The Summer School/Workshop on

Multivariate Splines and Their Applications

May 11--22, 2009, Athens, Georgia

Multivariate splines are smooth piecewise polynomnial functions defined on a triangulation or a collection of simplices in 2D, 3D or multi-dimensional Euclidean spaces. The study of these functions and their applications is rich. A vast literature on the subject can be seen on this website. A searchable site on the literature of univariate and multivariate splines is kept by Carl de Boor and can be accessed from here. A detailed theory of multivariate splines is summarized in a monograph "Spline Functions over Triangulations" written by Lai and Schumaker and published by Cambridge University Press in 2007. Some direct computational algorithms are available. These spline functions can be easily used for various applications. Some of them are listed below.

  • scattered data fitting and interpolation;
  • surface design;
  • spherical data fitting and interpolation ;
  • numerical solution of partial differential equations, e.g., 2D Navier-Stokes equations and simulation of fluid flows , 3D Navier-Stokes equations, and 2D and 3D plate elasticity equations;
  • construction of various multidimensional compactly supported wavelets, e.g. biorthogonal wavelets, prewavelets, tight wavelet frames, Riesz bases and pre-Riesz bases based on box splines;
  • mathematical imaging such as image denoising and image edge detections;
  • statistical data forecasting;
  • box spline functions for subdivision;
  • and etc..
  • Professors Larry L. Schumaker, Ming-Jun Lai, Paul Wenston, Jorg Peters , Gerard Awanou, Victoria Baramidze, Tatyana Sorokina, and other invited speakers will give their lectures for the summer school. A tentative schedule can be found here.

    Dr. Ming-Jun Lai's lecture notes can be found here: Lecture 1 and Lecture 2.

    A copy of Ms. Bree Ettinger's presentation can be read at here.

    Dr. Gerard Awanou's lecture notes are available now. Here are Lecture 1 and Lecture 2.

    Dr. Victoria Baramidze has made her lectures available on-line, Lecture 1 and Lecture 2.

    Dr. Qin Zhang presented a lecture on Wednesday afternoon. His lecture can be found at this link.

    The summer school is now only accepting applications for admission from all U.S. citizen or permenant graduate students, new Ph. D. (up to 3 years after graduation), and some qualified undergraduate students majoring in mathematics, applied mathematics, computer science, statistics, geoscience or other engineering sciences untill the enrollment is filled.

    If an applicant is a U.S. citizen or a permanent resident of the U.S., his or her accommodation and travel expenses will be covered. For other applicants, the limited travel fund is no longer available. Please find your own travel and local expenses to come. Send an email to Dr. Ming-Jun Lai(email address is mjlai at math dot uga dot edu) for any inquiry.

    On-Line Application Button

    All registered participants can be found from here.

    In addition to the summer school, we organize a workshop and cordially welcome everyone to come to listen the lectures and/or present a half hour talk during the week May 18--22. Please register for the workshop before March 1, 2009 by sending Dr. Lai an email.

    The summer school is partially supported by National Science Foundation under VIGRE grant #0738586. In addition, it is supported by the President's Venture Fund, the office of the vice president for research, the Dean office of the college of Arts and Sciences, and the Department of Mathematics of the University of Georgia. All supports are cordially appreciated.