Computational Conformal Geometry Summer Online Course

time: July 4th to September 4th, every Saturday and Sunday morning 9:00-10:30AM Beijing time

link：Zoom Webinar ID：871 6057 8498

Password: 156302

Attend: Introduction to the course, free and open to a worldwide audience

Content introduction: This series of lectures will introduce basic concepts and theorems in the fields of algebraic topology, surface differential geometry, Riemann surfaces and geometric partial differential equations, explain the calculation methods of surface homotopy groups, homology groups, harmonic maps, meromorphic differentials, leaf-like structures, conformal maps, quasi-conformal maps and curvature flows, and introduce the application of these theories and algorithms in computer graphics, computer vision, visualization, geometric modeling, wireless sensor networks, medical images and deep learning.

Abstract: This course will cover fundamental concepts and theorems from algebraic topology, surface differential geometry, Riemann surface theory and geometric partial differential equations; it also covers the computational methods for surface fundamental group，homology group, harmonic maps, meromorphic differentials, foliation, conformal mapping, quasi-conformal mapping and Ricci flow. Their applications in Computer Graphics, Computer Vision, Visualization, Geometric Modeling, Networking, Medical Imaging and Deep Learning will be briefly introduced as well.

Preliminary knowledge: Linear algebra, multivariable calculus, preferably programming in C++, Matlab and OpenGL

Prerequisite：linear algebra，multivariate calculus，coding in C++， Matlab and OpenGL

Textbook: "Computational Conformal Geometry - Theory" Gu Xianfeng, Qiu Chengtong, Higher Education Press 2020

《Computational Conformal Geometry》by Gu and Yau, High Education Press, International Press, 2008.

Textbook：《Computational Conformal Geometry》by Gu and Yau, High Education Press, International Press, 2008.

Bibliography.

Lecture courseware(Lecture Slides) ：Lecture Notes for Computational Conformal Geometry

http://www3.cs.stonybrook.edu/~gu/lectures/CCGL.html

Online demo（Online Demos）: Computational Conformal Geometry Demos

http://www3.cs.stonybrook.edu/~gu/demo/index.html

Online demonstrations, images, and videos can be viewed directly on your mobile phone by scanning the QR code on the corresponding page in "Computational Conformal Geometry - Theory".

Homework: The lecture series will provide a basic program library, and students can add and modify it to implement basic algorithms such as calculation topology, harmonic mapping, optimal transmission mapping, etc., and full-time teaching assistants will provide help in answering questions.

Assignments：This lecture series will offer elementary library, the students are encouraged to implement some of the fundamental algorithms, such as computational topology, harmonic map and optimal transport map. Teaching assistants will answer the equestions and offer some helps for coding.

Tsinghua Notes

Conformal geometry is rooted in basic mathematics and is the intersection of many fields: Riemann surface theory, complex analysis, differential geometry, algebraic topology, geometric partial differential equations, algebraic curves, etc. Computational conformal geometry is also related to computational geometry, digital geometry, and numerical partial differential equations in computer science. The birth of this discipline is due to the vigorous rise of 3D technology, especially 3D scanning technology (such as phase translation technology based on structured light), computer graphics technology (such as surface parameterization, texture mapping technology), computer vision technology (such as surface registration and registration, The rapid development of facial expression capture has made it impossible for traditional Euclidean geometry and linear algebra methods to solve the profound problems raised in these fields. The field of engineering and medical care must systematically introduce the ideas and methods of modern differential geometry and topology to develop rigorous and practical calculation methods. Computational conformal geometry responds to the call of the times and promotes the development of science and technology based on first principles.

Computational conformal geometry is an emerging interdisciplinary discipline that integrates modern geometry with computer science, extends theories in modern topology and differential geometry to discrete situations, develops computational methods and is widely used in fields such as computer graphics, computer vision, geometric modeling, networks, computational mechanics, and medical imaging. Its basic algorithms have been adopted by the industry. For example, conformal virtual colonoscopy technology is promoted by Siemens, surface parameterization technology is adopted by the animation film and television industry, and some core algorithms are adopted by game companies (such as Blizzard).

For the past ten years, Lao Gu has taught the course "Computational Conformal Geometry" at the Yau Shing-tung Mathematics Center of Tsinghua University every summer. The course is completely free and open to the entire society. Students come from all over the country, and some students come from Europe, the United States, Hong Kong and Macao. The backgrounds of the students include computer, electronics, automation and other engineering majors, including mathematics, physics and other science majors, as well as biomedicine and other majors; many engineers come from animation design, industrial testing, computational mechanics, fluid mechanics, and doctors in the field of radiology and imaging. Mr. Qiu Chengtong and Lao Gu compiled the contents taught over the years into a book and published "Computational Conformal Geometry - Theory". In our previous series of articles, we systematically introduced the theory, methods and applications of computational conformal geometry. We summarize it as follows: Students can click on the title to read the corresponding chapter in depth.

Introduction to the tutorial "Computational Conformal Geometry - Theory" , Ten years of hard work: "Computational Conformal Geometry (Theory)" is about to be published
Comprehensive application Geometry empowers all things - architecture, medical care, animation, games... | Phoenix TV Century Lecture Hall
Tsinghua Notes: Computational Conformal Geometry Lecture Notes (0) Background Introduction
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (1) Algebraic Topology
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (2) Algebraic Topology
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (3) Differential Topology
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (4) Simple Homology
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (4.5) Relative Homology Mayer-Vietoris Sequence
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (5) Cohomology Theory
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (6) Hodge Theory of Cohomology
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (7) Vector Field Design
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (8) Existence of Slit Map
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (9) Holomorphic Differential Calculus
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (10) Memorial to Mirzakhani - Teichmuller Space
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (11) Existence of Riemann Mapping
Tsinghua Notes: Computational Conformal Geometry Lecture Notes (12) Extremal length
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (13) Koebe Iterative Convergence
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (14) Calculation of Conformal Modules
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (15) Harmonic mapping of topological disks
Tsinghua Notes: Computational Conformal Geometry Lecture Notes (16) Harmonic mapping of topological spheres
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (17) holomorphic quadratic differential
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (18) Quasi-Conformal Map
Discrete Surface Ricci Flow I
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (20) Discrete Surface Ricci Flow II
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (21) Discrete Surface Ricci Flow III
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (22) Discrete Surface Ricci Flow IV
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (23) Discrete Surface Ricci Flow V
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (24) Teichmuller Mapping
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (25) Probabilistic Interpretation of Conformal Geometry
Tsinghua Notes: Lecture Notes on Computational Conformal Geometry (26) Proof of Unique Value Theorem
Computational Conformal Geometry Lecture Notes: Fiber Bundles and Chern Classes
Computational Conformal Geometry Lecture Notes: Abel’s Theorem
Computational Conformal Geometry Lecture Notes: Jacobi Theorem
Computational Conformal Geometry Lecture Notes: Riemann-Roch Theorem

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Meromorphic fourth differential on the Riemann surface.

Machine-translated from the Chinese original 计算共形几何暑假网上课程 (published 2020-07-04). WeChat original ↗