- Finite generation of extensions of associated graded rings along a valuation
- The role of defect and splitting in finite generation of associated graded rings along a valuation
- Rectilinearization of sub analytic sets as a consequence of local monomialization
- A stronger local monomialization theorem
- Local Monomialization of Analytic Maps
- A generalization of the Abhyankar Jung theorem to associated graded rings of valuations
- Ramification of valuations and local rings in positive characteristic
- Counterexamples to local monomialization in positive characteristic
- Asymptotic Multiplicities
- Ramification of local rings along valuations (with Pham An Vinh).
- Limits in commutative algebra and algebraic geometry
- Teissier's problem on inequalities of nef devisors
- Asymptotic multiplicities of graded families of ideals and linear series
- Multiplicities Associated to Graded Families of Ideals
- Complex analytic morphisms and etoiles
- Lectures on Geometric Methods in Commutative Algebra, from the 7th Japan Vietnam joint conference in commutative algebra.
- Valuation semigroups of two dimensional local rings (with Pham An Vinh).
- Asymptotic growth of saturated powers and epsilon multiplicity.
- A simpler proof of toroidalization of morphisms from 3-folds to surfaces.
- Errata to A simpler proof of toroidalization of morphisms from 3-folds to surfaces.
- A skeleton key to Abhyankar's proof of embedded resolution of characteristic p surfaces.
- Asymptotic Regularity of Powers of Ideals of Points in a Weighted Projective Space (with Kazuhiko Kurano).
- Abhyankar's Proof of Uniformization in $p$-cyclic Galois Extensions.
- Formal Prime Ideals of Infinite Value and Their Algebraic Resolution (with Samar ElHitti).
- Lectures on Resolution of Singularities, from the Workshop on Multiplicity Conjectures, Resolution of Singularities and Toric Geometry, IIT Madras, Dec. 22, 2008 - Jan 3, 2009.
- Growth of rank 1 valuation semigroups (with Kia Dalili and Olga Kashcheyeva).
- Semigroups of valuations on local rings, II (with Bernard Teissier).
- Asymptotic growth of algebras associated to powers of ideals (with Juergen Herzog and Hema Srinivasan).
- Semigroups of valuations dominating local domains.
- Algebraic Series and Valuation Rings over Nonclosed Fields (with Olga Kashcheyeva).
- Semigroups of valuations on local rings (with Bernard Teissier).
- Duality and tameness (with Marc Chardin, Juergen Herzog and Hema Srinivasan).
- Failure of tameness for local cohomology (with Juergen Herzog).
- Resolution of singularities for 3-folds in positive characteristic.
- Toroidalization of dominant morphisms of 3-folds.
- Strong toroidalization of dominant morphisms of 3-folds.
- Graded algebras associated to surface singularities.
- Strong toroidalization of birational morphisms of 3-folds.
- Toroidalization of Morphisms (Lectures from December 2004 Banff workshop).
- Factorizations of birational extensions of local rings (with Hema Srinivasan)
- Toroidalization of birational morphisms of 3-folds
- Asymptotic behavior of the length of local cohomology (with Tai Ha, Hema Srinivasan and Emanoil Thoedorescu)
- Completions of Valuation Rings (with Laura Ghezzi)
- Local Monomialization of Transcendental Extensions
- Poincare series of resolutions of surface singularities (with Juergen Herzog and Ana Reguerra)
- Poincare series of line bundles on varieties (in a volume in honor of Professor Seshadri's 70th birthday)
- Arithmetic Macaulayfication (with Huy Tai Ha, in a volume of Journal of Pure and Applied Algebra in honor of Professor Vasconcelos 65th birthday)
- Monomialization of Strongly prepared Morphisms from Nonsingular N-folds to Surfaces (with Olga Kashcheyeva, in Journal of Algebra)
- Ramification of Valuations (with Olivier Piltant, in Advances in Mathematics)
- Generically finite Morphisms and simultaneous resolution of singularities (in Contemporary Mathematics)
- Monomialization of Morphisms from 3 Folds to Surfaces (Springer Lecture Notes in Math 1786, 2002)
- Positivity and complexity of ideal sheaves (with L. Ein and R. Lazarsfeld), Math Ann. 2001
- Monomial Resolutions of Morphisms of Algebraic Surfaces (with O. Piltant)
- Vanishing of differentials along ideals and non-archimedean approximation (with Reinhold Huebl)
- Irrational asymptotic behaviour of Castelnuovo-Mumford regularity
- Local monomialization and factorization of morphisms
- Errata to Local monomialization and factorization of morphisms
- Simultaneous resolution of singularities
- Asymptotic behaviour of the Castelnuovo-Mumford regularity (with Juergen Herzog and Ngo Viet Trung)
- The Algebraic Fundamental Group of a Curve Singularity (with Hema Srinivasan)