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 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.
Recent Conferences
Spring Western Sectional Meeting of the AMS, University of Colorado, Boulder, CO, April 13 - 14, 2013.
Maurice Auslander Distinguished Lectures and International Conference, Woods Hole, MA, April 18 - 23, 2013.
Algebra, Combinatorics and Representation Theory: in memory of Andrei Zelevinsky, Boston, MA, April 24 - 28, 2013.
Cluster Algebras and Related Topics, Oberwolfach, Germany, December 2013.
Hall and cluster algebras, CRM, Montreal, May 2014.
Cluster Algebras and Representation Theory, Seoul, Nov 2014.
Cluster Algebras in Combinatorics and Topology, Seoul, Dec 2014
Strings, Quivers and Cluster Algebras in Mathematical Physics, Seoul, Dec 2014
Fall Western Section Meeting of the AMS, University of California, Riverside, CA, November 4 - 5, 2017.
CombinaTexas 2018, Texas A&M University, College Station, TX, February 10-11, 2018.