Mutations of noncommutative crepant resolutions in GIT

Noncommutative crepant resolutions (NCCR), introduced by Van den Bergh, are noncommutative analogue of crepant resolutions of singularities. An NCCR of a fixed singular variety is not unique in general, but it is known that all NCCRs of a fixed Gorenstein terminal 3-fold are related by certain transformations of them, which are called mutations. In this talk, we discuss mutations of NCCRs arising from quasi-symmetric torus representations, and  then we explain that a spherical twist on the derived category of a Calabi-Yau complete intersection corresponds to iterated mutations of NCCRs via noncommutative matrix factorizations. This talk is based on joint work with Wahei Hara.

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