Kyungyong Lee

Department of Mathematics

Purdue University

West Lafayette, IN 47907

e-mail : kyungl@purdue.edu, lee343@math.purdue.edu

About me

I am a Research Assistant Professor in the Department of Mathematics at Purdue University. I am partially supported by NSF grant DMS 0901367.

Research Interests

I am interested in Commutative algebra, Algebraic geometry, Algebraic Combinatorics and their interactions.

Publication

  • Robert Lazarsfeld, Kyungyong Lee, Local Syzygies of Multiplier ideals, Invent. Math. 167 (2007), no. 2, 409--418.

  • Kyungyong Lee, A short note on containment of cores, Comm. Algebra. 36 (2008), no. 10, 3890--3892.

  • Kyungyong Lee, Characteristic 2 approach to bivariate interpolation problems, Ricerche di Matematica. 57 (2008), no. 1, 81--93.

  • Robert Lazarsfeld, Kyungyong Lee and Karen E. Smith, Syzygies of multiplier ideals on singular varieties, Mich. Math. Journal, volume 57 in Honor of Mel Hochster, 511--522.

  • Kyungyong Lee, The degrees of plane curves with prescribed log canonical threshold, J. Algebra 322 (2009), 4205--4218.

  • The singularities of the principal component of the Hilbert scheme of points, submitted.

    When a Hilbert scheme of points is reducible, the principal (radical) component is particularly interesting. However the equations for the component have been mysterious. Recently I discovered previously unknown elements in the defining ideals of interesting affine open subschemes of principal components. Surprisingly they are of very large degrees in the natural embeddings. This implies that the Hilbert scheme of n points in C^d is not Cohen-Macaulay for d>7 and n>8. This provides a counterexample to a conjecture of Haiman.

  • Kyungyong Lee and Li Li, Notes on a minimal set of generators for the radical ideal defining the diagonal locus of $(\C^2)^n$, arXiv:0901.1176.

    We develop several techniques for the study of the radical ideal I defining the diagonal locus of (C^2)^n. Using these techniques, we give combinatorial construction of generators for I of certain bi-degrees.

  • Kyungyong Lee and Li Li, $q,t$-Catalan numbers and generators for the radical ideal defining the diagonal locus of $(\C^2)^n$. arXiv:0909.1612.

    Let I be the ideal generated by alternating polynomials in two sets of $n$ variables. Haiman proved that the q,t-Catalan number is the Hilbert series of the graded vector space $M(=\bigoplus M_{d_1,d_2})$ spanned by a minimal set of generators for I. In this paper we give simple upper bounds on the dimesnions of $M_{d_1, d_2}$ in terms of partition numbers, and find all bi-degrees (d_1,d_2) such that $\dim M_{d_1, d_2}$ achieve the upper bounds. For such bi-degrees, we also find explicit bases for $M_{d_1, d_2}$. The main idea is to define and study a nontrivial linear map from M to a polynomial ring $\C[\rho_1, \rho_2,...]$.

    Teaching

    Math 265 Fall 2009

    Course Page : http://www.math.purdue.edu/academic/courses/MA26500/

    Last updated : 10/13/2009

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