Syzygies and Hilbert Functions (06w5082)


(Cornell University)

(Cornell University)


Commutative algebra and algebraic geometry are the fields of mathematics which deal with understanding the solutions of a system of polynomial equations, possibly in a large number of variables and with a large number of equations. The solutions form a geometric object. Since the number of variables is often large, graphing is not possible. The main idea in these mathematical fields is to study the geometric properties using algebra. Syzygies and Hilbert functions are key techniques for understanding the structure of such geometric objects. Many of the world's top experts in commutative algebra will converge at the Banff International Research Station next week, October 14 - 19, 2006, where a workshop on recent developments in syzygies and Hilbert functions is hosted. This event is co-organized by Professor Michael Stillman, a professor at Cornell University, and a co-author of the popular computer algebra system Macaulay2, and by Professor Irena Peeva, also from Cornell University, and a highly regarded world expert in commutative algebra.

The workshop will focus on the hottest new results on syzygies and Hilbert functions. There has been a surge in interest and research in this direction during the last years: a great variety of new ideas and techniques have been introduced, and substantial progress has been made. Projects in this direction have been undertaken by both established mathematicians and graduate students or postdocs. However, many central conjectures and open problems are very challenging and remain wide open. One of the main goals is to spark further interaction. The workshop will be also an opportunity to focus on these problems and to explore new directions.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is administered by the Pacific Institute for the Mathematical Sciences, in collaboration with the Mathematics of Information Technology and Complex Systems Network (MITACS), the Berkeley-based Mathematical Science Research Institute (MSRI) and the Instituto de Matematicas at the Universidad Nacional Autonoma de Mexico (UNAM).