College of Arts and Sciences

University of Nebraska-Linocln

Department of MathematicsUniversity of Nebraska-Lincoln Email: klee24@unl.edu |

- Ph.D. in Mathematics, University of Michigan - Ann Arbor (Advisor : Robert Lazarsfeld)
- B.S. in Mathematics, Seoul National University

- 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

- Algebraic Geometry, Algebraic Combinatorics, Cluster Algebras, Commutative algebras, Non-commutative algebras, Representation Theory, Mathematical Physics

- NSA grant, 2014-2017
- University Research Grant, 2013-2014
- NSF grant DMS 0901367, 2009-2013

- 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.

- (with Li Li and Matthew R. Mills) A Dyck path formula for certain elements of upper cluster algebras, arXiv:1409.8177.
- (with Ilke Canakci and Ralf Schiffler) On cluster algebras from unpunctured surfaces with one marked point, arXiv:1407.5060.
- (with 8 co-authors) A new combinatorial formula for cluster monomials of equioriented type A quivers, preprint.
- (with Li Li, Dylan Rupel and Andrei Zelevinsky) The existence of greedy bases in rank 2 quantum cluster algebras, arXiv:1405.2414.
- (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 Ralf Schiffler) Positivity for cluster algebras, Ann. of Math., to appear.
- (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.

- 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