- The Role of defect and splitting in finite generation of extensions of associated graded rings along a valuation
- Rectilinearization of sub analytic sets as a consequence of local monomialization
- A stronger local monomialization theorem, to appear in ``Homological and Computational Methods in Commutative Algebra'', Springer.
- Local Monomialization of Analytic Maps, to appear in Advances in Math.
- A generalization of the Abhyankar Jung theorem to associated graded rings of valuations, Math. Proc. of the Cambridge Philosophical Society 160 (2016), 233 - 255.
- Ramification of valuations and local rings in positive characteristic, Communications in Algebra 44 (2016), 233 -255.
- Counterexamples to local monomialization in positive characteristic, Math. Annalen 362 (2015), 321 - 334.
- Asymptotic Multiplicities, Journal of Algebra 442 (2015), 2489 - 2505.
- Ramification of local rings along valuations (with Pham An Vinh), Journal of Pure and Applied Algebra 219 (2015), 2489 - 2505.
- Limits in commutative algebra and algebraic geometry, in ``Commutative Algebra and Noncommutative Algebraic Geometry'', Volume 67 of the MSRI book series, Cambridge Univ. 2015.
- Teissier's problem on inequalities of nef devisors (Abhyankar Volume) Journal of Algebra and its Applications 14 (2015), 139 - 147.
- Asymptotic multiplicities of graded families of ideals and linear series, Advances in Math. 264 (2014), 55 - 113.
- Multiplicities Associated to Graded Families of Ideals, Algebra and Number Theory 7 (2013), 2059 - 2083.
- \'Etoiles and valuations, J. Pure Applied Algebra 221 (2017), 588 - 610.
- 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), Proceedings of the London Math. Soc. 108 (2014), 25 - 384.
- Asymptotic growth of saturated powers and epsilon multiplicity, Math. Research Letters 18 (2011), 93 - 106.
- A simpler proof of toroidalization of morphisms from 3-folds to surfaces, Annales de L'Institut Fourier 63 (2013), 865 - 922.
- 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 (Hironaka Volume), Asian J. Math. 15 (2011), 369 - 416.
- Asymptotic Regularity of Powers of Ideals of Points in a Weighted Projective Space (with Kazuhiko Kurano), Kyoto Journal of Math. 51 (2011), 25 - 45.
- Abhyankar's Proof of Uniformization in $p$-cyclic Galois Extensions.
- Formal Prime Ideals of Infinite Value and Their Algebraic Resolution (with Samar ElHitti) Annales de La Facult\'e des Sciences de Toulouse, Math\'ematiques, 19 (2010), 635 - 649.
- 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) Communications in Algebra 38 (2010), 2768 - 2789.
- Semigroups of valuations on local rings, II (with Bernard Teissier) American J. Math., 132 (2010), 1223 - 1247.
- Finite Generation of Algebras Associated to Powers of Ideals (with Juergen Herzog and Hema Srinivasan) Math. Proc. of the Camb. Phil. Soc. 148 (2010), 55 -72.
- Algebraic Series and Valuation Rings over Nonclosed Fields (with Olga Kashcheyeva), J. Pure App. Alf. 212 (2008), 1996 - 2010.
- Semigroups of valuations on local rings (with Bernard Teissier), Mich. Math. J. 57 (2008), 173 - 194.
- Duality and tameness (with Marc Chardin, Juergen Herzog and Hema Srinivasan), Mich. Math. J. 57 (2008), 137 - 156.
- Failure of tameness for local cohomology (with Juergen Herzog), J. Pure App. Alg. 212 (2008), 1996 - 2010.
- Resolution of singularities for 3-folds in positive characteristic, Amer. J. Math. (2009), 59 - 127.
- Toroidalization of dominant morphisms of 3-folds, Memoirs of the AM, 190, AMS, Providence (2007), 222 pages.
- Graded algebras associated to surface singularities.
- Toroidalization of Morphisms (Lectures from December 2004 Banff workshop).
- Factorizations of birational extensions of local rings (with Hema Srinivasan in Griffith Volume) Illinois Journal of Math. 51 (2007), 41 -56.
- Toroidalization of dominant morphisms of 3-folds, Memoirs of the AM, 190, AMS, Providence (2007), 222 pages.
- Asymptotic behavior of the length of local cohomology (with Tai Ha, Hema Srinivasan and Emanoil Thoedorescu) Canadian J.Math. 57 (2005), 1178 - 1192.
- Completions of Valuation Rings (with Laura Ghezzi) Contemporary Math. 386 (2005), 13 - 34.
- Local Monomialization of Transcendental Extensions, Annales de L'Institut Fourier 55 (2005), 1517 - 1586.
- Poincare series of resolutions of surface singularities (with Juergen Herzog and Ana Reguerra) Transactions of the AMS 356 (2003), 1833 - 1874.
- Poincare series of line bundles on varieties, in ``A Tribute to C.S. Seshadri'', Hindustan Book Agency, 2003, 220 - 240.
- Arithmetic Macaulayfication (with Huy Tai Ha, in Vasconcelos Volume) Journal of Pure and Applied Algebra 201 (2005), 49 - 61.
- Monomialization of Strongly prepared Morphisms from Nonsingular N-folds to Surfaces (with Olga Kashcheyeva), Journal of Algebra 275 (2004), 275 - 320.
- Ramification of Valuations (with Olivier Piltant) Advances in Mathematics 183 (2004), 275 - 320.
- 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. 321 (2001), 213 - 234.
- Monomial Resolutions of Morphisms of Algebraic Surfaces (with O. Piltant) Communications in Algebra 28 (Hartshorne Volume) (2000), 5935 - 5960.
- Vanishing of differentials along ideals and non-archimedean approximation (with Reinhold Huebl) Math. Annalen 317 (2000), 295 - 308.
- Irrational asymptotic behaviour of Castelnuovo-Mumford regularity, Journal f\"ur die Reine und Angewandte Mathematik 522 (2000), 93 - 103.
- Local monomialization and factorization of morphisms, Ast\'erisque 260 (1999), 143 pages.
- Errata to Local monomialization and factorization of morphisms
- Simultaneous resolution of singularities, Proc. Amer. Math. Soc. 128 (2000), 1905 - 1910.
- Asymptotic behaviour of the Castelnuovo-Mumford regularity (with Juergen Herzog and Ngo Viet Trung) Compositio Math. 118 (1999), 243 - 261.
- The Algebraic Fundamental Group of a Curve Singularity (with Hema Srinivasan) J. Algebra 230 (Buchsbaum Volume) (2000), 101 -126.