Course Description

Differential geometry classically is a backbone of theoretical physics such as Einstein's theory of general relativity. Nowadays, differential geometric methods become important techniques for developing novel algorithms in big data analytics and computer vision. In this course, we will cover both classical differential geometry and their applications in computer vision. Key topics include curves, surfaces, manifolds, Riemannian metrics, differential forms, Statistical Manifold, Gauss curvature; isometries, covariant differentiation, parallel transport, geodesics with application to physics and computer vision. This course is intended for majors in physics or mathematics or Math-CS majors who aim for becoming research scientists.

Additionally, another goal of this course is to become comfortable using Amazon Web Services and GitHub as these tools are extremely prevalent in industry and academia when developing and deploying models. To that end, all code for your midterm and final projects will be hosted on GitHub.

Summary of Goals

  • Gain a comprehensive view of differential geometry as an academic discipline and understand the mathematics behind it.

  • Be able to read recent academic papers in the computer vision and theoretical physics literature and apply those algorithms and concepts to real world problems.

  • Become comfortable with industry and academia standard tools (such as AWS and GitHub) and be able to find and work with team members.