I am a Postdoc under Chelsea Walton in the Mathematics Department at Rice University. I completed my Ph. D. in April, 2020 at the University of Waterloo and my advisor is Jason Bell .

# Hongdi Huang

My research interests lie in representation theory and invariant theory of noncommutative algebras;
quantum symmetries including quantum groups, (weak) Hopf algebras and Poisson algebras and deformation quantization.

A video of my talk at BIRS workshop "Noncommutative Geometry and Noncommutative Invariant Theory" in September, 2022 on "Weighted Poisson algebras in dimension three" is available
here.

## Preprints

- (with T. Tang,
X. Wang and
J. J. Zhang
Valuation method for Nambu-Possion algebras, submitted,
arXiv:5269878/preview.
- (with K. Vashaw,
Group actions on monoidal triangulated categories and Balmer spectra,
arXiv:2209.11621.
- (with T. Tang,
X. Wang and
J. J. Zhang Poisson valuations, arXiv:2309.05511.
- (with T. Tang,
X. Wang and
J.J. Zhang) Weighted Poisson polynomial rings in dimension three, arXiv:2309.00714.
- (with V. Nguyen,
C. Ure,
K. Vashaw,
P. Veerapen
and X. Wang)
Twisting of Manin's universal quantum groups and comodule algebras,
arXiv:2209.11621.
- (with
F. Calderon ,
R. Won,
and E. Wicks)
Symmetries captured by actions of weak Hopf algebras,
arXiv:2209.11903.

## Publications/Accepted

- (with T. Tang,
X. Wang) A survey on Zariski cancellation problems for noncommutative and Poisson algebras, to appear in MS in Contemporary Mathematics,
arXiv:2304.05914.
- (with V. Nguyen,
C. Ure,
K. Vashaw,
P. Veerapen
and X. Wang)
A cogroupoid associated to preregular forms, to appear in J. Noncommutative Geom.
arxiv:2112.09098.
- (with V. Nguyen,
C. Ure,
K. Vashaw,
P. Veerapen
and X. Wang)
Twisting of graded quantum groups and solutions to the quantum Yang-Baxter equation, to appear in Transform. Groups,
arxiv:2109.11585.
- (with C. Walton,
R. Won
and E. Wicks) Universal quantum semigroupoids,
J. Pure Appl. Algebra 227 (2023), no. 2, 107193.
Journal.
- (with J. Bell, M. Hamidizadeh and H. Venegas)
Noncommutative analogues of a cancellation theorem of Abhyankar, Eakin and Heinzer, Beitr Algebra Geom (2020).
Journal.
- Hopf Ore Extensions. Algebr. Represent. Theory 23 (2020), no. 4, 1477–1486.
Journal
- (with Y. Li and G. Tang) On ∗-clean non-commutative group rings. J. Algebra Appl. 15 (2016), no. 8, 1650150, 17 pp.
Journal
- (with Y. Li and Y. Yuan) On ∗-clean group rings II. Comm. Algebra 44 (2016), no. 7, 3171–3181.
Journal
- (with Y. Li) On B(5,18) groups. Comm. Algebra 44 (2016), no. 2, 568–590.
Journal
- (with Y. Li) On B(4,14) non-2-groups. J. Algebra Appl. 14 (2015), no. 8, 1550118, 14 pp.
Journal

## Past Conference Talks

- Canadian Discrete and Algorithmic Mathematics, CanaDAM 2023, Special Session on many perspectives on Hopf algebras in
combinatorics, Winnpeg, MB, Canada, June 7, 2023.
- Summer Meeting of the CMS, Special Session on Noncommutative Algebra and Noncommutative Geometry, Ottowa, ON, Canada, June 4, 2023.
- Spring Western Sectional Meeting of the AMS, Special Session on Artin–Schelter Regular Algebras and Related Topics, Fresno, CA, May 6, 2023.
- Spring Central Sectional Meeting of the AMS, Special Session on Interactions Between Noncommutative Ring Theory and Algebraic Geometry, Cincinnati, OH, April 15, 2023.
- Seattle Noncommutative Algebra Day at University of Washington, Seattle, WA, March 17-18, 2023.
- AMS Special Session on Quantum groups, Hopf Algebras and Applications, in honor of Professor Earl J. Taft, at University of Utah, Salt Lake City, UT, October 2022.
- BIRS Workshop on Noncommutative Geometry and Noncommutative Invariant Theory, Banff, A.
B., Canada, September 2022.
- Recent Advances and New Directions in the Interplay of Noncommutative Algebra and Geometry, A Conference in Honor of S. Paul Smith on the occasion of his 65th Birthday, University of Washington, Seattle, WA,
June 2022.
- The 4th Canada-Mexico-USA Conference in Representation Theory at Noncommutative Algebra, and Categorification at Northeastern University, Boston, MA, June 2022.
- Spring Sectional Meeting of the AMS, Special Session on Hopf Algebras, Tensor Categories, and Related Homological Methods,
March 2021, online.
- AMS--MAA Joint Mathematics Meetings, Special Session on Interactions Between Noncommutative Algebra and Noncommutative Algebraic Geometry,
January 2021, online.
- The Joint International Meeting of CMS-AMS at Fudan University, Shanghai, China,
June 2018.
- Recent developments in noncommutative algebra and related areas at University of Washington, Seattle,
March 2018.
- International Conference on Groups, Rings and Group Rings at Brock University, ON, Canada,
July 2014.