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Organizers: Ela Celikbas and Olgur Celikbas

Spring 2020

Introduction to Triangulated Categories in Commutative Algebra

Hiroki Matsui | University of Tokyo, Japan

Friday, January 24 4 – 5:30 p.m. at ARM 315

Monday, January 27 4:30 – 6 p.m. at ARM 315

Notes on Semidualizing Modules

Tony Se | West Virginia University

Friday, January 24, February 14, February 21, February 28 4 – 5 p.m. at ARM 315

Abstract: We will survey some aspects of semidualizing modules, theory and applications.

On Burch Rings

Toshinori Kobayashi | Nagoya University, Japan

Friday, March 6 4:30 – 6 p.m. at ARM 315

Monday, March 9 4:30 – 6 p.m. at ARM 315

Abstract: I will introduce a class of ideals and their affiliated rings, which we call Burch ideals and Burch rings. While their definitions are quite simple, our investigation shows that they enjoy remarkable ideal-theoretic and homological properties. I will give some basic properties of Burch rings. Especially, a characterization of Burch rings will be given in terms of the second syzygy of the residue field. I will also talk about a classification of subcategories and trivial vanishing of Tor over these rings.