Algebra Seminar
Organizers:
Ela Celikbas and
Olgur Celikbas
Spring 2021
Explicit Minimal Free Resolutions of Fiber Products
Hugh Geller | Clemson University, USA
Saturday, February 27 9:00 a.m.-10:00 a.m.
Abstract: In 2006, Visscher gave an explicit construction for the minimal free resolution of the fiber product k[x] ×k k[y] ∼= k[x, y]/hxyi over k[x, y]. In this talk, we give an alternate description of Visschers resolution which we then use to resolve quotient rings (with certain constraints) of the form R/hI 0 , IJ, J0 i over R. We then show that this construction can be used to obtain minimal resolutions of fiber products and provides us with explicit formulas for the Betti numbers, Betti tables, and Poincar`e Series.
Saturday, February 13 9:00 a.m- 10:00 a.m.
Fall 2020
The Auslander-Reiten conjecture for certainnon-Gorenstein Cohen-Macaulay rings (Introductory Talk)
Shinya Kumashiro | Chiba University, JapanSaturday, September 5 9:00 a.m.-10:00 a.m. | Virtual
The Auslander-Reiten conjecture for certainnon-Gorenstein Cohen-Macaulay rings (Introductory Talk)
Castelnuovo-Mumfordregularity and its asymptotic behaviour (Introductory Talk)
To attend virtually, send a request to Dr. Ela Celikba or Dr. Olgur Celikbas
Castelnuovo-Mumfordregularity and its asymptotic behaviour (Research Talk)
To attend virtually, send a request to Dr. Ela Celkibas or Dr. Olgur Celikbas
A study of the structure of Sally modules (Introductory talk)
To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas
A study of the structure of Sally modules (Research Talk)
Saturday, October 17, 2020 9:00 a.m.- 10:00 a.m. | Virtual
To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas
Annihilator of Tor and Ext of subcategories of module category
Saturday, October 24, 2020 9:00 a.m.-10:00 a.m. | Virtual
To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas
FROBENIUS BETTI NUMBERS AND SYZYGIES OF FINITE LENGTHMODULES (Introductory Talk)
Parangama Sarkar | Indian Institute of Technology Palakkad, India
FROBENIUS BETTI NUMBERS AND SYZYGIES OF FINITE LENGTHMODULES (Research Talk)
Parangama Sarkar | Indian Institute of Technology Palakkad, India
Saturday, November 7, 2020 9:00 a.m.- 10:00 a.am.
To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas
Semidualizing Modules and the Divisor Class Group of Ladder Determinantal Rings (Introductory Talk)
Tony Se | West Virginia University, USA
Saturday, November 14, 2020 9:00 a.m.- 10:00 a.m.
To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas
Semidualizing Modules and the Divisor Class Group of Ladder Determinantal Rings (Research Talk)
Saturday, November 21, 2020 9:00 a.m.- 10:00a.m.
To attend virtually, send a request to Dr. Ela Celkibas or Dr. Olgur Celikbas
Pseudo-Frobenius numbers versus defining ideals (Introductory Talk)
Saturday, December 5, 2020 9:00a.m.- 10:00 a.m.
To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas
Pseudo-Frobenius numbers versus defining ideals (Research Talk)
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.