Ph.D. in Mathematics, University of Michigan - Ann Arbor (Advisor : Robert Lazarsfeld)
B.S. in Mathematics, Seoul National University
Positions
Assistant Professor, 2016-present, University of Nebraska-Lincoln
KIAS Scholar, 2015-present, KIAS
Assistant Professor, 2011-2015, Wayne State University
Postdoctoral Fellow, 2010-2011, University of Connecticut
Research Assistant Professor, 2008-2010, Purdue University
Research Interests
Algebra, Combinatorics, Data Science, and Mathematical Physics
Funding
NSF grant DMS 1800207, 2018-2021
University of Nebraska Collaboration Planning Grant (one of five PI/co-PIs), 2018-2019
NSA grant, 2014-2017
University Research Grant, 2013-2014
NSF grant DMS 0901367, 2009-2013
Awards
AMS Centennial Fellowship, 2015-2016
First prize, Korea National Mathematics Contest for College Students, 1997 (one of two winners).
Silver medal at International Mathematical Olympiad, Canada 1995.
Bronze medal at International Mathematical Olympiad, Hong Kong 1994.
Publications/Preprints
(with Li Li, Matthew Mills, Ralf Schiffler, and Alexandra Seceleanu) Frieze varieties : A characterization of the finite-tame-wild trichotomy for acyclic quivers, arXiv:1803.08459.
(with Kyu-Hwan Lee) Rigid reflections and Kac-Moody algebras, arXiv:1803.05373.
(with Ralf Schiffler) Cluster algebras and Jones polynomials, arXiv:1710.08063.
(with Kyu-Hwan Lee) A correspondence between rigid modules over path algebras and simple curves on Riemann surfaces, arXiv:1703.09113.
(with Li Li and Nicholas A. Loehr) A Combinatorial Approach to the Symmetry of q,t-Catalan Numbers, to appear in SIDMA.
(with Seok-Jin Kang and Kyu-Hwan Lee) A combinatorial approach to root multiplicities of rank 2 hyperbolic Kac-Moody algebras, Comm. Algebra 45 (2017), no. 11, 4785--4800.
(with Li Li and Ba Nguyen) New combinatorial formulas for cluster monomials of type A quivers, Electron. J. Combin. 24 (2017), no. 2, Paper 2.42, 41 pp
(with Li Li, Dylan Rupel and Andrei Zelevinsky) The existence of greedy bases in rank 2 quantum cluster algebras, Adv. Math. 300 (2016), 360--389.
(with Ilke Canakci and Ralf Schiffler) On cluster algebras from unpunctured surfaces with one marked point, Proc. Amer. Math. Soc. Ser. B 2 (2015), 35--49.
(with Ralf Schiffler) Positivity for cluster algebras, Ann. of Math. (2) 182 (2015), no. 1, 73--125.
(with Li Li and Matthew R. Mills) A combinatorial formula for certain elements of upper cluster algebras, SIGMA Symmetry Integrability Geom. Methods Appl. 11 (2015), Paper 049, 24 pp.
(with Li Li, Dylan Rupel and Andrei Zelevinsky) Greedy bases in rank 2 quantum cluster algebras, PNAS, vol. 111, 9712–9716, doi: 10.1073/pnas.1313078111.
Every finite acyclic quiver is a full subquiver of a quiver mutation equivalent to a bipartite quiver, arXiv:1311.0711.
(with Li Li and Andrei Zelevinsky) Positivity and tameness in rank 2 cluster algebras, J. Alg. Comb. 40 (2014), 823--840.
(with Li Li and Nicholas A. Loehr) Combinatorics of certain higher $q,t$-Catalan polynomials: chains, joint symmetry, and the Garsia-Haiman formula, J. Alg. Comb. 39 (2014), 749--781.
(with Li Li) On natural maps from strata of quiver Grassmannians to ordinary Grassmannians, 199--214, Contemp. Math., 592, Amer. Math. Soc., Providence, RI, 2013.
(with Li Li and Andrei Zelevinsky) Greedy elements in rank 2 cluster algebras, arXiv:1208.2391, Selecta Mathematica (N.S.) 20 (2014), no. 1, 57--82.
(with Ralf Schiffler) Positivity for cluster algebras of rank 3, Publ. Res. Inst. Math. Sci. 49 (2013), 601--649.
Plane automorphisms given by polynomials of scattered degrees, arXiv:1204.5956.
(with Li Li and Nicholas A. Loehr) Limits of Modified Higher (q,t)-Catalan Numbers, Electron. J. Combin. 20 (2013).
(with Ralf Schiffler) Proof of a positivity conjecture of M. Kontsevich on noncommutative cluster variables, Compositio Math. 148 (2012), 1821--1832.
(with Ralf Schiffler) A combinatorial formula for rank 2 cluster variables, J. Alg. Comb. 37 (2013) 67--85.
On cluster variables of rank two acyclic cluster algebras, Annals of Combinatorics. 16 (2012), 305--317.
Strong sign-coherency of certain symmetric polynomials, with application to cluster algebras, arXiv:1008.2194
(with Li Li) (q,t)-Catalan numbers and generators for the radical ideal defining the diagonal locus of (C^2)^n, Electron. J. Combin. 18 (2011), Research Paper.
(with Li Li) On the diagonal ideal of (C^2)^n and q,t-Catalan numbers, DMTCS Proceedings, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 881--888.
The singularities of the principal component of the Hilbert scheme of points, J. Algebra. 324 (2010), no. 6, 1347--1363.
The degrees of plane curves with prescribed log canonical threshold, J. Algebra. 322 (2009), 4205--4218.
On the realization of line arrangements as multiplier ideals, Ph.D. thesis (2008), 84 pp. ISBN: 978-0549-81780-2.
(with Robert Lazarsfeld and Karen E. Smith) Syzygies of multiplier ideals on singular varieties, Mich. Math. Journal, volume 57 (2008), 511--522.
Characteristic 2 approach to bivariate interpolation problems, Ricerche di Matematica. 57 (2008), no. 1, 81--93.
A short note on containment of cores, Comm. Algebra 36 (2008), no. 10, 3890--3892.
(with Robert Lazarsfeld) Local Syzygies of Multiplier ideals, Invent. Math. 167 (2007), no. 2, 409--418.