Correlated phases of bosons in novel geometries

This thesis is a study of different systems of strongly-interacting bosons, at low but finite temperature, in the presence of strong geometric constraints. Numerical techniques, particularly Path integral Monte Carlo, are employed to estimate quantities such as superfluid and condensate fraction, so that thermodynamic and quantum phases can be characterized and distinguished. The first part of the thesis (chapter 1 and 2) is an introduction to the Path integral Monte Carlo method. The second part (chapters 3, 4 and 5) describe the behavior of bosons in various quasicrystalline geometries. Finally, chapters 6 looks into the formation of supersolidity of bosons in a spherical geometry.