Entry requirements

120 credits including Mathematical Methods of Physics II.

Learning outcomes

On completion of the course, the student should be able to:

• analyse and solve simple problems in topology (e.g. simple homotopy, homology and cohomology calculations)
• perform simple manipulations with connections and characteristic classes on fibre bundles.
• use the geometrical tools that are used widely in modern quantum feld theory and string theory
• account for the geometrical notions behind the description of gauge theories
• discuss applications of topology in various physical problems

Content

Topology, smooth manifolds, Lie groups, homotopy, homology, cohomology, principal and vector bundles, connections on fibre bundles, characteristic classes and their application in physics, Yang-Mills theory and more advanced topics based on students' interests.

Instruction

Lectures and classes ("flipped classroom" might be used).

Assessment

Hand-in problems during the course.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other directives

The course is given in coordination with the third-cycle programmes.