FSF3675 Cohomology in Dynamics 7.5 credits
Information for research students about course offerings
Spring 2018
Content and learning outcomes
Course contents
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.
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.
Recommended prerequisites
Equipment
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
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
Opportunity to raise an approved grade via renewed examination
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.