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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
Deterministic
Sampling of Sparse Trigonometric Polynomials,
submitted for publication.
Multivariate splines and
polytopes, submitted for publicatoin
Application of multivariate
splines to discrete mathematics, submitted for publicatoin.
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, Signal Processing,
Volume 90,
Issue 7, July 2010, Pages 2308-2313.
Subspace modelling for structured
noise suppression, with Laura Rebollo-Neira, A. Plastino, Physica
A: Statistical Mechanics and its Applications, Volume
389, Issue 10, 15 May 2010, Pages 2030-2035
.Sagbi bases of Cox-Nagata
rings, with Bernd Sturmfels, Journal of the European Mathematical
Society, Volume 12, Issue 2, 2010.
Eulerian numbers: a spline interpretation , With R.
Wang, Y. Xu, Journal of Mathematical Analysis and
Applications, 370 (2010) 486–490.
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.
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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