## Colloquium: Non-commutative resolutions of singularities and the global spectrum

Author: UNB

Posted on Nov 29, 2013

Category:
Seminars and Colloquia

#### Colloquium

#### Non-commutative resolutions of singularities and the global spectrum

##### Eleonore Faber (University of Toronto)

##### Wednesday, November 13, 2013 at 2:30 pm

##### Tilley Hall Room 302

This talk is about non-commutative analogs of resolutions of singularities. In short, non-commutative desingularizations of a commutative ring R are endomorphism rings of certain R-modules of finite global dimension. After some motivating examples, we discuss several approaches to non-commutative resolutions (NCRs), namely, Van den Bergh's crepant NCRs and NCRs as recently defined by Dao, Iyama, Takahashi and Vial. Then we study their relevance for non-normal rings, in particular the question, under which conditions a non-commutative resolution exists. This leads us to consider the so-called global spectrum of a ring, that is, the set of all possible global dimensions of endomorphism rings of MCM-modules. This is joint work with H. Dao and C. Ingalls.
##### Dr. Eleonore Faber is a Post-Doctoral Fellow in Mathematics at the University of Toronto