In this course the focus will be on the analysis and application of cohomology in various areas in dynamical systems. Some of the topics will be: classification of Lie group extensions of Anosov systems via group valued cohomology, classification of time changes via real valued cohomology, Schrödinger cocycle reducibility and applications, cohomological stability for some homogeneous actions, the rigidity conjecture of Greenfield and Wallach on vector fields with almost trivial cohomology, the extension of Weil's result that trivial cohomology implies local rigidity to general isometric higher rank lattice actions, Livsic theorem for matrix cocycles.
FSF3675 Cohomology in Dynamics 7.5 credits
Information per course offering
Information for Spring 2025 Start 14 Jan 2025 programme students
- Course location
KTH Campus
- Duration
- 14 Jan 2025 - 2 Jun 2025
- Periods
- P3 (3.5 hp), P4 (4.0 hp)
- Pace of study
25%
- Application code
60870
- Form of study
Normal Daytime
- Language of instruction
English
- Course memo
- Course memo is not published
- Number of places
Places are not limited
- Target group
- No information inserted
- Planned modular schedule
- [object Object]
- Schedule
- Schedule is not published
- Part of programme
- No information inserted
Contact
Danijela Damjanovic (ddam@kth.se)
Course syllabus as PDF
Please note: all information from the Course syllabus is available on this page in an accessible format.
Course syllabus FSF3675 (Spring 2019–)Information for research students about course offerings
Spring 2018
Headings with content from the Course syllabus FSF3675 (Spring 2019–) are denoted with an asterisk ( )
Content and learning outcomes
Course contents
Intended learning outcomes
After the completed course the students will be able to:
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Compute cohomology over some dynamical systems
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Apply the concept of trivial cohomology to obtain qualitative information about the dynamical system
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Obtain classification of some classes of dynamical systems by using the concept of cohomology
Literature and preparations
Specific prerequisites
Sufficiently good knowledge in areas: General real and Functional analysis, Harmonic analysis, Algebraic topology, Riemannian geometry.
Equipment
No information inserted
Literature
The literature will consist of articles which will be announced before the course starts.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
Grading scale
P, F
Examination
- SEM1 - Seminars, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
The assessment will be based on: presentation (SEM1).
Other requirements for final grade
Presentation completed (SEM1)
Opportunity to complete the requirements via supplementary examination
No information inserted
Opportunity to raise an approved grade via renewed examination
No information inserted
Examiner
Ethical approach
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information
Course room in Canvas
Registered students find further information about the implementation of the course in the course room in Canvas. A link to the course room can be found under the tab Studies in the Personal menu at the start of the course.
Offered by
Main field of study
This course does not belong to any Main field of study.
Education cycle
Third cycle
Add-on studies
No information inserted
Contact
Danijela Damjanovic (ddam@kth.se)