I am an Assistant Professor at the Ozawa group, at the Advanced Institute for Materials Research (WPI-AIMR), Tohoku University.
I am a theoretical physicist with a strong inclination towards mathematical aspects. My research focuses mostly in quantum matter and the study of the geometrical and topological structures which capture the underlying physics. The study of critical behaviour of quantum matter through the change of the geometric and topological structures has been one of my main focuses in the past few years.
More recently, I have been interested in the role of Kähler geometry (a trinity of geometries!---Riemannian, Complex and Symplectic) in the stability of fractional Chern insulating phases. I have also been applying methods of geometric quantization and coherent state transforms in imaginary time to the study of the integer and fractional Hall effects, and also towards the engineering of band structures.
Finally, I have also been applying classical information geometry methods towards the problem of model selection in the context of high dimensional vector data but with small amount of instances. It seems that the curvature of statistical manifolds plays an intriguing role in this scenario.