LEARNING OUTCOMES
After the course, the student will be familiar with basic concepts of group theory, group representation theory, and topology. The student can identify different common groups, study if their representations are reducible, irreducible or not, and knows why the theory of groups and their unitary representations is important in quantum physics of systems with various symmetries. The student also understands distinctions between nonhomeomorphic topological spaces and understands the use of topological invariants (such as homotopy groups) in their classification.
CONTENT
Group theory: finite groups, continous groups, conjugacy classes, cosets, quotient groups
Representation theory of groups: complex vector spaces and representations, symmetry tranformations in quantum mechanics, reducible and irreducible representations, characters
Topology: topological spaces, topological invariants, homotopy, homotopy groups
