Uyen (Enni) Le.

Welcome 👋

Commutative Algebraist

West Virginia University

from Phan Rang, Vietnam

About.

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.

Talks.

AMS Fall Southeastern Sectional Meeting - Special Section on Combinatorial Commutative Algebra

AMS Fall Southeastern Sectional Meeting - Special Section on Combinatorial Commutative Algebra

October 14-15, 2022

WVU Algebra Seminar

WVU Algebra Seminar

October 5, 2022

Izmir Mathematics Days IV

Izmir Mathematics Days IV

June 15-17, 2022 (30-min talk)

Graduate Student Conference in Algebra, Geometry, and Topology

Graduate Student Conference in Algebra, Geometry, and Topology

May 20-22, 2022 (20-min talk)

Workshop in Commutative Algebra (Hanoi, Vietnam)

Workshop in Commutative Algebra (Hanoi, Vietnam)

May 6-8, 2021 (30-min talk)

AMS Virtual Spring Western Sectional Spring Meeting

AMS Virtual Spring Western Sectional Spring Meeting

May 1-2, 2021 (20-min talk)

Papers.

On the depth and reflexivity of tensor products

(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.

An extension of a depth inequality of Auslander

(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.

Remarks on a conjecture of Huneke and Wiegand and the vanishing of (co)homology

(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.

Teaching.

Math 153 (part 1 of 2-semester sequence of Calculus I)

INSTRUCTOR
Fall 2022

Math 154 (part 2 of 2-semester sequence of Calculus I)

ASSISTANT
Spring 2019

Math 155 (Calculus I - general)

INSTRUCTOR
Fall 2019

Math 155E (Calculus I - engineering)

ASSISTANT
Fall 2016

Math 156 (Calculus II)

INSTRUCTOR
Fall 2018
Spring 2020

Math 251 (Calculus III)

SUPPLEMENTAL INSTRUCTION LEADER
Spring 2016

Math 341 (Part 1 of Undergrad Modern Algebra)

ASSISTANT
Fall 2020

Math 343 (Undergrad Linear Algebra)

ASSISTANT
Fall 2020

Math 441 (Applied Linear Algebra)

ASSISTANT
Spring 2017

Math 456 (Undergrad Complex Analysis)

ASSISTANT
Spring 2017

Math 541 (Part 1 of Grad Modern Algebra)

ASSISTANT
Fall 2020

Contact.

Email: hle1@mix.wvu.edu

Phone: (304)-293-2011

Address:

West Virginia University
Armstrong Hall, 308C
Morgantown, West Virginia, 26505
USA

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