Research (under construction)

My research is in operator algebras, with a particular focus on subfactor theory and finite-index inclusions of von Neumann and C*-algebras. A central theme of my research is to understand the algebraic, geometric, and quantum structures associated with inclusions of algebras.

My work includes the study of intermediate subalgebras, Pimsner–Popa bases, unitary orthonormal bases, regular inclusions, normalizers, planar algebras, and finite-dimensional inclusions. I am also interested in geometric and information-theoretic aspects of operator algebras, including angles between subfactors, entropy, and relative entropy.

Another direction of my research concerns concrete constructions of subfactors, including those arising from Hadamard matrices, spin models, vertex models, and related finite-dimensional structures. More recently, I have been exploring quantum symmetries associated with finite-index inclusions, including connections with quantum groups, quantum hypergroups, tensor categories, and C*-algebraic structures.

A broader goal of my research is to understand how a finite-index inclusion encodes rich algebraic, geometric, combinatorial, and quantum structures, and to develop connections between these different aspects of operator algebra theory.