My current interest are:
Algebra, Geometry and Combinatorics of points in the plane or in higher dimensional spaces, which include: the ideal defining the diagonal locus in (C^2)^n and the related combinatorial object such as q,t-Catalan numbers; Hilbert scheme of points on a Deligne-Mumford stack.
Algebra, Geometry and Combinatorics of Schubert varieties.
Algebro-geometrical, topological and combinatorial properties of the
objects related to arrangement of subvarieties, including hyperplane arrangement and subspace arrangement; wonderful compactifications of arrangements of subvarieties;the relation of arrangement with the study of singularities.
The theory of Lawson homology and morphic cohomology.
Kazhdan-Lusztig polynomials and drift configurations ,
(with Alexander Yong), arXiv:1006.1887
Some degenerations of Kazhdan-Lusztig ideals and multiplicities of Schubert varieties,
(with Alexander Yong), arXiv:1001.3437
$q,t$-Catalan numbers and generators for the radical ideal defining the diagonal locus of $(\C^2)^n$,
(with Kyungyong Lee), arXiv:0909.1612
Notes on a minimal set of generators for the radical ideal defining the diagonal locus of $(\C^2)^n$,
(with Kyungyong Lee), arXiv:0901.1176
Lawson homology, morphic cohomology and Chow motives,
(with Wenchuan Hu), arXiv:0711.0383, Mathematische Nachrichten, to appear.
Higher cohomology of the pluricanonical bundle is not deformation
(with Ning Hao), arXiv:AG/0612006.
Chow Motive of Fulton-MacPherson configuration spaces and wonderful compactifications,
arXiv:AG/0611459, Michigan Math. J. 58 (2009), no. 2, 445--478.
Wonderful compactifications of arrangements of subvarieties,
arXiv:AG/0611412, Michigan Math. J. 58 (2009), no. 2, 415--443.
The Lawson homology and Deligne-Beilinson cohomology for Fulton-MacPherson configuration spaces,
(with Wenchuan Hu), arXiv:AG/0609824,
Algebraic & Geometric Topology 9 (2009) 455--471.
Chow Motive of Fulton-MacPherson configuration spaces and
The list of Catalan numbers and q-Catalan numbers.
The table of higher q,t-Catalan numbers.
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