Austyn Simpson

I am an NSF postdoctoral assistant professor in the Mathematics Department at the University of Michigan. My research interests are in commutative algebra and algebraic geometry with a focus on singularities in prime characteristic.

Papers

  1. Noncatenary splinters in prime characteristic (with S. Loepp), submitted. arXiv.
  2. Regular morphisms do not preserve F-rationality (with E. Quinlan-Gallego and A. K. Singh), submitted. arXiv.
  3. The perfection can be a noncoherent GCD domain. To appear in J. Commut. Algebra. JCA, arXiv.
  4. On F-pure inversion of adjunction (with T. Polstra and K. Tucker), to appear in Higher Dimensional Algebraic Geometry: A Volume in Honor of V.V. Shokurov. Book,arXiv.
  5. F-purity deforms in Q-Gorenstein rings (with T. Polstra). Int. Math Res. Not. IMRN (2023) no. 24, 20725–20747. IMRN, arXiv.
  6. F-nilpotent rings and permanence properties (with J. Kenkel, K. Maddox, T. Polstra). J. Commut. Algebra 15 (2023) no. 4, 559-575.
    JCA, arXiv.
  7. Hilbert-Kunz multiplicity of fibers and Bertini theorems (with R. Datta). J. Algebra 595 (2022), 479-522. J. Algebra, arXiv.

Papers with undergraduates

  1. Uniform arithmetic in local rings via ultraproducts (with C. Adams, F. Cantor, A. Gashi, S. Mujevic, S. Park, J. Zomback), submitted. arXiv.
  2. ACC for F-signature: a likely counterexample (with C. Adams and T. Sandstrom), submitted. arXiv.
  3. On localization of tight closure in Line-S4 quartics (with L. Borevitz, N. Nader, T. Sandstrom, A. Shapiro, J. Zomback). To appear in J. Pure Appl. Algebra. JPAA, arXiv.
email: austyn at umich dot edu