Group actions in algebraic geometry and commutative algebra


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Many applied and theoretical problems exhibit symmetry in the form of a group action (of a finite group, a torus, an infinite symmetric group, or of the cyclic group generated by the Frobenius map, among many other examples). It is then a challenge to understand this symmetry as well as the structural implications it presents. Two major reasons for studying objects with symmetry (besides their intrinsic significance) are: (a) they provide good testing grounds for general phenomena (e.g. toric varieties, homogeneous spaces); (b) they allow one to deduce general results that hold in the absence of symmetry (e.g. monomial ideals, singular curves). The goal of this minisymposium is to bring together researchers in algebraic geometry and commutative algebra and discuss recent developments where symmetry plays an important role.

  • Kangjin Han (KIAS, Korea) - On the singularities of the third secant varieties of Veronese embeddings
  • Luke Oeding (Auburn University) - Symmetrization of principal minors
  • David Swinarski (Fordham University) - Applications of flattening stratifications to equations of curves with automorphisms
  • Kevin Tucker (UI Chicago) - On the limit of the F-signature function in characteristic zero
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