Details of Grant 

EPSRC Reference:	GR/R80841/01
Title:	Agler Model Theory and Its Applications
Principal Investigator:	Dritschel, Dr M
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department:	Mathematics and Statistics
Organisation:	Newcastle University
Scheme:	Fast Stream
Starts:	01 September 2002	Ends:	30 November 2005	Value (£):	63,394
EPSRC Research Topic Classifications:	Logic & Combinatorics Mathematical Analysis
EPSRC Industrial Sector Classifications:	No relevance to Underpinning Sectors
Related Grants:
Panel History:
Summary on Grant Application Form
We proposed to carry out theoretical and practical research into Agler's model theory for families of representations and operators. Theoretical aspects will lead to a deeper understanding of the abstract model theory, with the goal of finding additional tools which can be applied to the task of discovering models for particular classes of representations and operators , especially in the multivariable setting, as well as discerning whihc families have good models. Practical aspects will cover a host of applicaitons. For example, interpolations problems can be productively solved by means of model theory, as Agler, McCarthy, and others have shown. Commutant lifting problems can be phrased in terms of multivariable model theory, and these have proved useful in control theory. Model theory is connected to Arverson's notion of a boundary representation and C* envelope. We wish to determine whether irreducible boundary representations always exist for operator algebras. Finally, the rational dilation problem has been solved for only a handful of spectral sets. Agler and a student of his have numerical evidence that it does not hold for certain three-holed domains. One of our goals will be to give criteria for the validity of rational dilation in terms of what Agler calls the hereditary bimodule associated to a model.
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Organisation Website:	http://www.ncl.ac.uk