The paper explores 1/2 BPS excitations in $AdS \times S$ configurations within type IIB string theory and M-theory. These excitations are described by free fermions in the dual field theories. The configurations corresponding to arbitrary droplets of free fermions in phase space correspond to smooth geometries without horizons. The ten-dimensional geometry contains a special two-dimensional plane that can be identified with the phase space of the free fermion system. The topology of the resulting geometries depends only on the topology of the droplets on this plane. These solutions also provide explicit realizations of geometric transitions between branes and fluxes. The paper also describes 1/2 BPS excitations of plane wave geometries, reducing the problem to solving a Laplace or Toda equation with simple boundary conditions. A large class of explicit solutions is presented. Additionally, the paper discusses $AdS_5$ compactifications of M-theory preserving $\mathcal{N} = 2$ superconformal symmetry and smooth geometries corresponding to various vacua of the maximally supersymmetric mass-deformed M2 brane theory. Finally, a smooth 1/2 BPS solution of seven-dimensional gauged supergravity is presented, corresponding to a condensate of one of the charged scalars.The paper explores 1/2 BPS excitations in $AdS \times S$ configurations within type IIB string theory and M-theory. These excitations are described by free fermions in the dual field theories. The configurations corresponding to arbitrary droplets of free fermions in phase space correspond to smooth geometries without horizons. The ten-dimensional geometry contains a special two-dimensional plane that can be identified with the phase space of the free fermion system. The topology of the resulting geometries depends only on the topology of the droplets on this plane. These solutions also provide explicit realizations of geometric transitions between branes and fluxes. The paper also describes 1/2 BPS excitations of plane wave geometries, reducing the problem to solving a Laplace or Toda equation with simple boundary conditions. A large class of explicit solutions is presented. Additionally, the paper discusses $AdS_5$ compactifications of M-theory preserving $\mathcal{N} = 2$ superconformal symmetry and smooth geometries corresponding to various vacua of the maximally supersymmetric mass-deformed M2 brane theory. Finally, a smooth 1/2 BPS solution of seven-dimensional gauged supergravity is presented, corresponding to a condensate of one of the charged scalars.