I'm currently a PhD student at West Virginia University. My major is commutative algebra, and I'm specially interested in Tor-rigidity, depth, torsion properties of finitely generated modules over local rings.
(Joint work with O. Celikbas and H. Matsui)
In this paper we study the depth of tensor products of homologically finite complexes over commutative Noetherian local rings. As an application of our main result, we determine new conditions under which the factors of a nonzero reflexive tensor product of finitely generated modules over hypersurface rings can be reflexive. A result of Asgharzadeh shows that nonzero symbolic powers of prime ideals in a local ring cannot have finite projective dimension, unless the ring in question is a domain. We make use of this fact in the appendix and consider the reflexivity of tensor products of prime ideals over hypersurface rings.
(Joint work with O. Celikbas and H. Matsui)
In this paper, we consider a depth inequality of Auslander which holds for finitely generated Tor-rigid modules over commutative Noetherian local rings. We raise the question of whether such a depth inequality can be extended for n-Tor-rigid modules, and obtain an affirmative answer for 2-Tor-rigid modules that are generically free. Furthermore, in the appendix, we use Dao's eta function and determine new classes of Tor-rigid modules over hypersurfaces that are quotient of unramified regular local rings.
(Joint work with O. Celikbas, H. Matsui, and A. Sadeghi)
In this paper we study a long-standing conjecture of Huneke and Wiegand which is concerned with the torsion submodule of certain tensor products of modules over one-dimensional local domains. We utilize Hochster's theta invariant and show that the conjecture is true for two periodic modules. We also make use of a result of Orlov and formulate a new condition which, if true over hypersurface rings, forces the conjecture of Huneke and Wiegand to be true over complete intersection rings of arbitrary codimension. Along the way we investigate the interaction between the vanishing of Tate (co)homology and torsion in tensor products of modules, and obtain new results that are of independent interest.
INSTRUCTOR
Fall 2022
ASSISTANT
Spring 2019
INSTRUCTOR
Fall 2019
ASSISTANT
Fall 2016
INSTRUCTOR
Fall 2018
Spring 2020
SUPPLEMENTAL INSTRUCTION LEADER
Spring 2016
ASSISTANT
Fall 2020
ASSISTANT
Fall 2020
ASSISTANT
Spring 2017
ASSISTANT
Spring 2017
ASSISTANT
Fall 2020
Email: hle1@mix.wvu.edu
Phone: (304)-293-2011
Address:
West Virginia University
Armstrong Hall, 308C
Morgantown, West Virginia, 26505
USA