2022 Lecture Series: Computational Conformal Geometry

Instructor: David Gu
Email: gu@cs.stonybrook.edu
Date:Every Lecture 8:30-10:00am EST
Duration:Start From July 4th
Voov Meeting ID:933 8415 7259
Live Streaming: Use a web browser to open the live streaming link online.conformalgeometry.org
Participants:Public to general audience

Abstract: This course will cover fundamental concepts and theorems in algebraic topology, surface differential geometry, Riemann surface theory and geometric partial differential equations, as well as optimal transportation theory; 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.


Reference books:

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.

Online Demo: The online demo is written using WebGL, you can observe the conformal mappings of 3D surfaces interactively. More videos, images can be accessed by scanning the bar codes in the text book.

Lecture Slides

The lecture slides of the previous year can be found here.

Week OneAlgebraic Topology
1.07/04/2022Introduction to Computational Conformal Geometry[pdf]
2.07/05/2022Optimal Transportatiton Theory in AI[pdf]
3.07/06/2022Algebraic Topology: Fundamental group, Covering space [pdf]
4.07/07/2022Algebraic Topology: Simplicial Homology and Cohomology [pdf]
Assignment 1.07/15/2022Algorithm Implementation for Fundamental Group [Data Structure] [Algorithm] [Skeleton Code] [Demo]
Theoretic Proof for Homology Group [Problem Set]
Week TwoDifferential Topology
5.07/11/2022Geometric Programming : Halfedge Data Structure and Algorithmic Design Principle [Data Structure][Algorithm][demo]
6.07/12/2022Fixed point, Poincare-Hopf Index theorem, Characteristic Class of Fiber Bundle [pdf]
7.07/13/2022deRham Cohomology, Hodge Decomposition [pdf]
8.07/15/2022Surface Immersion Regular Homotopy [pdf]
Assignment 2.07/22/2022Algorithm Implementation for Hodge Decomposition [Algorithm] [Skeleton Code] [Demo]
Theoretic Proofs for Differential Topology [Problem Set]
Week ThreeRiemannian Metric Structure
9.07/18/2022Geometric Programming : Hodge Decomposition [Algorithm] [demo]
10.07/19/2022Surface Differential Geometry, Movable Frame Method [pdf]
11.07/20/2022Yamabe Equation and Geodesics [pdf]
12.07/21/2022Surface Harmonic Maps [pdf]
Assignment 3.07/22/2022Algorithm Implementation for Hodge Decomposition [Algorithm] [Skeleton Code] [Demo]
Theoretic Proofs for Surface Differential Geometry [Problem Set]
Week FourConformal Structure
13.07/25/2022Conformal Modules via Geometric Complex Analysis [pdf]
14.07/26/2022Circle Domain Mapping: Koebe's Theorem' [pdf]
15.07/27/2022Convergence Analysis of Koebei's Iteration [pdf]
16.07/28/2022Surface Uniformization [pdf]
Assignment 4.07/29/2022Algorithm Implementation for Koebe Iteration [Algorithm] [Skeleton Code] [Demo]
Theoretic Proofs for Conformal Structure [Problem Set]
Week Five3D Vision
17.08/01/20223D Acquisition Algorithmic Pipeline [pdf]
18.08/02/2022Phase Shifting Structured Light Method [pdf]
19.08/03/2022Camera Calibration, Point Cloud Fusion and Surface Reconstruction [pdf]
Assignment 5.08/05/2022Algorithm Implementation for Stereo-matching using Phase Shifting Structured Light [Algorithm] [Skeleton Code] [Demo]
Week SixPersistent Homology
20.08/08/2022Persistent Homology [pdf]
21.08/09/2022Combinatorial Map [pdf]
22.08/10/2022Abelian Differential [pdf]
Assignment 6.08/12/2022Handle and Tunnel Loops based on persistent homology [Algorithm] [Skeleton Code] [Demo]
Week SevenRiemann Surface Theory
23.08/15/2022Abel Differential and Mesh Generation [pdf]
24.08/16/2022Abel-Jacobi Theory [pdf]
25.08/17/2022Riemann-Roch Theory [pdf]
26.08/18/2022Algebraic Function Field on Riemann Surfaces [pdf]
Assignment 7. 08/22/2022 Verification of Abel-Jacobi Theorem [Algorithm] [Data]
Week EightSurface Ricci Flow
27.08/22/2022Discrete Surface Ricci Flow [pdf]
28.08/24/2022Generalized Discrete Surface Ricci Flow [pdf]
29.08/26/2022Hyperbolic Geometry [pdf]
30.08/27/2022Discrete Dynamic Yamabe flow [pdf]
Assignment 8. 08/28/2022 Surface Hyperbolic Structure [Algorithm] [Data]
Week NineOptiaml Transportation
31.08/29/2022Duality Theory [pdf]
32.09/05/2022Convex Geometric View [pdf]
33.09/07/2022Spherical Optimal Transportation [pdf]
34.09/09/2022Fluid Dynamics View [pdf]
35.09/10/2022Computational Methods [pdf]
Assignment 9. 09/10/2022 Euclidean Optimal Transportation [Algorithm] [Skeleton Code] [Demo Video]

This lecture briefly introduces the concept of conformal mapping, uniformization theorem, main types of computational algorithms and direct applications in graphics, vision, geometric modeling, networking, medical imaging and deep learning.

Discussion Group: By scanning the following bar codes to join the discussion group: