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Algebra Seminar

Organizers: Ela Celikbas and Olgur Celikbas


Spring 2021


Test modules, weakly regular homomorphisms, andcomplete intersection dimension


Ehsan Tavanfar Institute
| for Research in Fundamental Sciences (IPM), Iran

Saturday, April 10, 2021, 9:00 a.m.- 10:00 a.m.

To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas



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.

To attend virtually, send a request to Dr. Ela Celikbas or Dr. Olgur Celikbas.


Integrally closed ideals in Arf rings

Ryotaro Isobe | Chiba University, Japan

Saturday, January 30 9:00 a.m.- 10:00 a.m | Virtual

Discussion on I-Ulrich modules


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, Japan 

Saturday, 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

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

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, India

Saturday, 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)

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.

Tony Se | West Virginia University, USA

Saturday, November 21, 2020 9:00 a.m.- 10:00a.m.

Naoyuki Matsuoka | Meiji University, Japan

Saturday, December 5, 2020 9:00a.m.- 10:00 a.m.

Naoyuki Matsuoka | Meiji University, Japan

Saturday, December 12, 2020 9:00a.m.- 10:00 a.m.

To attend virtually, send a request to Dr. Ela Celikbas or Dr. 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.