Dr. Jia Huang

Associate Professor

Office: WRNH 2146 | 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 (Spring 2020)

MATH 250 Foundations of Math

MATH 260 Calculus III

Course materials and other useful resources are available on Canvas.

Office hours: 9:15--10:45AM M--F

Courses Taught at UNK

MATH 102 College Algebra
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 413 Discrete Mathematics
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, 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 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
Gamaliel Montero Alcaraz, 2019--2020

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