How does an irreducible representation of a group decompose when restricted to a subgroup? This question lies at the heart of branching problems, a fundamental topic in representation theory with deep connections to other areas of mathematics.

For reductive groups, the relative Langlands program predicts hidden spectral structures underlying such problems. However, much less is known for non-linear covers of reductive groups.

In this talk, we discuss several examples of branching problems for covering groups, with particular emphasis on multiplicity-free restrictions.