Hongdi Huang

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 .

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

  1. (with T. Tang, X. Wang and J. J. Zhang Valuation method for Nambu-Possion algebras, submitted, arXiv:5269878/preview.

  2. (with K. Vashaw, Group actions on monoidal triangulated categories and Balmer spectra, arXiv:2209.11621.

  3. (with T. Tang, X. Wang and J. J. Zhang Poisson valuations, arXiv:2309.05511.

  4. (with T. Tang, X. Wang and J.J. Zhang) Weighted Poisson polynomial rings in dimension three, arXiv:2309.00714.

  5. (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.

  6. (with F. Calderon , R. Won, and E. Wicks) Symmetries captured by actions of weak Hopf algebras, arXiv:2209.11903.

Publications/Accepted

  1. (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.

  2. (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.

  3. (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.

  4. (with C. Walton, R. Won and E. Wicks) Universal quantum semigroupoids, J. Pure Appl. Algebra 227 (2023), no. 2, 107193. Journal.

  5. (with J. Bell, M. Hamidizadeh and H. Venegas) Noncommutative analogues of a cancellation theorem of Abhyankar, Eakin and Heinzer, Beitr Algebra Geom (2020). Journal.

  6. Hopf Ore Extensions. Algebr. Represent. Theory 23 (2020), no. 4, 1477–1486. Journal

  7. (with Y. Li and G. Tang) On ∗-clean non-commutative group rings. J. Algebra Appl. 15 (2016), no. 8, 1650150, 17 pp. Journal

  8. (with Y. Li and Y. Yuan) On ∗-clean group rings II. Comm. Algebra 44 (2016), no. 7, 3171–3181. Journal

  9. (with Y. Li) On B(5,18) groups. Comm. Algebra 44 (2016), no. 2, 568–590. Journal

  10. (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.

Past Seminar Talks

  • Algebra and Number Theory Seminar, Louisiana State University, LA, US, Nov. 2023.

  • Rocky Mountain Representation Theory Seminar, University of Colorado, CO, US, October 2023.

  • Algebra and Combinatorics Seminar at Texas A&M University, TX, US, March 2023.

  • Algebra Seminar at Sun Yat-Sen university, Zhuhai, Guangdong, China, September 2022, online.

  • Algebra Seminar at Hangzhou Normal University, Zhejiang, China, September 2022, online.

  • Long Feng Science Forum at CUHK-Shenzhen, Shenzhen, China, August 2022, online.

  • Hodge Seminar at the University of Edinburgh, Edinburgh, UK, December 2021, online.

  • Northeastern Representation Theory and Related Topics Seminar at Northeastern University, MA, November 2021, online.

  • Representation Theory seminar at University of California, Riverside, CA, November 2021, online.

  • Algebra Seminar at University of Illinois at Urbana-Champaign, IL, September 2019.

  • Algebra Seminar at Nanning Normal University, Guangxi, China, May 2015.

  • Algebra Seminar at Brock University, ON, Canada, March 2014.

    • Workshop Participation

  • The Physical Mathematics of Quantum Field Theory School, University of Massachusetts Amherst, Amherst, MA, July 17-21, 2023.

  • Quantum symmetries at the CRM, Symmetries: Algebras and Physics at the Centre of Researches Mathematics, University of Montreal, Montreal, QC, Canada, October 16-21, 2022.

  • SQuaRE grant, American Institute of Mathematics, (one week-long program focused collaborative research with Van Nguyen, Charlotte Ure, Kent Vashaw, Padmini Veerapen and Xingting Wang per year) San Jose, CA, 2021--2024.

    • Upcoming Conferences and Seminars

  • Co-organizing with Zheng Hua, Brent Pym, Xiaolan Yu, James Zhang, Poisson geometry and Artin-Schelter regular algebras, Banff International Research Station, October 2024 (expected).

  • Joint Math Meetings, Special Session on Homological Techniques in Noncommutative Algebra, January 3-6, 2024 (invited talk) (expected).

  • Fall Southeastern Sectional Meeting of the AMS, Special Session on New Directions in Noncommutative Algebras and Representation Theory, October 13-15, 2023 (invited talk) (expected).

  • The Rocky Mountain Representation Theory seminar at Florencia Orosz, October 2023, (invited talk) (expected).

    • Teaching

  • Instructor, Calculus II (Math 102), Rice University, Spring 2021, Fall 2021, Fall 2022, Fall 2023.

  • Instructor, Abstract Algebra II (Math 357), Rice University, Spring 2022, Spring 2023.

  • Instructor, Abstract Algebra I (Math 356), Rice University, Fall 2020, Fall 2023.

    • Seminar Services

  • 2021--2023, Colloquium committee at Math department of Rice University.

  • 2020--2023, Co-organizing AGNT Seminar at Math department of Rice University.

    • Contact