Dr. Jia Huang

Associate Professor

Office: DSCH 377 | Phone: (308) 865-8494 | Email: huangj2@unk.edu

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 2022)

MATH 202 Calculus II with Analytic Geometry, MATH 413 Discrete Mathematics
Course materials and other useful resources are available on Canvas.

Courses Taught at UNK

MATH 102 College Algebra, MATH 103 Plane Trigonometry, 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 400 History of Mathematics, MATH 404 Theory of Numbers, MATH 413 Discrete Mathematics, MATH 440 Linear Algebra, MATH 864 Geometry for Teachers (new course development)

Courses Taught at the 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: 2017, 2018, 2019, 2020 (canceled due to COVID), 2022

Recent Presentations:

Norton algebras of some distance regular graphs, Graph Theory, Algebraic Combinatorics and Mathematical Physics, Centre de recherches mathématiques (CRM), Université de Montréal, August 2022.
The Norton algebras of some distance regular graphs, Discrete Mathematics Seminar, Texas State University, November 2020.
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:

N. Hein and J. Huang, Variations of the Catalan numbers from some nonassociative binary operations, Discrete Mathematics 345 (2022), Paper No. 112711, 18 pp.
J. Huang, Norton algebras of the Hamming Graphs via linear characters, Electronic Journal of Cominatorics 28 (2021), #P2.30, 36 pp.
J. Huang, Nonassociativity of the Norton algebras of some distance regular graphs, Electronic Journal of Cominatorics 27 (2020), #P4.27, 22pp.
J. Huang, Hecke algebras of simply-laced type with independent parameters, Algebraic Combinatorics 3 (2020), no.~3, 667--691.
J. Huang, Compositions with restricted parts, Discrete Mathematics 343 (2020), Paper No. 111875, 9 pp.
D. Grinberg, J. Huang, and V Reiner, Critical groups for Hopf algebra modules, Mathematical Proceedings of the Cambridge Philosophical Society 168 (2020), 473--503.
J. Huang, Domination ratio of integer distance digraphs, Discrete Applied Mathematics 262 (2019), 104–115.
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 J. Shen, New upper bounds for the bondage number of a graph in terms of its maximum degree and Euler characteristic, Ars Combinatoria 140 (2018) 373--387.
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:

Gamaliel Montero Alcaraz, 2019--2020
Evan Olson, 2018--2019 (currently a graduate student at University of Kansas)
Jianbai Xu, 2016--2017 (his presentation, his master thesis later at University of Windsor, and his LinkedIn profile)
Madison Mickey, 2016--2017 (her presentation in the Undergraduate Research Mathematics Mini-Symposium)
Chenli Huang, Fall 2016