# Program

A significant development over the last 20 years is the role that commutative algebra is taking as a tool for solving problems from a rapidly expanding list of disciplines. In oversimplified terms, the process could be described as follows: Mathematicians with various backgrounds discover ways of encoding information of interest into commutative rings and their modules, then use algebraic concepts, methods, and results to analyze that information efficiently. A famous example of such encoding is the translation of an abstract finite simiplicial complex into an ideal represented by the zeroes of square-free monomials in a set of variables corresponding to the vertices of the simplicial complex. Of course, the existing body of work in commutative algebra is not tailored to suit all new demands. This is precisely where the subject benefits most from the recent surge of external interest, as it receives an influx of novel questions, points of view, and expertise.

Our year-long program will highlight these recent developments and will include the following areas:

- Tight closure and characteristic
*p*methods - Toric algebra and geometry
- Homological algebra
- Representation theory
- Singularities and intersection theory
- Combinatorics and Grobner bases

**Primary Mathematics Subject Classification**No Primary AMS MSC

**Secondary Mathematics Subject Classification**No Secondary AMS MSC

September 09, 2002 - September 13, 2002 | Introductory Workshop in Commutative Algebra |

December 02, 2002 - December 06, 2002 | Commutative Algebra: Local and Birational Theory |

February 03, 2003 - February 07, 2003 | Commutative Algebra: Interactions with Homological Algebra and Representation Theory |

March 13, 2003 - March 15, 2003 | Computational Commutative Algebra |

March 29, 2003 - April 03, 2003 | Commutative Algebra and Geometry (Banff Int'l Research Station Workshop) |