|Wednesday 13 December 2017|
|Events for day: Thursday 14 December 2017|
| 11:00 - 13:00 Lecture|
DG Homological Algebra and Vanishing of (Co)homology over Local Rings
The use of techniques from differential graded (DG) homological algebra was established by Avramov, Buchsbaum, Eisenbud, Halperin, Kustin, Miller, and Weyman in commutative algebra, for instance, via DG algebra structures on Koszul complexes and free resolutions. It has been shown recently that these techniques can be applied to solve non-trivial problems in commutative algebra. In this talk, we will discuss the following major problems: Auslander-Reiten Conjecture (1975). If M is a finitely generated module over a local ring R with Ext^i_R(M, M ⊕ R) = 0 for all i large enough, then pdR(M) < ∞. Vasconcelos' Conjectu ...