My research pursuits range from mathematics and physics education to mathematical physics. In education research, I am specifically interested in understanding how students learn to use mathematical and computational tools to solve applied problems. Moreover, in my current position I am developing models to determine what factors affect student retention and persistence in pursuing their degree. 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.

I am also working on mathematical foundations of quantum information theory. In particular, I want to develop novel linear and non-linear positive maps that characterize entanglement and the space of quantum states. I have been successful in describing several families of such linear maps in even dimension. A rigorous proof of the behavior of their non-linear counterparts remains a challenging open issue in mathematical physics. Currently I am examining the constructions of maps in arbitrary dimensions, nonlinear extension and the nature of detectable entangled states.


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