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, multiplicities, intersection algebras, Frobenius complexity. I am also interested in applications of polynomial algebras to digital circuit design. Below there is a list of my papers.

Papers

Computing Boolean functions from polynomial ideals with prescribed zeroes, (with Priyank Kalla and Jiamin Pan), 2023, submitted for publication.
The growth recurrence and Gelfand-Kirillov base for the ordinary cusp, (with Alan Dills), accepted for publication, Proc. AMS, 2024.
Graded rings of rational twist in prime characteristic, (with Yongwei Yao), accepted for publication, Journal of Pure and Applied Algebra, 2024.
F-rational rings and rational singularities, refereed invited book chapter, International Center for Theoretical Physics Trieste, (2022), submitted for publication, revisions requested in 2023.
Counting skew monomials in the Frobenius skew polynomial ring, (with Alan Dills), Communications in Algebra, DOI: 10.1080/00927872.2022.2148256, 51:5, 1965-1988 (2023).
The generators, relations and type of the Backelin semigroup, (with Arun Suresh), Communications in Algebra, Vol 49, no 12, December 2021, pp. 5083-5092(10).
On the resolution of fan algebras of principal ideals over a Noetherian ring (with T. Cortadellas Benitez and Carlos D'Andrea)
Journal of Algebra (2020), 541 61--97, preprint version.
The Frobenius exponent of Cartier subalgebras (with Felipe Pérez)
Journal of Pure and Applied Algebra 223 ( 2019), 3879-3888, journal, arXiv.
Strong test ideals associated to Cartier algebras (with Irina Ilioaea)
Journal of Algebra and its Applications 19 (2020), no. 3, 2050044, 16 pp journal, arXiv.
Computing the invariants of intersection algebras for principal monomial ideals (with Sandra Spiroff)
Intern. Journal of Alg and Computation 29 2019 no 2 309-332 journal, arXiv.
Test ideals in rings with finitely generated anti-canonical algebras (with Alberto Chiecchio, Lance Edward Miller, Karl Schwede)
J. Inst. Math. Jussieu 17 (2018), no. 1, 171--206
On the Frobenius complexity of determinantal rings (with Yongwei Yao)
J. Pure Appl. Algebra 222 (2018), no. 2, 414--432, arXiv:1503.03164 [mathAC]. Pdf
On subfield-compatible polynomials and a class of Vandermonde-like matrices (with John Hull)
Special volume dedicated to Dorin Popescu. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 60(108) (2017), no. 4, 387--397.
The Frobenius complexity of a local ring of positive prime characteristic (with Yongwei Yao)
J. Algebra 459 (2016), 133--156, arXiv: 1401.0234v1 [mathAC]. Pdf
Intersection algebras for principal monomial ideals in polynomial rings, (with Sara Malec)
J. Algebra Appl. 14 (2015), no. 7, 1550108, 23 pp arXiv version .
New estimates for Hilbert-Kunz multiplicities for local rings of fixed dimension (with I. M. Aberbach)
Nagoya Math Journal, 212 (2013), 59--85. Pdf
Finite-dimensional vector spaces with Frobenius action
"Progress in Commutative Algebra. Ring Theory, Homology, and Decompositions" edited by Sean Sather-Wagstaff, Christopher Francisco, Lee Klingler, and Janet C. Vassilev, publisher: De Gruyter, Germany, 2012.
A finiteness condition on local cohomology in positive characteristic
Journal of Pure and Applied Algebra, 261 (2011) no 1, 115-118.
The lower semicontinuity of the Frobenius splitting numbers (with Yongwei Yao)
Math. Proc. Cambridge Philos. Soc. 150 (2011), no. 1, 35--46. Pdf
Local cohomology and F-stability
Special volume dedicated to Paul Roberts. J. Algebra 332 (2009) 3063--3077. Pdf
Lower bounds for Hilbert-Kunz multiplicities for local rings of fixed dimension (with Ian M. Aberbach)
Special volume in honor of Melvin Hochster. Michigan Math. J. 57 (2008), 1--16. Pdf
The Frobenius structure of local cohomology (with Melvin Hochster)
Algebra Number Theory 2 (2008), no. 7, 721--754. 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) 51 (2007), no. 1, 29--39. 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

Efficient Groebner Basis Reductions for Formal Verification of Galois Arithmetic Field Circuits,
Jinpeng Lv, Priyank Kalla, Florian Enescu, IEEE Transactions on CAD, vol 32, issue 9, 1409-1420, Sept 2013.

Efficient Groebner Basis Reductions for Formal Verification of Galois Field Multipliers,
Jinpeng Lv, Priyank Kalla, and Florian Enescu, Design Automation and Test in Europe (DATE) Conf., 899--904, IEEE 2012.

Verification of Composite Galois Field Multipliers over GF ((2^m)^n) using Computer Algebra Techniques,
Jinpeng Lv, Priyank Kalla, and Florian Enescu, in IEEE High-Level Design Validation and Test Workshop (HLDVT 2011), 2011

Simulation Bounds for Equivalence Verification of Polynomial Datapaths using Finite Ring Algebra
(with Namrata Shekhar, Priyank Kalla, M. Brandon Meredith) IEEE Trans. on VLSI, special section on Design Validation and Verification, April 2008.

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.