| Summary: | The first part of this thesis investigates the Gromov width of maximal dimensional
coadjoint orbits of compact simple Lie groups. An upper bound for the Gromov width
is provided for all compact simple Lie groups but only for those coadjoint orbits that satisfy a certain technical assumption, whereas the lower bound is proved only for
groups of type A, but without the technical restriction. The two bounds use very
different techniques: the proof of the upper bound uses more analytical tools, while
the proof of the lower bound is more geometric.
The second part of the thesis is a short report on a joint project with my supervisor, which was concerned with the relationship between two different definitions of orbifolds: one using Lie groupoids and the other involving diffeologies. The results are summarized in Chapter 5 of this text.
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