Supersymmetric quantum mechanics on noncommutative space
  We construct supersymmetric quantum mechanics in terms of two real supercharges on noncommutative space in arbitrary dimensions. We obtain the exact eigenspectra of the two and three dimensional noncommutative superoscillators. We further show that a reduction in the phase-space occurs for a critical surface in the space of parameters. At this critical surface, the energy-spectrum of the bosonic sector is infinitely degenerate, while the degeneracy in the spectrum of the fermionic sector gets enhanced by a factor of two for each pair of reduced canonical coordinates. For the two dimensional noncommutative `inverted superoscillator', we find exact eigenspectra with a well-defined groundstate for certain regions in the parameter space, which have no smooth limit to the ordinary commutative space. 
Pijush K. Ghosh