After completing 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
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, index theorems
Lectures and classes ("flipped classroom" might be used).
Hand-in problems during the course.
The course is given in coordination with the third-cycle programmes.