EMAIL: nepstei2 'at' gmu.edu
I have been a tenure-track
assistant professor at George Mason since August, 2012. My research
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).
| research statements (2011 , 2017)
tight closure analogue of analytic spread,
Math. Proc. Cambridge Philos. Soc. 139 (2005), no. 2, 371-383.
depth and flat base change, Proc. Amer. Math. Soc. 134
depth and stable phantom exactness,
Trans. Amer. Math. Soc. 359 (2007), 4829-4864.
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.
of ideals, and matroids (with Joseph P.
Brennan), Proc. Amer.
Math. Soc. 139 (2011), no. 8,
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
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.
Stanley-Reisner rings (with Hop D. Nguyen), arXiv:1301.3967, J. Pure
Appl. Algebra 218 (2014), no.
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
Collect. Math. 68 (2017), no. 1, 69-85.
Continuous closure, axes
natural closure (with Mel Hochster), arXiv:1106.3462, to appear in Trans. Amer. Math. Soc.
(with Bernd Ulrich),
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
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 semicontent algebras (with Jay Shapiro), in preparation.
Homogeneous equational closures,
tight closure, and localization (with Mel Hochster),
Unmixed Hilbert-Kunz multiplicity
(with Yongwei Yao),
Special and central parts of
Brenner), in preparation.
Non-Noetherian tight closure,