Login for PhD students/staff at UCPH      Login for others
Analysis on Manifolds
Provider: Faculty of Science

Activity no.: 5610-19-07-31 
Enrollment deadline: 01/09/2019
PlaceDepartment of Mathematical Sciences
Date and time02.09.2019, at: 09:00 - 10.11.2019, at: 16:00
Regular seats50
ECTS credits7.50
Contact personNina Weisse    E-mail address: weisse@math.ku.dk
Enrolment Handling/Course OrganiserRyszard Nest    E-mail address: rnest@math.ku.dk
Written languageEnglish
Teaching languageEnglish partially in English
Semester/BlockBlock 1
Scheme groupC
Exam formContinuous assessment
Exam formContinuous assessment
Exam details7 written assignments during the course of which the 5 best counts equally towards the final grade All aids allowed
Exam aidsAll aids allowed
Grading scale7 point grading scale
Course workload
Course workload categoryHours
Lectures45.00
Class Exercises27.00
Course Preparation134.00
Sum206.00
Content
Basic properties of differential operators on manifolds,
Relations between ellipticity and Fredholm properties.
Riemannian geometry, Levi - Civita connection and Laplace operator.
Hodge theorem.
Dirac operators and properties of heat kernels

Learning outcome
Knowledge:
The student will obtain detailed understanding of the properties of elliptic differential operators on manifolds and their applications to topology and geometry.

Skills:
At the end of the course the student will be able to prove basic properties of elliptic differential operators and demonstrate the ability to use them in applications.

Competences:
The student will be able to use analysis of differenial operators on manifolds to study their topological and geometric properties.

Literature
Steve Rosenberg, "The Laplacian on a Riemannian Manifold" or equivalent textbook

Teaching and learning methods
5 lectures and 3 exercise classes per week for 9 weeks

Search
Click the search button to search Courses.


Course calendar
See which courses you can attend and when
JanFebMarApr
MayJunJulAug
SepOctNovDec



Publication of new courses
All planned PhD courses at the PhD School are visible in the course catalogue. Courses are published regularly.