讲座内容：

Moving curves and moving surfaces serve as a bridge between the parametric forms and implicit forms of rational curves and surfaces. Their algebraic counterparts are special syzygies of the parametric equations of rational curves or surfaces. Over the past thirty years, the technique of moving curves and moving surfaces have been proven to be significant in solving many important problems in geometric modeling, such as fast implicitization, intersection computation, singularity computation, reparametrization as well as providing easy inversion formulas for points. We review our research on µ-bases theory and applications for rational curves and surfaces over the past ten years, and raise unsolved problems for future research.