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FSF3675 Cohomology in Dynamics 7.5 credits

Course offerings are missing for current or upcoming semesters.
Headings with content from the Course syllabus FSF3675 (Spring 2019–) are denoted with an asterisk ( )

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:

  • Compute cohomology over some dynamical systems

  • Apply the concept of trivial cohomology to obtain qualitative information about the dynamical system

  • 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

No information inserted

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)

Postgraduate course

Postgraduate courses at SCI/Mathematics