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. Flat morphisms with regular fibers do not preserve F-rationality (with E. Quinlan-Gallego, A. K. Singh). Rev. Mat. Iberoam. 40 (2024) no. 5, 1989-2001. RMI, arXiv.
  3. The perfection can be a noncoherent GCD domain. J. Commut. Algebra 16 (2024) no. 3, 363-367. JCA, arXiv.
  4. On F-pure inversion of adjunction (with T. Polstra, 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. JofA, arXiv.

Papers with undergraduates

  1. ACC for F-signature: a likely counterexample (with C. Adams, T. Sandstrom), submitted. arXiv.
  2. Uniform arithmetic in local rings via ultraproducts (with C. Adams, F. Cantor, A. Gashi, S. Mujevic, S. Park, J. Zomback). Beitr. Algebra Geom. (2024). BZAG, arXiv.
  3. On localization of tight closure in Line-S4 quartics (with L. Borevitz, N. Nader, T. Sandstrom, A. Shapiro, J. Zomback). J. Pure Appl. Algebra 228 (2024). JPAA, arXiv.
email: austyn at umich dot edu