I'm a second year PhD student under the supervision of Prof. Michael Ruzhansky.
The major topic of my PhD’s project is to carry out some explicit analysis in the context of stratified groups. The first aim is to extend the pseudo-differential analysis explicitly available on the Heisenberg group to the context of Angel and Cartan groups. This will include explicit expressions for the infinitesimal representations of invariant vector fields and the sub-Laplacian, versions of the Kohn-Nirenberg and Weyl type quantizations, with applications to the analysis of Gevrey spaces and wave type equations. Consequently, one aims at extending this to the setting of more general stratified groups aided by the explicit sights obtained from these specific cases.