Algebra Seminar
Organizers:
Ela Celikbas and
Olgur Celikbas
Spring 2021
Saturday, April 10, 2021, 9:00 a.m.- 10:00 a.m.
A Gorenstein analogue of the New Intersection Theorem
Kamran Divaani-Aazar | Alzahra University, Iran
Saturday, March 13, 2021, 9:00 am - 10:00 am (Eastern Time USA)
Abstract: Let (R,m,k) be a local ring. The celebrated New Intersection theorem implies many other
intersection theorems. Also, it yields Bass's conjecture and Auslander's Zero-divisor conjecture. There is
much evidence supporting Holm’s claim: “Every result in Classical Homological Algebra should have a counterpart
in Gorenstein Homological Algebra”. Thus, it is natural to look for a Gorenstein analogue of the New Intersection
theorem.
In this talk, we first review the New Intersection theorem and some of its immediate implications. Then, we
establish a Gorenstein analogue of the New Intersection theorem, when R is a quasi-specialization of a
G-regular local ring.
This talk is based on a joint work with Fatemeh Mohammadi Aghjeh Mashhad, Ehsan Tavanfar and Massoud Tousi.
To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas
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.
Sarasij Maitra | Univeristy of Virginia, USA
Saturday, February 13 9:00 a.m- 10:00 a.m.
To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas.
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)
Shinya Kumashiro | Chiba University, Japan
Saturday, September 5 9:00a.m.- 10:00 a.m. | Virtual
To attend virtually, send a request to Dr. Ela Celikba or Dr. Olgur Celikbas
Castelnuovo-Mumfordregularity and its asymptotic behaviour (Introductory Talk)
Dipankar Ghosh | Indian Institute of Technology Hyderabad, India
Saturday, September 26 9:00 a.m.- 10:00 a.m. | Virtual
To attend virtually, send a request to Dr. Ela Celikba or Dr. Olgur Celikbas
Castelnuovo-Mumfordregularity and its asymptotic behaviour (Research Talk)
Dipankar Ghosh | Indian Institute of Technology Hyderabad, India
Saturday, October 3 9:00 a.m.- 10:00 a.m. | Virtual
To attend virtually, send a request to Dr. Ela Celkibas or Dr. Olgur Celikbas
A study of the structure of Sally modules (Introductory talk)
Kazuho Ozeki | Yamaguchi University, Japan
Saturday, October 10, 2020 9:00 a.m- 10:00 a.m. | Virtual
To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas
A study of the structure of Sally modules (Research Talk)
Kazuho Ozeki | Yamaguchi University, Japan
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
Souvik Dey | University of Kansas, USA
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, IndiaSaturday, October 31, 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 (Research Talk)
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)
Tony Se | West Virginia University, USA
Saturday, November 21, 2020 9:00 a.m.- 10:00a.m.
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)
Naoyuki Matsuoka | Meiji University, Japan
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)
Naoyuki Matsuoka | Meiji University, Japan
Saturday, December 12, 2020 9:00a.m.- 10:00 a.m.
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.