, Professor B
Other Investigators:	Wilkie, Professor A
Researcher Co-Investigators:
Project Partners:
Department:	Mathematical Institute
Organisation:	University of Oxford
Scheme:	Standard Research (Pre-FEC)
Starts:	18 March 2002	Ends:	17 October 2005	Value (£):	187,719
EPSRC Research Topic Classifications:	Algebra & Geometry Logic & Combinatorics
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
In the last few years some of the principal investigator's research exhibited a class of new structures (pseudo-analytic structures) that look strikingly similar to classical analytic structures over the complex numbers. The problem of identifying these structures with their classical counterparts has been basically reduced to several, classical, conjectures about transcendental analytic functions, eg. the Schanuel conjecture in transcendental number theory. In some simpler cases, as was shown by the co-investigator, the analytic prototypes indeed have to a large extent the same theory as their pseudo-analytic counterparts. On the other hand the mdoel theory of these new structures looks to be very rich, and presumably could be developed by means of Shelah's stability theory for non-elementary classes (though so far Shelah's technically profound theory has been developed without applications in mind). One of the conserquences of applying stability theory to pseudo-analytic structures could be new geometric and technical ideas for treating the above mentioned analytic and number theoretic objects (an example worth mentioning here is Hrushovski's treatment of the Mordell-Lang and Mumford-Mainin conjectures). Another possibility may be to use the pseudo-analytic structures as substitutes for the genuine aantytic objects (eg. universal overs) arising in algebraic geometry and other fields, when the complex ones are not readily applicable.
Key Findings
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Potential use in non-academic contexts
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Impacts
Description This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk Summary Date Materialised
Sectors submitted by the Researcher
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
Project URL:
Further Information:
Organisation Website:	http://www.ox.ac.uk