|Date: Friday, April 04, 2014
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: Grobner bases for twisted commutative algebras
Abstract: Recent work of Draisma-Kuttler, Snowden, and Church-Ellenberg-Farb in commutative algebra, algebraic geometry, and homological algebra, seeks to understand stability results (say, of some invariant of a sequence of algebraic objects) as the finite generation of some other algebraic object. Examples include the Delta-modules in the study of free resolutions of Segre embeddings and FI-modules in the study of cohomology of configuration spaces. This finite generation often reduces to establishing the Noetherian property: subobjects of finitely generated objects are again finitely generated. I will discuss the situation of modules over twisted commutative algebras, which realize some of these topics as special cases. I will introduce a Grobner basis theory and show how it proves these Noetherian results. The talk will be mostly combinatorial and I will suggest some open problems. This is based on joint work with Andrew Snowden.
Speaker: Steven Sam
Institution: UC Berkeley