## 49076 Osnabrück, Germany

**EMAIL: nepstein 'at' uni-osnabrueck.de**

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.