Computational Conformal Geometry | |
Student No.： | 50 |
Time： | Mon/Wed 15:10-17:00, 2016-07-04~ 2016-08-29 |
Instructor： | Xianfeng David Gu [State University of New York at Stony Brook] |
Place： | 【Updated】Lecture Hall, Floor 3, Jin Chun Yuan West Building |
Starting Date： | 2016-7-4 |
Ending Date： | 2016-8-29 |
Description:
Computational Conformal Geometry is an emerging interdisciplinary field combing mathematics and computer science. In mathematics, conformal geometry is the intersection among complex analysis, differential geometry, algebraic topology, Riemann surface theory and partial differential equation. In computer science, it has been widely applied for many fields, such as computer graphics, computer vision, digital geometry processing, geometric modeling, networking, scientific computing and medical imaging.
This course will cover fundamental mathematics theories in conformal geometry, including homotopy theory and homology theory in algebraic topology; Hodge theory, exterior calculus, De Rham cohomology; surface differential geometry; harmonic mapping theory; Riemann surface theory; Teichmuller quasi-conformal geometry; elliptic partial differential equation and surface Ricci flow. If time allows, we will cover convex geometry, optimal mass transportation theory.
The course also cover fundamental algorithms in computational topoplogy, computational geometry and digitial geometry processing, including algorithms for homotopy group, homology/cohomology group, Hodge decomposition, holomorphic differential forms, conformal structure, conformal module, conformal mapping, quasi-conformal mapping, harmonic maps, Teichmuller map, discrete surface Ricci flow, discrete mass transportation and so on.
The course only requires linear algebra and multi-variable calculus. All students from pure mathematics, applied mathematics, and engineering departments are welcomed. Programming skills are preferred but not required.
Reference:
X. Gu and S.-T. Yau, “Computational Conformal Geometry”, Internation Press and High Education Press China
W. Zeng and X. Gu, “Ricci Flow for Shape Analysis and Surface Registration”, Springer