This course will cover the basic concepts and theorems in algebraic topology, Riemann surface, differential geometry and quasi-conformal geometry. The computational methods will be explained in details, including non-linear harmonic map, holomorphic differentials based on Hodge theory, discrete surface Ricci flow and so on. The applications in computer graphics, computer vision, deep learning, geometric modeling, wireless sensor networks, and medical imaging will be discussed in depth.

Linear algebra, multivariable calculus, algorithm, data structure

Xianfeng Gu and Shing-Tung Yau. Computational Conformal Geometry, Series: Advanced Lectures in Mathematics, Vol 3, Publisher: International Press and Higher Education Press, ISBN 978-1-57146-171-1, 2007.