CV

• CV (in entirety)

Education

• PhD in Mathematics, University of Texas at Arlington, 2013

• Masters in Mathematics, University of Texas at Arlington, 2008

• Bachelors of Science with Honors in Psychology, University of Texas at Arlington, 2005

• Bachelors of Arts in Philosophy, University of Texas at Arlington, 2005

Employment

• Tennessee Tech University

Associate Professor, Aug 2018 - present

Assistant Professor, Aug. 2013 - July 2018

• University of Texas at Arlington, 2007 - 2013

Graduate Teaching Assistant

Publications (accepted/submitted)

• On Hopf Algebras (inc. Manin's universal quantum groups)

1. Quantum-symmetric equivalence is a graded Morita invariant (with H. Huang, V. C. Nguyen, K. Vashaw, and X. Wang), to appear in Proc. of AMS, (arXiv)

2. Twisting Manin's universal quantum groups and comodule algebras (with H. Huang, V. C. Nguyen, C. Ure, K. Vashaw, and X. Wang), Adv. in Math. Vol. 445 (2024), https://doi.org/10.1016/j.aim.2024.109651. (arXiv)

3. A cogroupoid associated to preregular forms (with H. Huang, V. C. Nguyen, C. Ure, K. Vashaw, and X. Wang), to appear in the J. Noncommutative Geom. (arXiv) 

4. Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation (with H. Huang, V. C. Nguyen, C. Ure, K. Vashaw, and X. Wang), Transf. Groups (2022), doi: 10.1007/s00031-022-09779-9. (arXiv, journal article) 

• On Regular Algebras & Noncommutative Projective Geometry

5. A Primer on Twists in the Noncommutative Realm with a Focus on Algebra, Representation Theory, and Geometry  (with P. Ocal and K. Ueyama), Contemporary Math. 801 (2024), 179-194. (arXiv)

6. Reflection Groups and Rigidity of Poisson Algebras (with Jason Gaddis & Xingting Wang), Algebr Represent Theor 26, 329-358 (2023). (arXiv, journal article)

7. A notion of rank for noncommutative quadratic forms on four generators (with Leah Frauendienst & Jessica Cain), J. Alg and its Apps. 21(10), (2022). (arXiv)

8. Associating geometry to the Lie Superalgebra sl(1|1) & to the color Lie algebra sl_2^c (with S. Sierra, S. Spenko, M. Vancliff, & E. Wiesner), Proc. Amer. Math. Soc. 147(10), (2019), 4135-4146. (arXiv, journal article)

9. Graded Clifford algebras and Graded Skew Clifford Algebras & their role in the classification of Artin-Schelter Regular Algebras, Adv. in App. Cliff. Algs 27 # 3 (2017), 2856-2871. (arXiv, journal article)

10. Point modules over regular graded skew Clifford algebras (with M. Vancliff), J. Algebra 420 (2014), 54-64. (arXiv, journal article)

11. Generalizing the notion of rank to noncommutative quadratic forms (with M. Vancliff) in "Noncommutative Birational Geometry, Representations and Combinatorics,'' Eds. A. Berenstein and V. Retakh, Contemporary Math. 592 (2013), 241-250. (arXiv, journal article)

12. Point Modules over regular graded skew Clifford algebras. (Dissertation)

Talks

1. 25-min invited talk at the AWM Research Symposium (May 2025)

2. Algebra Colloquium talk (April 2025)

3. 25-min invited talk at AMS-JMM (Jan 2025)

4. 25-min invited talk at QuaSy-Con II (May 2024, title: ``Manin's universal quantum groups under 2-cocycle twists" at the University of Notre Dame)

5. 25-min invited talk at the JMM (Jan. 2024 , title: ``AS-regular algebras of dimension four and twisted homogeneous coordinate rings of quadrics" in San Francisco)

6. 25-min invited talk at the CMS Summer Meeting (June 2023, title: 2-cocycle twists, twists of Manin's universal groups and applications" at the University of Ottawa)

7. 25-min invited talk at Seattle Noncommutative Algebra Days (Mar. 2023, title: ``2-cocycle twists and certain homological invariants" at the University of Washington, Seattle)

8. 25-min invited talk at Workshop on Noncommutative Geometry and Noncommutative Invariant Theory  (Sept. 2022, title: ``Can twists of algebras be realized as 2-cocycle twists of Hopf algebras" at Banff International Research Station, Banff, Canada)

9. 25-min invited talk at Conference on "Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry" in honor of S. Paul Smith's 65th Birthday (in June 2022, title: ``Twists of algebras and twists of certain Hopf algebras in Seattle)

10. AMS 25-min invited talk in a special session (Mar. 2022, title: ``Zhang twists of algebras and twists of Hopf algebras" in Charlottesville (canceled due to COVID concerns))

11. AMS 20-min invited talk in a special session on ``Noncommutative algebra and noncommutative invariant theory" ( Jan. 2022, title: ``Zhang twists of algebras and twists of Hopf algebras" in Seattle (canceled due to COVID concerns))

12. TTU Graduate Student Seminar  (Apr. 2021, title: ``Deformations and Hochschild (co)homology")

13. AMS 20-min invited talk in a special session on ``Homological aspects of Quantum Symmetries and related topics" ( Jan. 2021, title: ``Reflection groups of the homogenized $n^{th}$ Weyl Poisson algebra") virtually (formerly in Washington D.C.)

14. TTU Graduate Student Seminar  (Oct. 2020, title: ``An introduction to Poisson algebras.")

15. AMS 20-min invited talk in a special session on  ``Connections between Noncommutative Algebra and Algebraic Geometry"

16. AMS 20-min invited talk in a special session on  ``Noncommutative Ring Theory and Noncommutative Algebra" in Brunswick, Maine

17. 5-minute talk at the Fields Institute on ``Graded Skew Clifford Algebras"  (July 2015, in Toronto, Canada)

18. AMS 20-min invited talk in a special session on  ``New developments in Noncommutative Algebra" (Apr. 2015, in Las Vegas, Nevada)

19. AMS 20-min invited talk in a special session on  ``Noncommutative Algebra, Deformations, and Hochschild Cohomology" (Sept. 2017, in Lubbock, Texas)

20. Poster presented at the MSRI workshop on ``Connections for Women: Noncommutative Algebraic Geometry and Representation Theory" (Jan. 2013, in Berkeley, California)

21. AMS 10-min contributed session talk in an AMS session on ``Noncommutative Algebra" (Jan. 2013 in San Diego, California).

22. 15-min talk at the 92nd Annual Meeting of the Texas Section of the MAA in Dallas, Texas, Apr. 2012

23. Poster presented at the Southwest Local Algebra Meeting in Lubbock, Texas, Mar. 2012

24. AMS 20-min invited talk in a special session on ``Noncommutative Birational Geometry and Cluster Algebras (Jan. 2012 in Boston, Massachusetts)

25. AMS 20-min invited talk in a special session on ``Noncommutative Algebra" (Sept. 2011 in Winston-Salem, N. Carolina)

26. Poster presented at UT Metroplex Day (Jan. 2012, in Dallas, Texas)

27. 20-min talk at ACES NSF GK-12 MAVS Program Special Session (Mar. 2011 in Arlington, Texas)

28. AMS 10-min contributed session talk in an AMS session on ``Rings and Algebras" (Jan 2011 in New Orleans, Louisiana)

29. Poster presented at New Trends in Noncommutative Algebra: A conference in honor of Ken Goodearl's 65th birthday (Aug. 2010 in Seattle, Washington)

30. Poster presented at the Southwest Local Algebra Meeting Mar. 2010 in Arlington, Texas

31. 30-min talk at the Graduate Student Seminar (Nov. 2010 in Arlington, Texas)

32. A 60-min talk at the Conference for the Advancement of Mathematics Teaching (title: ``What's all the fuss about the commutative property?" in Jul. 2011 in Grapevine, Texas.

33. A 75-min talk at the NSF GK-12 Annual Conference (title: ``Facilitating the Integration of Research-Level Mathematics into the Classroom" in Mar. 2011). Joint Presentation with James Epperson, Minerva Cordero,Theresa Jorgensen, Kelli Randell, Kimberly Helixon, Angela Brown in Washington, D.C.

34. A 60-min talk at the Conference for the Advancement of Mathematics Teaching in San Antonio, Texas (title: ``Non-commutativity! C'mon, all variables commute!" in Jul. 2010)

35. A 10-min talk at the NSF Regional GK-12 Conference in Fort-Worth, Texas (title: ``Integrating Noncommutative Algebra in the High-School Curriculum" in  Nov. 2009