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. F-injectivity does not imply F-fullness in normal domains (with A. De Stefani, T. Polstra), submitted. arXiv.

  2. Noncatenary splinters in prime characteristic (with S. Loepp). J. Algebra 677 (2025), 61-87. JofA, arXiv.

  3. 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.

  4. The perfection can be a noncoherent GCD domain. J. Commut. Algebra 16 (2024) no. 3, 363-367. JCA, arXiv.

  5. On F-pure inversion of adjunction (with T. Polstra, K. Tucker). Higher Dimensional Algebraic Geometry: A Volume in Honor of V. V. Shokurov. Book,arXiv.

  6. F-purity deforms in Q-Gorenstein rings (with T. Polstra). Int. Math Res. Not. IMRN (2023) no. 24, 20725–20747. IMRN, arXiv.

  7. F-nilpotent rings and permanence properties (with J. Kenkel, K. Maddox, T. Polstra). J. Commut. Algebra 15 (2023) no. 4, 559-575.
    JCA, arXiv.

  8. Hilbert-Kunz multiplicity of fibers and Bertini theorems (with R. Datta). J. Algebra 595 (2022), 479-522. JofA, arXiv.

Papers with undergraduates

  1. On deformation of perfectoid purity in Gorenstein domains (with B. Baily, K. Dovgodko, J. Westbrook), submitted. arXiv.

  2. ACC for F-signature: a likely counterexample (with C. Adams, T. Sandstrom), to appear in Exp. Math. Exp. Math., arXiv.

  3. 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.

  4. 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