Department of Mathematics

(567 Lake Hall)

Northeastern University

Boston, MA 02115

Email: v.nguyen@northeastern.edu

Office: 536 Nightingale Hall

Office Phone: 1-617-373-5232

Contact me
### About me

I am a Zelevinsky Research Instructor (formerly Postdoctoral
Teaching Associate) at the
Department of Mathematics of Northeastern University (Boston MA), working with Professors Alexander Martsinkovsky and Gordana Todorov. I am finishing my postdoc at Northeastern and currently on this year’s job market.

I received my Ph.D. in Mathematics from Texas
A&M University in August 2014. My thesis advisor is 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 and commutative algebra.
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 looking at other (broader) objects, for examples, I would like to work more with questions related to artin algebras, Lie algebras, Gorenstein rings, quivers, preprojective algebras, and cluster algebras. This chart briefly summarizes my research projects and interests.

*Publications and Preprints:*

*Gerstenhaber brackets on Hochschild cohomology of twisted tensor products*, *joint with L. Grimley and S. Witherspoon*, to appear in J. Noncommutative Geometry.
*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).
*Tate-Hochschild
cohomology ring of a group algebra*, submitted (2013).
*Finite
generation of Tate cohomology of symmetric Hopf
algebras*, submitted (2013).
*Hopf-actions on Lie algebras*, joint with A. Martsinkovsky, in preparation.
*Pointed $p^3$-dimensional Hopf algebras in positive characteristic*, joint with X. Wang, in preparation.
*Find a determiner of a map in hereditary algebra*, joint with Y. Ji, G. Todorov, and S. Zhu, in preparation.

*Selected Talks and Posters:*

**Invited speaker**, *TBD*, New Developments in Noncommutative Algebra and Representation Theory, Joint Mathematics Meetings, Atlanta (Jan 7, 2017).
**Invited speaker**, *On classification of quantum $p$-groups via primitive deformations*.
**---**, Noncommutative Algebras and Their Representations, AMS Fall Central Sectional Meeting #1123, University of St. Thomas, Minneapolis (Oct 29-30,2016).
**---**, Quantum Algebra, AMS Fall Western Sectional Meeting #1122, University of Denver, Denver (Oct 8-9,2016).
**Speaker**, *On the Gerstenhaber structure of twisted tensor products*, 17th International Conference on Rep. of Algebras (ICRA), Syracuse University (Aug 9-19, 2016).
**Speaker**, *Complete classification of connected prime-cube dimensional Hopf algebras*, MAA General Contributed Paper Session on Algebra, Joint Mathematics Meetings, Seattle (Jan 5-10, 2016).
**Invited speaker**, *Recent work on various cohomology theories*, Algebra Seminar, University of Sherbrooke, Quebec, Canada (Nov 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 (Oct 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 (Feb 26, 2015).
**Invited speaker**, *The negative side of cohomology for Hopf algebras*, Infinite-dimensional Algebra Seminar, MIT-Massachusetts Institute of Technology, Cambridge (Feb 20, 2015).
**Speaker**, *Finite generation of Tate cohomology for symmetric Hopf algebras*, XXVIth Meeting on Representation Theory of Algebras, University of Sherbrooke, Sherbrooke, Canada (Sept 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 (Feb 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 (Jan 15-18, 2014).
**Speaker**, * The negative side of cohomology for
symmetric Hopf algebras*, Algebra and Algebraic Geometry Seminar,
University of Washington, Seattle (Nov 17-20, 2013).
**---**, Commutative Algebra Seminar, University of
Nebraska-Lincoln, Nebraska
(Nov 4-7, 2013).
**---**, Algebra Seminar, University of Kansas, Lawrence
(Oct 30 -
Nov 2, 2013).
**---**, Algebra and Combinatorics Seminar, Texas
A&M University (Oct 18, 2013).
**Invited speaker**, *Finite generation behaves
differently in
negative cohomology*, Recent Developments in Noncommutative Algebra,
AMS Fall Eastern Sectional Meeting, Temple University, Philadelphia
(Oct 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 (Feb 11-17, 2013).
**Speaker**, *Cohomology of Hopf algebras*,
Introductory talk,
MSRI, Berkeley (Jan 23, 2013).
**Invited speaker**, *Tate cohomology for finite
dimensional
Hopf algebras*, Algebra Seminar, University of Texas at Arlington
(Nov 2, 2012).
**Speaker**, *Tate cohomology for finite dimensional
Hopf
algebras*, Algebra and Combinatorics Seminar, Texas A&M
University, College
Station (Oct 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 (Aug 1-5, 2012).