Commutative algebra was born in the 19th century from algebraic geometry, invariant theory, and number theory. Today it is a mature field with activity on many fronts.
The year-long program will highlight exciting recent developments in core areas such as free resolutions, homological and representation theoretic aspects, Rees algebras and integral closure, tight closure and singularities, and birational geometry. In addition, it will feature the important links to other areas such as algebraic topology, combinatorics, mathematical physics, noncommutative geometry, representation theory, singularity theory, and statistics. The program will reflect the wealth of interconnections suggested by these fields, and will introduce young researchers to these diverse areas.
New connections will be fostered through collaboration with the concurrent MSRI programs in Cluster Algebras (Fall 2012) and Noncommutative Algebraic Geometry and Representation Theory (Spring 2013).
For more detailed information about the program please see, http://www.math.utah.edu/ca/.Updated on May 19, 2013 07:55 pm PDT
Over the last few decades noncommutative algebraic geometry (in its many forms) has become increasingly important, both within noncommutative algebra/representation theory, as well as having significant applications to algebraic geometry and other neighbouring areas. The goal of this program is to explore and expand upon these subjects and their interactions. Topics of particular interest include noncommutative projective algebraic geometry, noncommutative resolutions of (commutative or noncommutative) singularities,Calabi-Yau algebras, deformation theory and Poisson structures, as well as the interplay of these subjects with the algebras appearing in representation theory--like enveloping algebras, symplectic reflection algebras and the many guises of Hecke algebras.Updated on May 06, 2013 04:21 pm PDT