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Applied differential geometry
Provider: Faculty of Science

Activity no.: 5180-20-02-31 
Enrollment deadline: 28/09/2020
PlaceDepartment of Computer Science
Universitetsparken 1, 2100 København Ø
Date and time02.10.2020, at: 09:00 - 06.11.2020, at: 12:00
[antalgange]6
Regular seats10
ECTS credits5.00
Contact personJon Sporring    E-mail address: sporring@di.ku.dk
Enrolment Handling/Course OrganiserJon Sporring    E-mail address: sporring@di.ku.dk
Written languageEnglish
Teaching languageEnglish
Semester/BlockAutumn
Exam formAndet/Other
Grading scaleCompleted/ Not completed
Content
This course is the first of a series of phd-courses with the main focus of teaching computer scientists the fundamental tools and concepts of Riemannian differential geometry. Other topics which are expected to be covered in the near future are Lie Algebra and Differential Geometry in Machine Learning. This course will consider smooth manifolds, vectors and convectors, and differential geometry, and we will investigate Cartan's method of moving frames for curves and patches in R^3. Once the basic concepts are in place, we will develop computational methods for grids and meshed objects. A part of the course we will also look at computational tools such as Theano and Jax for visualization and computational support.

Formel requirements
The student must have knowledge of basic mathematical analysis, linear algebra, and python programming.

Learning outcome
- Experience with matrix differential calculus
- Understanding of the difference between vectors and covectors and how these relate to the notion of distance on curved manifolds
- The ability to develop and explain Cristoffel symbols using Cartan's method of moving frames
- The ability to write a program, which calculates differential geometric properties of discrete data on a grid (images) and as meshes

Literature
Magnus, Matrix Differential Calculus with Applications to Simple, Hadamard, and Kronecker Products, Journal of mathematical psychology 29, 474-492, 1985 (https://www.janmagnus.nl/papers/JRM012.pdf)
Excerpts from Koenderink, Solid shape
Excerpts from Crane, Discrete Differential Geometry: An Applied Introduction, (https://www.cs.cmu.edu/~kmcrane/Projects/DDG/)
Please note:
The student is expected to have read Magnus prior to the first meeting

Target group
10 seats - priority will be given to phd-students from DIKU (Dept. of Computer Science)

Teaching and learning methods
Blended learning, depending on the Corona situation in the period.
The course will start with lectures by the teacher, followed by seminars, where the students presents basic concepts, and ending with student projects.

Lecturers
Jon Sporring

Workload
5 ECTS = 3 weeks full time ~ 120h

18h: 3 hours of lectures each week in 6 weeks = 18 hours
18h: 3 hours of preparation time for each class
24h: 1 seminar presentation per student
60h: project work

Remarks
Presence teaching :
Department of Computer Science, UP1
Rooms: 1-1-N116A+B

Possible web-based teaching link: to be announced if necessary

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