I also want to develop novel linear and non-linear positive maps that to characterize entanglement in quantum systems and delineate the space of quantum states. I have been successful in describing several families of such linear maps in even dimensions. However, a rigorous proof of the behavior of their non-linear counterparts remains a challenging open issue. Currently, I am examining the constructions of maps in arbitrary dimensions, nonlinear extension and the nature of detectable entangled states.
In education research, I am specifically interested in understanding what factors affect student retention and persistence in pursuing their degree. Using social network analysis, I look at the correlations between students’ overall embeddedness within the in- and out-of-class network and their odds of persistence into the second semester in a sequence. I also investigate how the attitudes toward learning with peers translate into actual behaviors. My objective is to provide a concrete basis for efforts to increase overall student retention and graduation rates at both the departmental and university levels.