Back to Departmental Colloquium: Spring 2010
Departmental Colloquium
Date: Thursday, Feb 11, 2010
Time: 4:15PM
Location: JWB 335
Hai Long Dao
University of Kansas
Title |
Playing with Ext and Tor: study singularities via homological algebra |
Abstract |
To understand an algebraic object (groups, rings, etc.) it often pays to understand some category such object acts on. For example, when our object is a commutative ring R, we wish to explore the category mod(R) of (finitely generated) modules over R. Two fundamental operations in mod(R) are tensor product and Hom. Studying these operations naturally leads to their respective derived functors, namely Tor and Ext. Despite the relatively simple definitions involving these functors, their actual behaviour remain quite mysterious. In this talk I will describe how understanding simple questions such as when the Ext and Tor modules vanish can lead to concrete results on seemingly unrelated topics such as non-commutative crepant resolutions or torsions in Picard groups of certain singularities. Most of the talk will be accessible to non-experts. |
Commutative Algebra