Frontiers in Mathematical Sciences 7th Conference University of Isfahan - January 1-3, 2020
 Title: Vanishing of (CO)Homology over Local Rings Speaker: Arash Sadeghi, IPM Date, Time, and Venue:  Thursday, January 2 | 09:45-10:30 | Hall 2 Abstract: In this talk, we will discuss about the vanishing of (co)homology over commutative Noetherian local rings. A remarkable consequence of the vanishing of homology is the depth formula, $\text{depth}_{R}(M)+\text{depth}_{R}(N) = \text{depth}(R)+\text{depth}_{R}(M\otimes_{R}N),$ established by Auslander when $R$ is regular. In the first part of this talk, we will discuss about the depth formula over Gorenstein rings. In the second part, we will talk about Auslander–Reiten Conjecture. This is one of the most celebrated conjectures in the representation theory of algebras. We will present various criteria for freeness of modules over local rings in terms of vanishing of cohomology, which recover a lot of known results on the Auslander–Reiten Conjecture.