Introductory Workshop: Noncommutative Algebraic Geometry: "Mutations of noncommutative crepant resolutions in GIT"

February 9, 2024
  • Noncommutative geometry
  • derived categories
  • Derived Algebraic Geometry
  • Infinity Categories
  • Deformation Theory
  • Categorical Resolutions
  • noncommutative resolutions
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.