| Abstract: Conformal parametrizations of surfaces play an important role in both theory and applications. They preserve angles locally and are closely related to complex analysis and Riemann surfaces. They have many applications in computer graphics and medical imaging. In the 1980s, William Thurston proposed circle packing as a discrete model of conformal maps, which leads to efficient algorithms for computing parametrizations. In this talk, I will explain how conformal parametrizations can be computed using circle packing and its friends, show some pictures of their applications, and discuss the convergence issue behind these methods. |