Probing SUSY in the EW sector at HL/LHC: light neutralino and heavy higgses [Special Colloquium, part of the D P Roy Memorial Lecture]

I will talk about corners of the SUSY parameter space that are still admissible in the light of the LHC data, particularly in the EW sector. I will first focus on the case of a light LSP in general   and discuss the case of a light neutralino (lighter than half the Higgs mass) in particular, both in the MSSM as well as in the NMSSM.  I would  report on possibility of exploring  this part of the parameter space in the upcoming experiments:  ElectroWeakino  production at the LHC,  in the direct detection experiments as well as at the linear colliders through the invisible Higgs decays. I would then report on some aspects of our investigations into probing SUSY in the heavy higgs sector through their decays into Supersymmetric  final states.