Last Update 2021/04/05
My research interest is a mathematical study of theories arising from conformal field theory. In particular, I study the algebraic structure and representation theory of W-algebras, which are an important family of vertex algebras in conformal field theory. The W-algebras not only shed new light on the mathematical structure in conformal field theory but also related to affine Lie algebras, modular tensor categories, and quantum geometric Langlands programs so that W-algebras will play an important role to connect various representation theories with each other. My main tool to study W-algebras is screening operators, which give rise to new realizations of W-algebras and is useful to prove non-trivial isomorphisms between W-algebras. In fact, I have recently applied screening operators to prove Feigin-Semikhatov conjectures (dualities between W-algebras) and to study the representation theory of the W-algebras. I also research the relationship between screening operators and geometric realizations of W-algebras.
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