Research Interest

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Research Interest

My research interest lies in the field of commutative algebra with applications towards algebraic geometry. I investigate the structure of local rings by analyzing their singularities with algebraic tools. Current topics of interest include tight closure theory, local cohomology, direct summand conjecture, multiplicities. I am also interested in applications of polynomial algebras to digital circuit design. Below there is a list of my papers.

Papers

Local cohomology and F-stability
preprint Pdf
Lower bounds for Hilbert-Kunz multiplicities for local rings of fixed dimension (with Ian M. Aberbach)
Michigan Math. Journal, to appear. Pdf
The Frobenius structure of local cohomology (with Melvin Hochster)
Algebra and Number Theory, to appear. Pdf
Briancon-Skoda for Noetherian filtrations
Analele Stiintifice Univ. Ovidius, Seria Math, vol XV 2007, fasc. 1, pages 91--96 (volume dedicated to Prof. Dorin Popescu with the occasion of his sixtieth birthday). Pdf
Asymptotic growth of powers of ideals (with Cătălin Ciupercă and Sandra Spiroff)
Illinois Journal of Mathematics (volume in honor of Phillip Griffith), to appear. Dvi Pdf
When does the F-signature exist? (with Ian M. Aberbach)
Ann. Fac. Sci. Toulouse Math. (6), 15, 2006, no. 2, 195--201. Dvi Pdf
On the upper-semicontinuity of the Hilbert-Kunz multiplicity (with Kazuma Shimomoto)
Journal of Algebra, 285, no. 1, pages 222-237 [To journal] Postscript Dvi Pdf
The Structure of F-pure rings (with Ian M. Aberbach)
Math. Zeit., 240, no. 4, 2005, 791--806. [To journal] Postscript Dvi Pdf
On rings with small Hilbert-Kunz multiplicity (with Manuel Blickle)
Proc. Amer. Math. Soc. 132 (2004), no. 9, 2505--2509 (electronic). Postscript Pdf
An inequality involving tight closure and parameter ideals (with Cătălin Ciupercă)
Bulletin of the London Math. Society, 36 (2004), no. 3, 351--357 Postscript Dvi Pdf To journal
Strong test modules and multiplier ideals
manuscripta mathematica, 111 (2003), no. 4, 487--498. Postscript Dvi Pdf [To journal]
F-injective rings and F-stable primes
Proceedings of the AMS, 131 (2003), 3379--3386. Postscript Dvi Pdf[To journal]
Applications of pseudocanonical covers to tight closure problems
Journal of Pure and Applied Algebra, 178 (2003) 159--167. Postscript Pdf[To journal]
Test ideals and base change problems in tight closure theory (with Ian M. Aberbach)
Trans. Amer. Math. Soc. 355, no. 2, (2003), 619--636 . Dvi Postscript Pdf[To journal]
On the behavior of F-rational rings under flat base change
J. Algebra 233 (2000), no. 2, 543--566. [ To journal]
Infinitesimal module deformations in the Thom-Sebastiani problem (with Gerhard Pfister and Dorin Popescu)
Arch. Math. (Basel) 69 (1997), no. 3, 196--208. [ To journal]

Papers on polynomial algebra applications to digital circuit design

Simulation Bounds for Equivalence Verification of Polynomial Datapaths using Finite Ring Algebra
(with Namrata Shekhar, Priyank Kalla, M. Brandon Meredith) Submitted, in review IEEE Trans. on VLSI, special section on Design Validation and Verification.

Equivalence Verification of Polynomial Datapaths using Ideal Membership Testing
(with Namrata Shekhar, Priyank Kalla)
To appear in IEEE Trans. on CAD.

Optimization of Arithmetic Datapaths with Finite Word-Length Operands
(with Sivaram Gopalakrishnan, Priyank Kalla)
To appear in Asia/South-Pacific DAC, ASP-DAC (2007).

Simulation Bounds for Equivalence Verification of Arithmetic Datapaths with Finite Word-Length Operands
(with Namrata Shekhar, Priyank Kalla, M Brandon Meredith)
To appear in Formal Methods in Computer-Aided Design, FMCAD - 2006.

Equivalence Verification of Arithmetic Datapaths with Multiple Word-Length Operands
(with Namrata Shekhar, Priyank Kalla)
To appear in Proceedings of the Design Automation and Test in Europe (DATE) Conf., March 2006.

Equivalence Verification of Polynomial Datapaths with Fixed-Size Bit-Vectors using Finite Ring Algebra
(with Namrata Shekhar, Priyank Kalla, Sivaram Gopalakrishnan)
To appear in Proceedings of the Intl. Conf. on Computer-Aided Design ICCAD, Nov. 2005.

Exploiting Vanishing Polynomials for Equivalence Verification of Fixed-Size Arithmetic Datapaths
(with Namrata Shekhar, Priyank Kalla, Sivaram Gopalakrishnan)
To appear in Proceeding of the Intl. Conf. on Computer Design ICCD, Oct. 2005.