Login for PhD students/staff at UCPH      Login for others
Non-commutative geometry (NCG)
Provider: Faculty of Science

Activity no.: 5552-18-07-31 
Enrollment deadline: 14/11/2018
PlaceDepartment of Mathematical Sciences
Universitetsparken 5, 2100 København Ø
Date and time19.11.2018, at: 09:00 - 27.01.2019, 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
Semester/BlockBlock 2
Scheme groupB
Exam requirementsThe student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course
Exam formContinuous assessment
Exam details7 written assignments during the course of which 5 must be approved. One internal examiner
Grading scalePassed / Not passed
Course workload
Course workload categoryHours
Lectures35.00
Class Exercises22.00
Course Preparation149.00
Sum206.00
Content
Algebra of compact operators, Fredholm operators and index, the Toeplitz algebra, reminder on K-theory and the proof of Bott periodicity, introduction to K-homology.
Elements of periodic cyclic homology, characteristic classes of manifolds and Chern character, Index theorem.

Formel requirements
Recommended Academic Qualifications:
Elementary knowledge of K-theory, operator algebras and de Rham cohomology.

Learning outcome
Knowledge:
The student will obtain detailed understanding of K-theory and learn basic facts about K-homology, cyclic cohomology and characteristic classes. The student will have a basic understanding of the applications of homological methods for both topological spaces and non-commutative C*-algebras

Skills:
At the end of the course the student will be able to prove basic properties of topological K-theory and K-homology, demonstrate the ability to compute it in some examples. He/she will have a basic knowledge of yclic theory

Competences:
The student will be able to use K-theory, K-homology and cyclic homology in both topological and C*-algebraic problems.

Literature
Notes,
N. Higson, J. Roe Analytic K-homology, Oxford Mathematical monographs, Oxford University Press, 2000.

Teaching and learning methods
5 lectures and 3 exercise classes per week for 7 weeks.

Remarks
Academic qualifications:
Elementary knowledge of K-theory, operator algebras and de Rham cohomology.

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.