# Homotopy theory and projective modules

*Algebra/Geometry/Topology Seminar*

*by Aravind Asok*

*Institution:*USC

*Date: Fri 2nd November 2012*

*Time: 3:15 PM*

*Location: 213 Richard Berry*

*Abstract*: If R is a commutative unital ring, and P is a projective R-module of rank n, a basic question in algebra is: when does P split as a direct sum P' + R, where P' is a projective module of rank n-1. After recalling some history of this question, I will introduce some aspects of the homotopy theory of algebraic varieties (constructed by F. Morel and V. Voevodsky) and discuss how this theory may used to study the splitting problem above.