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We are proposing a one-week regular conference (40 participants) on commutative algebra, with an emphasis on interactions with algebraic geometry, polyhedral geometry and combinatorics. This conference would be held in the Spring of 2003 and is part of the Special Program 2002/03 on Commutative Algebra at MSRI Berkeley.
It is our intention to invite younger researchers and to also include first-rate mathematicians who work not in commutative algebra proper but in nearby fields. Specifically, we shall invite several leading algebraic geometers. In selecting lectures we will place a particular emphasis on recent developments, applications and future directions.
The following is a sample of topics to be discussed in this workshop: toric rings and varieties, Koszul algebras, toric K-theory, exterior algebra methods, arrangements of linear subspaces, Flag varieties and Schubert varieties, Grobner bases, sagbi bases, zero-dimensional schemes, elimination theory, Hilbert schemes, singularities, invariant theory.
All of these topics are highly relevant for applications of commutative algebra, both within mathematics and outside of mathematics. To give a concrete example for the usefulness of Commutative Algebra as scientific tool, we wish to mention the recent interaction with Statistics. An introduction to this can be found in the book Giovanni Pistone, Eva Riccomagno and Henry Wynn: Algebraic Statistics: Computational Commutative Algebra in Statistics, Chapman and Hall, Boca Raton, London, 2001, ISBN: 1-58488-204-2 The proposed workshop at Banff deals with fundamental problems whose solutions will benefit practical applications such as those in "Algebraic Statistics".
The timing of the proposed workshop is perfect: it will take place at the end of a One-Year Program on Commutative Algebra at MSRI Berkeley. There will be many new and interesting developments emerging during that year, and the workshop at Banff will help to summarize and disseminate these results. The Oberwolfach format at Banff will allow us to keep the meeting very focussed and provide an excellent contrast to the seminars at MSRI.