Neil Epstein

Universität Osnabrück

Institut für Mathematik

49076 Osnabrück, Germany

EMAIL: nepstein 'at'

I am currently a postdoctoral researcher (wissenschaftlicher Mitarbeiter), under a grant from the DFG (Deutsche Forschungsgemeinschaft, or German Research Foundation) since 2009.  My research concerns commutative algebra.  I have an energetic and wide-ranging research program, with many collaborators representing several distinct projects. My methods include prime characteristic, homological, and non-commutative algebra. My work has close connections with algebraic geometry, combinatorics, and even complex-valued continuous functions.  I received my Ph.D. in Mathematics in 2005 at the University of Kansas, under the direction of Craig Huneke, after which I was an NSF Postdoctoral Researcher at the University of Michigan from 2005-2009.

I will be a tenure-track assistant professor in the department of mathematical sciences at George Mason University, starting in August of 2012.

curriculum vitae  |  research statement 

Refereed publications

  • A tight closure analogue of analytic spread, Math. Proc. Cambridge Philos. Soc. 139 (2005), no. 2, 371-383.

  • Phantom depth and flat base change, Proc. Amer. Math. Soc. 134 (2006), 313-321.

  • Phantom depth and stable phantom exactness, Trans. Amer. Math. Soc. 359 (2007), 4829-4864.

  • A length characterization of *-spread (with Adela Vraciu), Osaka J. Math. 45 (2008), no. 2, 445-456.

  • Reductions and special parts of closures, J. Algebra 323 (2010), no. 8, 2209-2225.

  • Noether normalization, reductions of ideals, and matroids (with Joseph P. Brennan), Proc. Amer. Math. Soc. 139 (2011), no. 8, 2671-2680.

  • Criteria for flatness and injectivity (with Yongwei Yao), Math. Z. (2011).

  • A guide to closure operations in commutative algebra, to appear in the De Gruyter volume “Progress in Commutative Algebra”, 2012.

  • Preprints and projects

  • Continuous closure, axes closure, and natural closure (with Mel Hochster), arXiv:1106.3462, submitted.

  • Homogeneous equational closures, tight closure, and localization (with Mel Hochster), in preparation.

  • Some extensions of Hilbert-Kunz multiplicity (with Yongwei Yao), arXiv:1103.4730, submitted.

  • Unmixed Hilbert-Kunz multiplicity (with Yongwei Yao), in preparation.

  • Liftable integral closure (with Bernd Ulrich), preprint 2010.

  • A dual to tight closure theory (with Karl Schwede), arXiv:1110.4647, submitted.

  • Special and specific parts of closures (with Holger Brenner), in preparation.

  • Hilbert-Kunz multiplicity of products of ideals (with Javid Validashti), in preparation.

  • Zero-divisor graphs of nilpotent-free semigroups (with Peyman Nasehpour), arXiv:1112.0185, submitted.

  • Pseudostar operations, in preparation.