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Applied differential geometry
Provider: Faculty of Science

Activity no.: 5180-20-02-31
	Enrollment deadline: 28/09/2020

Place	Department of Computer Science
Date and time	02.10.2020, at: 09:00 - 06.11.2020, at: 12:00
[antalgange]	6
Regular seats	10
ECTS credits	5.00

Contact person	Jon Sporring E-mail address: sporring@di.ku.dk

Enrolment Handling/Course Organiser	Jon Sporring E-mail address: sporring@di.ku.dk
Written language	English
Teaching language	English
Semester/Block	Autumn
Exam form	Andet/Other
Grading scale	Completed/ 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. Formal 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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