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 statement (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 a semicontent algebra (with Jay Shapiro), submitted.
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,