Bibliography
Employment
Associate Professor, Department of Mathematics and Statistics, University of Nebraska at Kearney, 2018--present
Assistant Professor, Department of Mathematics and Statistics, University of Nebraska at Kearney, 2014--2018
Postdoctoral Associate, School of Mathematics, University of Minnesota-Twin Cities, 2013--2014
Education
Ph.D. in Mathematics, University of Minnesota-Twin Cities
B.S. in Mathematics and Applied Mathematics, University of Science and Technology of China
Teaching
Current Teaching (Fall 2019)
MATH 102-02 College Algebra
MATH 310-01 College Geometry
MATH 413-01 Discrete Mathematics
Course materials and other useful resources are available on Canvas.
Office hours: 8:30--10:00 MWF, 8:30--9:20 TuTh
Courses Taught at UNK
- MATH 123 Applied Calculus I
- MATH 115 Calculus I with Analytic Geometry
- MATH 202 Calculus II with Analytic Geometry
- MATH 250 Foundations of Math
- MATH 260 Calculus III
- MATH 310 College Geometry
- MATH 350 Abstract Algebra
- MATH 365 Complex Analysis
- MATH 404 Theory of Numbers
- MATH 864 Geometry for Teachers
Courses Taught at University of Minnesota
- MATH 1272 Calculus II
- MATH 1372 CSE Calculus II
- MATH 2263 Multivariable Calculus
Research
My research interests include Discrete Mathematics and its connections with other fields (more specifically, Algebraic and Enumerative Combinatorics, Combinatorial Representation Theory, and Graph Theory).
I received my Ph.D. at the University of Minnesota under the supervision of Professor Victor Reiner. My Thesis is 0-Hecke algebra actions on flags, polynomials, and Stanley-Reisner rings.
I use mathematics software such as GAP, Magma, and Sage in my research.
I am the organizer for the annual UNK Undergraduate Research Mathematics Mini-Symposium. See the schedule of this year.
Recent Presentations:
- Integer Tillings and Domination Ratio, Combinatorics and Graph Theory Seminar, Anhui University, June 2019.
- Variations of the Catalan number from nonassociative binary operations, Combinatorics Seminar, University of Wisconsin, April 2019.
- Ordered set partitions and the 0-Hecke algebra, The 30th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC), Dartmouth College, July 2018.
- An improved upper bound for the bondage number of graphs on surfaces, Graph Theory and Combinatorial Network Theory Conference, Beijing Normal University, June 2018.
- Polynomial invariants of finite groups of sparse matrices, Public Talk, Beijing Normal University, June 2018.
- Critical groups for Hopf algebra modules, Great Plains Combinatorics Conference, Kansas State University, April 2018.
- 0-Hecke algebra actions on quotients of polynomial rings, Algebra Seminar at University of Science and Technology of China and Combinatorics Seminar at Shanghai Jiao Tong University, December 2017.
- Combinatorics of non-associative binary operations, Combinatorics Seminar at Anhui University, China, December 2017.
- Domination ratio of infinite circulant graphs, Graph Theory Seminar at University of Science and Technology of China and Jiangsu Normal University, China, December 2017.
- Nilpotent ideals of upper triangular matrices and Variations of the Catalan numbers, Algebraic Combinatorics and Mathematical Physics Seminar, University of Nebraska--Lincoln, October 2017.
- Nonassociativity of some binary operations, Combinatorics Seminar, University of California San Diego, June 2017.
- Nonassociativity of some binary operations, Midwest Combinatorics Conference, University of Minnesota, May 2017.
- Hecke algebras with independent parameters, AMS Spring Central Sectional Meeting, North Dakota State University, April 2016.
- Arithmetic without parentheses, Undergraduate Research Opportunities: Mathematics Mini-Symposium, UNK, March 2016.
- Modular Catalan numbers (joint work with N. Hein), Combinatorics Seminar, University of Kansas, September 2015.
- 0-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra, The 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC), Chicago, June 2014.
Recent Publications:
- D. Grinberg, J. Huang, and V Reiner, Critical groups for Hopf algebra modules, to appear in the Mathematical Proceedings of the Cambridge Philosophical Society.
- J. Huang, B. Rhoades, and T. Scrimshaw, Hall-Littlewood polynomials and a Hecke action on ordered set partitions, Proceedings of the American Mathematical Society 147 (2019), 1839--1850.
- J. Huang and B. Rhoades, Ordered set partitions and the 0-Hecke algebra, Algebraic Combinatorics 1 (2018), 47--80.
- J. Huang, M. Mickey, and J. Xu, The nonassociativity of the double minus operation, Journal of Integer Sequences 20 (2017), Article 17.10.3.
- J. Huang, A uniform generalization of some combinatorial Hopf algebras, Algebras and Representation Theory 20 (2017) 379--431.
- J. Huang, J. Lewis, and V Reiner, Absolute order in general linear groups, Journal of the London Mathematical Society 95 (2017) 223--247.
- N. Hein and J. Huang, Modular Catalan numbers, European Journal of Combinatorics 61 (2017) 197--218.
- J. Huang, A tableau approach to the representation theory of 0-Hecke algebras, Annals of Combinatorics 20 (2016) 831--868. (arXiv preprint)
- J. Huang, Hecke algebras with independent parameters, Journal of Algebraic Combinatorics 43 (2016) 521-551.
- J. Huang, 0-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra, Annals of Combinatorics 19 (2015) 293--323.
- J. Huang, 0-Hecke algebra actions on coinvariants and flags, Journal of Algebraic Combinatorics, 40 (2014) 245--278.
See also my Google Scholar profile and my ResearchGate profile.
Student Research:
I have mentored the following students through UNK's Undergraduate Research Fellows program:
- Chenli Huang, Fall 2016
- Madison Mickey, 2016--2017 (her presentation in the Undergraduate Research Mathematics Mini-Symposium)
- Jianbai Xu, 2016--2017 (his presentation in the Undergraduate Research Mathematics Mini-Symposium)
- Evan Olson, 2018--2019
Math Stories
The Twin Prime Hero
The largest Known Prime Number (As of January 2018)
Coloring the Plane
33 = x³ + y³ + z³
A Big Bang Theory Episode Inspired A Mathematical Discovery
New breakthroughs
The power of imagination
Rich tradition. Bright future.
Taking care of business
