Department of Mathematics

567 Lake Hall

Northeastern University

Boston, MA 02115

Email: v.nguyen@neu.edu

Office: 536 Nightingale Hall

Office Phone: 1-617-373-5232

Contact me
### About me

I am a Research Instructor (Postdoctoral
Teaching Associate) at the
Department of Mathematics of Northeastern University (Boston MA), working with Professors Alexander Martsinkovsky and Gordana Todorov.

I received my Ph.D. in Mathematics from Texas
A&M University (TAMU), under supervision of Professor Sarah
Witherspoon.

My non-math hobbies include cooking, hiking, coffee-shop hopping, travelling and reading. I love food and love to try/cook various cuisines. It is my favorite way to
expose to different cultures, people, and backgrounds; and it goes very
well with my travel interest.

**I am the faculty advisor for the
Northeastern MATH CLUB.** I’d love to share ideas for undergraduate Math club activities.

### Research Interests

- Homological algebra
- (finite dimensional) Hopf algebras
- Representation theory of finite dimensional algebras

### Education

- Ph.D., Mathematics, Texas A&M University, August 2014
- B.A., Mathematics, University of California, San Diego, June 2008
- B.S., Management Science, University of California, San Diego,
June 2008

### Awards

- 2015 AMS-Simons Travel Grant (2015-2017)
- Ethel Ashworth-Tsutsui Memorial
Award for Research (Nov.
2013)
- 2013 L. F. Guseman Prize in
Mathematics (April 2013)

### Research

I am interested in homological algebra, Hopf algebras, and
representation theory. In particular, I study various cohomology structures and their properties: finite generation of cohomology ring, Gerstenhaber structure of Hochschild cohomology, Tate and Tate-Hochschild cohomology rings of finite dimensional Hopf algebras and related algebraic objects, as well as some homological conjectures in representation theory.
Many important examples of Hopf algebras come up in different fields of mathematics. Understanding these properties will be applicable to such fields.

Recently, I am also interested in branching out of Hopf algebras into other fields, for examples, I would like to work more with Lie algebras, Gorenstein rings, Cohen-Macaulay rings, complete intersections, quivers, and cluster algebras. This chart briefly summarizes my research projects and interests.

*Publications and Preprints:*

*Classification of connected Hopf algebras of dimension $p^3$ I *, *joint with L. Wang and X. Wang*, J. Algebra, 424 (2015), pp. 473–505.
*Finite
generation of the cohomology of some skew group algebras*, *joint
with S. Witherspoon*, Algebra & Number Theory, 8 (2014), no. 7, pp. 1647-1657.
*Tate and Tate-Hochschild cohomology for finite dimensional Hopf algebras*, J. Pure Appl. Algebra, 217 (2013), no. 10, pp. 1967-1979.

*Primitive deformations of quantum p-groups*, *joint with L. Wang and X. Wang*, submitted (2015).
*Gerstenhaber brackets on Hochschild cohomology of twisted tensor products *, *joint with L. Grimley and S. Witherspoon*, submitted (2015).
*Tate-Hochschild
cohomology ring of a group algebra*, submitted (2013).
*Finite
generation of Tate cohomology of symmetric Hopf
algebras*, submitted (2013).

*Selected Talks and Posters:*

**Speaker**, *Complete classification of connected prime-cube dimensional Hopf algebras*, MAA General Contributed Paper Session on Algebra, Joint Mathematics Meetings, Seattle (January 5-10, 2016).
**Invited speaker**, *Recent work on various cohomology theories*, Algebra Seminar, University of Sherbrooke, Quebec, Canada (November 10-14, 2015).
**Invited speaker**, *Finite generation of cohomology rings*, Cohomology of Algebras and Deformation Theory, AMS Central Fall Sectional Meeting #1112, Loyola University, Chicago, Illinois (October 3-4, 2015).
**Invited speaker**, *On the Hochschild cohomology ring of twisted tensor products*, New Developments in Noncommutative Algebra, AMS Spring Western Section Meeting #1110, University of Nevada, Las Vegas, Nevada (April 18-19, 2015).
**Invited speaker**, *Finite generation of cohomology rings*, Southwestern Group Theory Day, University of Arizona, Tucson, Arizona (March 21, 2015).
**Invited speaker**, *Tate cohomology relation for finite dimensional Hopf algebras*, Representation Theory and Related Topics Seminar, Northeastern University, Boston (March 6, 2015).
**Speaker**, *Informal discussion on the universal enveloping algebra of a Lie algebra*, Commutative Algebra Reading Seminar, Northeastern University, Boston (February 26, 2015).
**Invited speaker**, *The negative side of cohomology for Hopf algebras*, Infinite-dimensional Algebra Seminar, MIT-Massachusetts Institute of Technology, Cambridge (February 20, 2015).
**Speaker**, *Finite generation of Tate cohomology for symmetric Hopf algebras*, XXVIth Meeting on Representation Theory of Algebras, University of Sherbrooke, Sherbrooke, Canada (September 5-6, 2014).
**Invited speaker**, * Finite generation of cohomology
rings*, Maurice Auslander
Distinguished Lectures and International Conference, Woods Hole
Oceanographic Institute, Quissett Campus, Woods Hole, Massachusetts
(May 1-6, 2014).
**Invited speaker**, * On complete resolutions over
two-sided Noetherian Gorenstein rings*, KUMUNUjr, University of
Nebraska-Lincoln, Nebraska (April 26-27, 2014).
**Invited speaker**, * Tate-Hochschild cohomology*,
Noncommutative Algebra,
Deformations, and Hochschild Cohomology, AMS Spring Central
Sectional Meeting, Texas Tech University, Lubbock,
Texas (April 11-13, 2014).
**Colloquium speaker**, * Tate cohomology relation for
finite dimensional Hopf algebras*, Colloquium Talk,
Wake Forest University, Winston-Salem, North Carolina (February 6-8,
2014).
**Poster presenter**, *Finite generation behaves
differently in
negative cohomology*, 5th Southwest Local Algebra Meeting (SLAM),
Texas A&M University, College Station (March 1-2, 2014).
**---**,AWM Workshop Poster Presentations and
Reception, Joint
Mathematics Meetings, Baltimore, Maryland (January 15-18, 2014).
**Speaker**, * The negative side of cohomology for
symmetric Hopf algebras*, Algebra and Algebraic Geometry Seminar,
University of Washington, Seattle (November 17-20, 2013).
**---**, Commutative Algebra Seminar, University of
Nebraska-Lincoln, Nebraska
(November 4-7, 2013).
**---**, Algebra Seminar, University of Kansas, Lawrence
(Oct. 30 -
Nov. 2, 2013).
**---**, Algebra and Combinatorics Seminar, Texas
A&M University (October 18, 2013).
**Invited speaker**, *Finite generation behaves
differently in
negative cohomology*, Recent Developments in Noncommutative Algebra,
AMS Fall Eastern Sectional Meeting, Temple University, Philadelphia
(October 12-13, 2013).
**Poster presenter**, *Tate cohomology relation for
finite
dimensional Hopf algebras with an application to group algebra*, IMA
Career Options for Women in Mathematical Sciences, University of
Minneapolis (March 3-5, 2013).
**Invited speaker**, *Tate cohomology relation for
finite
dimensional Hopf algebras with an application to group algebras*,
Workshop in Representation Theory, Homological Algebra, and Free
Resolutions, MSRI, Berkeley (February 11-17, 2013).
**Speaker**, *Cohomology of Hopf algebras*,
Introductory talk,
MSRI, Berkeley (January 23, 2013).
**Invited speaker**, *Tate cohomology for finite
dimensional
Hopf algebras*, Algebra Seminar, University of Texas at Arlington
(November 2, 2012).
**Speaker**, *Tate cohomology for finite dimensional
Hopf
algebras*, Algebra and Combinatorics Seminar, Texas A&M
University, College
Station (October 26, 2012).
**Poster presenter**, *Tate and Tate-Hochschild
cohomology for
finite dimensional Hopf algebras*, Workshop in Cohomology and
Support in Representation Theory and Related Topics, University of
Washington,
Seattle (August 1-5, 2012).