$ Flat Band and the Compact Localized States
$ Topological phases and Topological phase transition
$ Aharanov-Casher/ Aharonov-Bohm caging
$ Spin Filtering effects in aperiodic systems 
$ Variation of Anderson Localization in decorated lattices
$ Spectral profiles of Density of States, Transport of disordered quasiperiodic geometries.