  This work concerns the numerical simulation of the Vlasov-Poisson set of
equations using semi- Lagrangian methods on Graphical Processing Units (GPU).
To accomplish this goal, modifications to traditional methods had to be
implemented. First and foremost, a reformulation of semi-Lagrangian methods is
performed, which enables us to rewrite the governing equations as a circulant
matrix operating on the vector of unknowns. This product calculation can be
performed efficiently using FFT routines. Second, to overcome the limitation of
single precision inherent in GPU, a {\delta}f type method is adopted which only
needs refinement in specialized areas of phase space but not throughout. Thus,
a GPU Vlasov-Poisson solver can indeed perform high precision simulations
(since it uses very high order reconstruction methods and a large number of
grid points in phase space). We show results for rather academic test cases on
Landau damping and also for physically relevant phenomena such as the bump on
tail instability and the simulation of Kinetic Electrostatic Electron Nonlinear
(KEEN) waves.
