We model the effects of collisions and close encounters on the stellar populations observed in the Milky Way nuclear stellar cluster (NSC). Our analysis is based on $N$-body simulations in which the NSC forms by accretion of massive stellar clusters around a supermassive black hole. We attach stellar populations to our $N$-body particles and follow the evolution of their stars, and the rate of collisions and close encounters. The most common encounters are collisions between pairs of main-sequence stars, which lead to mergers: destructive collisions between main-sequence stars and compact objects are rare. We find that the effects of collisions on the stellar populations are small for three reasons. First, our models possess a core which limits the maximum stellar density. Secondly, the velocity dispersion in the NSC is similar to the surface escape velocities of the stars, which minimises the collision rate. Finally, whilst collisions between main-sequence stars destroy bright giants by accelerating their evolution, they also create them by accelerating the evolution of lower-mass stars. These two effects approximately cancel out. We also investigate whether the G2 cloud could be a fuzzball: a compact stellar core which has accreted a tenuous envelope in a close encounter with a red giant. We conclude that fuzzballs with cores below $2,M_odot$ have thermal times-scales too short to reproduce G2. A fuzzball with a black-hole core could reproduce the surface properties of G2 but the production rate of such objects in our model is low.
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