Research

TALKS:
a list
of some recent talks.

CV: my
curriculum
vitae as a pdf
file (latest update April 2010)

GRANTS:
my research was supported in part by the following grants

- NSF:
grant
for 2005-2008 in the amount of $71,994. Project: Ultraproducts
of Noetherian local rings:
properties and applications.

- PSC-CUNY:
one-year grants from 2005-2010.

- COLLABORATIVE
INCENTIVE: grant for 2005-2008 in the amount of
$74,922. This project is a collaboration between 6 CUNY faculty,
Professors Apter (Baruch), Hamkins (CSI), Miller (Queens), Kossak,
Liebman (BCC) and myself (Citytech), to do research and organize seminars/conferences in mathematical
logic. A detailed description of our project can be found here:
**CUNY Collaboration in Mathematical Logic.**

RESEARCH
INTEREST

- Algebraic Model Theory: Definability and constructibility in algebraic geometry and commutative algebra, transfer principles, uniform bounds, Artin Approximation, dimension theory, generalized Grothendieck groups.
- Commutative Algebra: Tight closure, big Cohen-Macaulay algebras, homological conjectures, number of generators of an ideal, flatness, local rings of finite embedding dimension, order dimension, Gorenstein hulls.
- Algebraic
Geometry: Constructible properties and invariants, set-theoretic
complete
intersections, rational singularities, vanishing theorems,
classification of singularities, motivic rationality, infinite cycles.

- Rigid Analytic Geometry: Rigid subanalytic sets, flattening.
- Valuation theory: singular valuations, average of a valuation and value semi-groups, total blow-up ring.