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Research Interests
My research interests are centered around the approximation theory,
computational harmonic analysis and discrete mathematics. Topics that
I worked on include
- Box splines and algebra
- Frame
theory
- Vector quantization
- Computer Aided Geometry
Design
- Compressed
sensing
Education
Ph.D.,
2003.7 Department of Applied Mathematics, Dalian University of
Technology.
Dissertation:
Multivariate Spline, Piecewise Algebraic Curve and Linear
DIOPHANTINE Equations.
B.A.
, 1998.7 Department of Applied Mathematics, Dalian University of
Technology .
1998.8,
Summer School, Nanking University, Differential Geometry
2001.8,
Summer School, Zhejiang University, Finite Element
Working Experience
2009.3- Associate Professor, Academy
of Mathematics and Systems Sciences, Chinese Academy of Sciences
2005.7-2009.3 Assistant Professor, Academy of
Mathematics and Systems Sciences, Chinese Academy of Sciences
2007.7-
2008.7, Research Fellow, TU Berlin,
Germany
2003.8- 2005.7
, Postdoc, Department of Computer Science, Tsinghua University.
2000.3-2000.6,
Research Assistant, Hong
Kong Baptist University.
Honour
1993
won third prize in the math competition for nationwide high school student
(before
undergraduate ).
1997
Attended nationwide “CHALLENGE CUP”(TIAO ZHAN BEI) science and
technology
competition which is the highest-level competition for college
student in China
and
won the first place of northeast area and the second prize of the nation.
1994-2000
DAQI scholarship, LIANXIANG scholarship, etc…..
1997,
the 117th place of the 10th Dalian
international marathon race.
(undergraduate and
graduate student)
Teaching
Computational Harmonic Analysis, Spring 2010, Chinese Academy of Sciences
Numerical Approximation, Autumn 2009, Chinese Academy of
Sciences
Advanced Numerical Approximation, Autumn, 2005, Chinese Academy
of Sciences;
Design
and analysis of algorithms, Spring,2004, Tsinghua University;
Design
and analysis of algorithms, Spring,2005, Tsinghua University;
Freshman
Seminar, TA, Autumn, 2003, Tsinghua University;
Freshman
Seminar, TA, Autumn,2004, Tsinghua University.
Grants
China
Postdoctoral Science Grant for 2004, PDE methods in Computer Graphics;
China
Natural Science Foundation for 2005-2007, multivariate splines and
counting lattice points in polytope.
China
Natural Science Foundation for 2009-2011, multivariate splines and some
problems in discrete geometry.
Selected Publications
Hierarchical
zonotopal spaces, with O. Holtz and A. Ron, To appear in Trans.
Amer. Math. Soc.
Adaptive
non-uniform B-spline dictionaries on a compact interval, With Laura
Rebollo-Neira, to appear in Signal Processing .
Subspace
modelling for structured noise suppression, with Laura
Rebollo-Neira, A. Plastino, to appear in Physica A.
Sagbi bases of Cox-Nagata
rings, with Bernd Sturmfels, to
appear in Journal of the European Mathematical Society.
Refinement equations
and spline functions, with A. Dubickas, Adv. Comp. Math.
32: 1-23, 2010.
Marginal Likelihood
Integrals for Mixtures of Independence Models, with Shaowei Lin and
Bernd Sturmfels, Journal of
Machine Learning Research, 10(Jul):1611--1631, 2009.
Multivariate
F-splines and fractional box splines, Journal of Fourier Analysis and Applications,
15:723-738, 2009.
Multivariate splines and
polytopes, submitted for publicatoin
A spline
interpretation of Eulerian numbers, With R. Wang, Y. Xu, submitted for
publication.
Application of multivariate splines to discrete mathematics,
submitted for publicatoin.
Discrete Schemes for
Gaussian Curvature and Their Convergence, with Guoliang Xu, Computers
and Mathematics with Applications, 2009.
An explicit formulation for two dimensional vector partition
functions, Contemporary Math : Integer points in polyhedra--Geometry,
Number Theory, Representation Theory, Algebra, Optimization, Statistics,
2008 PDF
Let
me tell you my favorite lattice-point problem, with MATTHIAS BECK,
BENJAMIN NILL, BRUCE REZNICK, CARLA SAVAGE and IVAN SOPRUNOV, Contemporary Math: Integer points in
polyhedra--Geometry, Number Theory, Representation Theory, Algebra,
Optimization, Statistics, 2008.
Analytic and algebraic properties of canal surfaces, Journal
of Computational and Applied Mathematics. 195(2006)(With Jiaguang Sun,
etc).PDF
Multi-dimensional
versions of a formula of Popoviciu, Science in China Series
A. , 2006, PDF
A
robust algorithm for finding the real intersection of three quadric
surfaces, Computer Aided Geometric Design, Vol 22, Issue 6, 1
(2005), 515-530. .(With Xiaoshen Wang, etc.) PDF
Convergence
analysis of discrete differential geometry operators over surfaces,
Lecture Notes in Computer Science, Mathematics of Surfaces XI, 2005.PDF
The Structural Characterization and Locally Supported Bases
for Bivariate Super Splines, with Ren-hong Wang, Journal of
Computational Mathematics.6(2004).PS
The
Estimation of the Bezout Number of Piecewise Algebraic Curve, with Ren-hong
Wang, Science in China Series A, 2003 Vol.46 No.5, 710-717.PDF
Discrete
Truncated Power And Lattice Points In Rational Polytope, with Ren-Hong
Wang, Journal of Computational and Applied Mathematics 159 (2003) 149-159.PDF
On the dimension for multivariate weak spline function spaces,
with Ren-hong Wang, Journal of mathematical research &
Exposition Vol.22, No.1,7-12, February, 2002.
The
instability degree in the dimension of spaces of bivariate spline, with
Ren-hong Wang, Approx. Theory & its Appl., 18:1,2002,68-80. PS
Multivariate
weak spline function space, with Ren-hong Wang, Journal of
Computational and Applied Mathematics, Vol.144, No.1-2, 2002.
Some properties about crossing cut partition, with
Ren-hong Wang, Numerical Mathematics A journal of Chinese Universities,
2001, No.4.
Reasonable layout of pollution sources in nearshore
waters, with Liu Shu-Zhen, Feng En-min, Liu Heng-kui, Acta
Oceanologic Sinica, 2000, No.2.
Application
of uniform design to computer experiments, with Wai-Man Ho, Journal
of the Chinese Statistical Association,2000,No.4.
Numerical simulation of tidal motion and parameter
identification, with Liu Shu-Zhen Feng En-min, J. Dalian Uni. Tech., 1999,
No.3.
Album
Miscellanea
An optional
talk about splines, wavelets and subdivision, in chinese
Slides: box splines and Mahler’s conjecture
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