Olgur Celikbas 

On a Conjecture of Huneke and Wiegand

Abstract: 

There are many conjectures from the representation theory of finite-dimensional algebras that have been transplanted to commutative algebra, and this process has enriched both fields significantly.

An example is the celebrated Auslander-Reiten Conjecture [1]. This long-standing conjecture is closely related to other important conjectures such as the Finitistic Dimension Conjecture and Tachikawa Conjecture from representation theory. The Auslander-Reiten Conjecture originates in representation theory of algebras, but it has re cently received considerable attention in commutative algebra.

In 1994 Huneke and Wiegand [2] proposed a conjecture on tensor products of torsion-free modules over one-dimensional commuta tive Noetherian integral domains. This conjecture, which is still open, implies the Auslander-Reiten Conjecture for a large class of commutative rings.

In this talk I will discuss the connection between the Huneke-Wiegand Conjecture and the Auslander-Reiten Conjecture, and survey the literature on these topics with emphasis on recent progress. Part of the talk is based on an ongoing joint work with Shiro Goto, Ryo Takahashi and Naoki Taniguchi.

References:

[1] M.Auslander and I. Reiten, On a generalized version of the Nakayama conjecture, Proc. Amer. Math. Soc. 52 (1975), 69-74.

[2] C. Huneke and R. Wiegand, Tensor products of modules and the rigidity of Tor, Math. Ann. 299 (1994), no. 3, 449-476.

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Short biography: ​

Employment:

Postdoctoral Fellow at University of Connecticut, Storrs, CT, U.S.A. August 2014 – present

Postdoctoral Fellow  at University of Missouri, Columbia, MO, U.S.A. August 2011 – August 2014

Lecturer/Research Assistant at University of Kansas, Lawrence, KS, U.S.A. August 2010 – August 2011

Graduate Teaching Assistant at University of Nebraska – Lincoln, Lincoln, NE, U.S.A. August 2003 – August 2010

Education:

Ph.D. Mathematics, August 2005 – August 2010 University of Nebraska – Lincoln, Lincoln, NE, U.S.A. Thesis: Vanishing of Ext and Tor over complete intersections Advisors: Mark E. Walker (Willa Cather Professor of Mathematics) Roger Wiegand (Willa Cather Professor Emeritus of Mathematics)

M.S. Mathematics, August 2003 – May 2005 University of Nebraska – Lincoln, Lincoln, NE, U.S.A.

Early Graduate Work. Mathematics, September 2001 – May 2003 Middle East Technical University, Ankara, Turkey.

B.S. Mathematics, September 1995 – June 1999 Ankara University, Ankara, Turkey (GPA: 94/100)

Research Interests: Commutative algebra, Homological algebra, Representation Theory

January 7, 2016 at 14:00, in FENS 1040