Papers since 1999

Kahler differentials, almost mathematics and deeply ramified fields

Generating Sequences of valuations on simple extensions of domains (with Razieh Ahmadian).

Kahler differentials of extensions of valuation rings and deeply ramified fields (with Franz-Viktor Kuhlmann).

Epsilon multiplicity and analytic spread of filtrations (with Parangama Sarkar), to appear in Illinois Journal of Math.

On the Computation of Kahler Differentials and Characterization of Galois Extensions with Independent Defect  (with Franz-Viktor Kuhlmann and Anna Rzepka).

A counterexample to strong local monomialization in a tower of two independent Artin-Schreier extensions, to appear in Annales de la Faculte des Sciences Toulouse. 

The Asymptotic Samuel Function of a Filtration (with Smita Praharaj). 

Analytic spread and associated primes of divisorial filtrations, to appear in Proc. AMS.

Analytic spread of filtrations on two dimensional normal local rings, Nagoya Math. Journal 249 (2023), 239 - 268.

Erratic birational behavior of mappings in positive characteristic, to appear in Mathematische Nachrichten.

Abhyankar's fundamental work on resolution of singularities, to appear in The Mathematics Student.

The Minkowski equality of big divisors, to appear in Michigan Math. Journal. 

Analytic spread of filtrations and symbolic algebras (with Parangama Sarkar),  Journal of the London Math. Soc. 106 (2022), 2635 - 2662.

Multiplicities and mixed multiplicities of arbitrary filtrations (with Parangama Sarkar),  Research in the Mathematical Sciences 9, volume in honor of Juergen Herzog (2022).

Multiplicities and mixed multiplicities of filtrations (with Hema Srinivasan), in Commutative Algebra: Expository papers dedicated to David Eisenbud on the occasion of his 75th birthday, Irena Peeva editor, Springer Cham, 2021, 299 - 316.

Volumes of line bundles on schemes (with Roberto Nunez), Proc. AMS. 149 (2021), 4099 - 4108. 

The Minkowski equality of filtrations, Advances in Math. 388 (2021).

Examples of multiplicities and mixed multiplicities of filtrations in Commutative Algebra - 150 years with Roger and Sylvia Wiegand, Contemporary Math. 773 (2021), 19 - 34.

Local uniformization of Abhyankar valuations,  Michigan Math. J. 71 (2022), 859 - 896. 

Essential finite generation of valuation rings in characteristic zero algebraic function fields, to appear in Algebra and Number Theory 

Essentially finite generation of valuation rings in terms of classical invariants (with Josnei Novacoski), Math. Nachrichten 294 (2021), 15 - 37

Extensions of valuations to the Henselization and completion of a local ring, in Banach Center Publications Vol 121, Proceedings of the 5th joint conference on Algebra, Logic and Number Theory  

Mixed multiplicities of divisorial filtrations, Adv. Math. 358 (2019) 

Positivity of mixed multiplicities of filtrations (with Hema Srinivasan and Jugal Verma), Bulletin London Math. Soc. 52 (2020), 335 - 348 

On the construction of valuations and generating sequences on hypersurface singularities (with Hussein Mourtada and Bernard Teissier), Algebraic Geometry, Foundation Compositio Mathematica 8 (2021), 19 - 34 

Mixed multiplicities of filtrations (with Parangama Sarkar and Hema Srinivasan), Transactions Amer. Math. Soc. 372 (2019), 6183 - 6211

Extensions of valuations to the Henselization and completion, Acta Mathematica Vietnamica 44 (2019), 159 - 172 

Defect and local uniformization (with Hussein Mourtada), Revista de la Real Acadadamia de Ciencias Exactas, Fisicas y Naturales, Serie A. Mathematicas (Volume in honor of Felipe Cano), 113 (2019), 4211 - 4266 

On finite and nonfinite generation of associated graded rings of Abhyankar valuations, in Singularities, Algebraic Geometry, Commutative Algebra and related topics, Festschrift for Antonio Campillo on the occasion of his 65th birthday, Springer 2018  

Errata to: On finite and nonfinite generation of associated graded rings of Abhyankar valuations 

Fibers of rational maps and Jacobian matrices (with Mark Chardin and Quang Hoa Tran), Journal of Algebra (Volume in honor of Craig Huneke) 571 (2021), 40 - 54 

Finite generation of extensions of associated graded rings along a valuation, J. London Math. Soc. 98 (2018), 177 - 203

The role of defect and splitting in finite generation of associated graded rings along a valuation, Algebra Number Theory 11 (2017), 1461 - 1488.

A stronger local monomialization theorem, in Homological and computational methods in commutative algebra, Springer INdAM Series 20 (2017) 

Local monomialization of analytic maps, Advances in Math. 307 (2017), 833 - 902

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), 2828 - 2866

Counterexamples to local monomialization in positive characteristic, Math. Annalen 362 (2015), 321 - 334

Ramification of local rings along valuations (with Phan An Vinh), Journal of Pure and Applied Algebra 219 (2015), 2489 - 2505

Asymptotic multiplicities, Journal of Algebra 442 (2015), 260 - 298

Limits in commutative algebra and algebraic geometry, in Volume 67 of the MSRI book series, Cambridge Univ. 2015

Teissier's problem on inequalities of nef divisors, Journal of Algebra and its Applications 14 (2015) (volume in honor of Shreeram Abhyankar) 

Asymptotic multiplicities of graded families of ideals and linear series, Advances in Mathematics 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, Proceedings of the 7th Japan-Vietnam joint seminar on commutative algebra, Quy Nhon University, Vietnam, Dec. 12 - 16, 2011

Valuation semigroups of two dimensional local rings (with Pham An Vinh), Proceedings of the London Math. Soc. 108 (2014), 250 - 284

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, Asian Journal of Math. 15 (2011), 369 - 416 (volume in honor of Hironaka)

Asymptotic regularity of powers of ideals of points in a weighted projective space (with Kazuhiko Kurano), Kyoto Journal of Math. 51 (2011), 25 - 45 (volume in honor of Nagata)

Formal prime ideals of infinite value and their algebraic resolution  (with Samar ElHitti), Annales de la Faculte des Sciences de Toulouse, Mathematiques 19 (2010), 635 - 649

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 Herzon and Hema Srinivasan), Math. Proc. Camb. Phil. Soc. 148 (2010), 55 - 72

Algebraic series and valuation rings over nonclosed fields (with Olga Kascheyeva), J. Pure and Applied Algebra 212 (2008), 1996 - 2010

Semigroups of valuations on local rings (with Bernard Teissier), Mich. Math. J. 57 (2008), 173 - 194 (volume in honor of Hochster)

Duality and tameness (with Marc Chardin, Juergen Herzog and Hema Srinivasan), Mich. Math. J. 57 (2008), 137 - 156 (volume in honor of Hochster)

Failure of tameness for local cohomology  (with Juergen Herzog), J. Pure and Applied Algebra 211 (2007), 428 - 432

Resolution of singularities for 3-folds in positive characteristic, Amer. J. Math 131 (2009), 59 - 127

Toroidalization of dominant morphisms of 3-folds, Memoirs of the AMS, Volume 190, American Math. Soc., Providence (2007)

Multi-graded algebras associated to surface singularities, Contemporary Math. 390 (2005), 73 - 84

Factorizations of birational extensions of local rings (with Hema Srinivasan), Illinois Journal of Math. 51 (2007), 41 - 56 (volume in honor of Phil Griffith)

Asymptotic behavior of the lengh of local cohomology  (with Tai Ha, Hema Srinivasan and Emanoil Theodorescu), 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 Reguera), Transactions of the AMS 356 (2003), 1833 - 1874

Poincare series of line bundles on varieties in A tribute to C.S. Sheshadri, Hindustan Book Agency, 2003, 147 - 158

Arithmetic Macaulayification of projective schemes (with Tai Ha), Journal of Pure and Applied Algebra 201 (2005), 49 - 61 (volume in honor of Vasconcelos)     

Monomialization of strongly prepared morphisms from nonsingular N-folds to surfaces (with Olga Kascheyeva), Journal of Algebra 275 (2004), 275 - 320

Ramification of valuations (with Olivier Piltant), Advances in Math. 183 (2004), 1 - 79

Generically finite morphisms and simultaneous resolution of singularities, in Commutative Algebra (Grenoble/Lyon 2001), Contemporary Math. 331 (2003), 75 - 99

Monomialization of morphisms from 3-folds to surfaces, Springer Lecture Notes LNM 1786 (2002)  

Positivity and complexity of ideal sheaves (with Lawrence Ein and Robert Lazarsfeld), Math. Annalen 321 (2001), 213 - 234

Monomial resolutions of morphisms of algebraic surfaces (with Olivier Piltant), Communications in Algebra 28 (2000), 5935 - 5960 (volume in honor of Hartshorne)

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 fur die Reine und Angewandte Mathematik 552 (2000), 93 - 103 

Local monomialization and factorization of morphisms, Asterisque 260 (1999)

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. (1999), 243 - 261 

The algebraic fundamental group of the complement of a curve singularity (with Hema Srinivasan), J. Algebra 230 (2000), 101 - 126 (Buchsbaum volume)