Neil Epstein

Assistant Professor
George Mason University
Department of Mathematical Sciences

EMAIL: nepstei2 'at'

I have been a tenure-track assistant professor at George Mason since August, 2012. 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.  Recently I am branching out to applications of commutative algebra in mathematical biology as well. 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, followed by a postdoctoral research position at the University of Osnabrueck from 2009-2012 via the German Research Foundation (DFG).

curriculum vitae  |  research statement (2017) |  teaching

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. 271 (2012), no 3-4, 1193-1210.

  • A guide to closure operations in commutative algebra, in Progress in commutative algebra 2, 1-37, Walter de Gruyter, Berlin, 2012.

  • Zero-divisor graphs of nilpotent-free semigroups (with Peyman Nasehpour), J. Algebraic Combin. 37 (2013), no. 3, 523-543.

  • A dual to tight closure theory (with Karl Schwede), arXiv:1110.4647, Nagoya Math. J 213 (2014), 41-75.

  • Algebra retracts and Stanley-Reisner rings (with Hop D. Nguyen), arXiv:1301.3967, J. Pure Appl. Algebra 218 (2014), no. 9, 1665-1682.

  • Strong Krull primes and flat modules (with Jay Shapiro), arXiv:1303.7458, J. Pure Appl. Algebra 218 (2014), no. 9, 1712-1729.

  • Semistar operations and standard closure operations, arXiv:1304.8067, Comm. Algebra 43 (2015), no. 1 (Special Issue, dedicated to Marco Fontana), 325-336.

  • A Dedekind-Mertens theorem for power series rings (with Jay Shapiro), arXiv:1402.1100, Proc. Amer. Math. Soc. 144 (2016), no. 3, 917-924.

  • The Ohm-Rush content function (with Jay Shapiro), arXiv:1405.1300, J. Algebra Appl. 15 (2016), no. 1, 1650009.

  • Perinormality – a generalization of Krull domains (with Jay Shapiro), arXiv:1501.03411, J. Algebra 451 (2016), 65-84.

  • Some extensions of Hilbert-Kunz multiplicity (with Yongwei Yao), arXiv:1103.4730, Collect. Math. 68 (2017), no. 1, 69-85.

  • Continuous closure, axes closure, and natural closure (with Mel Hochster), arXiv:1106.3462, to appear in Trans. Amer. Math. Soc.

  • Liftable integral closure (with Bernd Ulrich), arXiv:1309.6966, to appear in J. Commut. Algebra.

  • Perinormality in pullbacks (with Jay Shapiro), arXiv:1511.06473, to appear in J. Commut. Algebra.

  • Hilbert-Kunz multiplicity of products of ideals (with Javid Validashti), arXiv:1601.00014, to appear in J. Commut. Algebra.

  • Preprints and projects

  • The Ohm-Rush content function II. Noetherian rings, valuation domains, and base change (with Jay Shapiro), submitted.

  • Gaussian elements of a semicontent algebra (with Jay Shapiro), submitted.

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

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

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

  • Non-Noetherian tight closure, in preparation.