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Host: Banff International Research Station
Homepage: http://www.pims.math.ca/birs/workshops/2004/04w5534/
Organizers: Deirdre Haskell (McMaster University), Jan Denef (Leuven), Ehud Hrushovski (Hebrew University), Angus Macintyre (Edinburgh), Anand Pillay (UIUC), Patrick Speissegger (Wisconsin & McMaster).
Description:
In the past decade, model theory has reached a new maturity, strengthening of its connections with other areas of mathematics and producing striking applications to diophantine geometry, analytic geometry and Lie theory, as well as strong interactions with group theory, representation theory of finite-dimensional algebras, and the study of the $p$-adics. In the proposed BIRS workshop, we want to focus on these applications, while maintaining input from the pure model theorists whose new work is relevant to the applications.
The semester-long program on the model theory of fields at MSRI in 1998 brought together model theorists, number theorists and algebraic and analytic geometers, and set a new precedent for communication between the various groups. The semester concluded with a workshop entitled {\it Model theory, algebra and arithmetic}, remarkable for the breadth of its reach. In the intervening four years, there have been exciting new developments. For applications we mention the work of Zil'ber on ``pseudo-analytic'' structures, that of Pillay and Scanlon towards classification of compact complex manifolds, Denef and Loeser on motivic integration. On the pure model theory side we have seen the development of new notions of independence, immediately relevant for algebraically closed valued fields and PAC fields. There have not been any major conferences since 1998 which brought the researchers from different fields together. In 1999 there was a small workshop at the ICMS in Edinburgh focused on the applications of model theory especially in valued fields. In 2002 there was a {\it Euroconference on Model Theory and Applications}, with principal topic the model theory of fields and a Luminy conference on simple theories within pure model theory. Each was well attended by students and postdoctoral researchers new to the subject since 1998. We will want to include several of them in the BIRS workshop, to build for the future. A conference at BIRS in 2004 would be a timely mechanism to refocus researchers from the different areas on their common interests. It would also look forward to the semester program on {\it Model theory and applications to algebra and analysis} at the Newton Institute in 2005.
For the BIRS conference, we wish to repeat the excitement of the MSRI workshop, once again bringing together researchers from different fields who are creating new developments in the exciting interface of the relevant areas. It is particularly important to allow time for research collaborations as well as for expositions of new results. As such, we propose three talks in the mornings, an afternoon free for interaction and collaboration, and one or two more talks in the early evening. The problem session of the ICMS meeting was enormously successful, in large measure due to the variety of perspectives present. We would expect to replicate this success at BIRS.
Date received: January 14, 2004
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