Shigenori Nakatsuka
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My mathematical research focuses on W-superalgebras, which provide a large family of vertex superalgebras, i.e., symmetries of 2-dimensional chiral conformal field theories. In particular, I am interested in their representation theory or relation to higher dimensional quantum field theories, and soliton theory or certain geometry appearing in the classical limit.
Recently, I obtained a duality of subregular W-algebra and principal W-superalgebra of A type originally conjectured by B. Feigin and A. Semikhatov in a joint work with T. Creutzig and N. Genra. Moreover, I upgraded this duality to a correspondence between their representation categories in a joint work also with R. Sato. Currently, I am trying to reinterpret and generalize these dualities in terms of geometry.
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