Homological Days 2012

June 4-6, 2012

at the

Department of Mathematics, University of Kansas,

organized by

Hailong Dao

This mini-workshop, partially sponsored by NSF and the University of Kansas, will focus on several homological aspects of (non)commutative algebra. The 2011 version can be found here .

Location: Department of Mathematics, University of Kansas. The talks will be held at 306 Snow Hall.


Speakers and schedule:

Kosmas Diveris (Syracuse University) 2:00pm-4:00pm (with a 20 mins break at 2h50), June 4, 306 Snow

Title: Introduction to derived categories and Buchweitz's theorem.

Abstract: We will give a tutorial on derived categories, with a focus on D^b(mod R). The second part will explain Buchweitz's theorem on equivalence of the stable category of maximal Cohen-Macaulay modules and the singularity category over Gorenstein rings.

Saeed Nasseh (North Dakota State University) 2:00pm-4:00pm (with a 20 mins break at 2h50), June 5, 306 Snow

Title: Some conjectures on AB rings I and II.
Abstract: We will discuss some open questions on the finite Ext indices of commutative Noetherian rings. The Gorenstein local rings with finite Ext-index are known as AB rings and were introduced and studied by Huneke-Jorgensen. This is partly joint work with Yuji Yoshino.

Kosmas Diveris (Syracuse University) 2:00 - 2:50pm, June 6, 306 Snow

Title: Generalized Auslander-Reiten condition and finitistic extension degree

Abstract: We introduce the finitistic extension degree of a ring and investigate rings for which it is finite. The Auslander-Reiten Conjecture is proved for rings of finite finitistic extension degree and these rings are also shown to have finite finitistic dimension. We apply these results to better understand a generalized version of the Auslander-Reiten Conjecture for Gorenstein rings. We also discuss the relationship between the finiteness of the finitistic extension degree and Auslander's condition concerning the vanishing of cohomology.

Saeed Nasseh (North Dakota State University) 3:00 - 3h50pm, June 6, 306 Snow

Title: On the Auslander-Reiten conjecture.

Abstract: