11 citations · 19 across the 14 of their papers we have counts for
15 papers
Programmable Compute-in-Transit using Integrated Photonics
Imon Kundu, Livi Hammond, Jamie Todd +8
Modern hardware designs for AI and cryptography treat data transit and processing separately. At Optalysys we have demonstrated programmable Photonic hardware that computes mathema…
New versions of Frobenius and integral closure of ideals
Kriti Goel, Kyle Maddox, William D. Taylor
In this article, we define three new operations on ideals which generalize integral closure and Frobenius closure of ideals, whose definitions incorporate an auxiliary ideal and a…
Computing mixed multiplicities, mixed volumes, and sectional Milnor numbers
Kriti Goel, Vivek Mukundan, Sudeshna Roy +1
This is an expository version of our paper [arXiv:1902.07384]. Our aim is to present recent Macaulay2 algorithms for computation of mixed multiplicities of ideals in a Noetherian r…
Local cohomology of modular invariant rings
Kriti Goel, Jack Jeffries, Anurag K. Singh
For a field, consider a finite subgroup of with its natural action on the polynomial ring . Let denote the homo…
On the Hilbert-Samuel coefficients of Frobenius powers of an ideal
Arindam Banerjee, Kriti Goel, J. K. Verma
We provide suitable conditions under which the asymptotic limit of the Hilbert-Samuel coefficients of the Frobenius powers of an -primary ideal exists in a Noetherian…
Affine semigroups of maximal projective dimension
Om Prakash Bhardwaj, Kriti Goel, Indranath Sengupta
We generalize the notion of symmetric semigroups, pseudo symmetric semigroups, and row factorization matrices for pseudo Frobenius elements of numerical semigroups to the case of s…
On Row-Factorization relations of certain numerical semigroups
Om Prakash Bhardwaj, Kriti Goel, Indranath Sengupta
Let be a numerical semigroup minimally generated by an almost arithmetic sequence. We give a description of a possible row-factorization $(\RF)$ matrix for each pseudo-Frobeniu…
Generalized Hilbert-Kunz function of the Rees algebra of the face ring of a simplicial complex
Arindam Banerjee, Kriti Goel, J. K. Verma
Let be the face ring of a simplicial complex of dimension and be the Rees algebra of the maximal homogeneous ideal of We…
Hilbert-Kunz function and Hilbert-Kunz multiplicity of some ideals of the Rees algebra
Kriti Goel, Mitra Koley, J. K. Verma
We prove that the Hilbert-Kunz function of the ideal of the Rees algebra , where is an -primary ideal of a -dimensional local ring $(R…
Algorithms for computing mixed multiplicities, mixed volumes and sectional Milnor numbers
Kriti Goel, Vivek Mukundan, Sudeshna Roy +1
We present a package 'MixedMultiplicity' for computing mixed multiplicities of ideals in a Noetherian ring which is either local or a standard graded algebra over a field. This ena…
On the Vanishing of the normal Hilbert coefficients of ideals
Kriti Goel, Vivek Mukundan, J. K. Verma
Using vanishing of graded components of local cohomology modules of the Rees algebra of the normal filtration of an ideal, we give bounds on the normal reduction number. This helps…
Nullstellensätze and Applications
Kriti Goel, Dilip P. Patil, Jugal Verma
In this expository paper, we present simple proofs of the Classical, Real, Projective and Combinatorial Nullstellensätze. Several applications are also presented such as a classica…
The Minkowski equality and inequality for multiplicity of ideals
Kriti Goel, R. V. Gurjar, J. K. Verma
In this exposition of the equality and inequality of Minkowski for multiplicity of ideals, we provide simple algebraic and geometric proofs. Connections with mixed multiplicities o…
Tight Closure of powers of ideals and tight Hilbert polynomials
Kriti Goel, Vivek Mukundan, J. K. Verma
Let be an analytically unramified local ring of positive prime characteristic For an ideal , let denote its tight closure. We introduce the tight Hi…
Eakin-Sathaye type theorems for joint reductions and good filtrations of ideals
Kriti Goel, Sudeshna Roy, J. K. Verma
Analogues of Eakin-Sathaye theorem for reductions of ideals are proved for -graded good filtrations. These analogues yield bounds on joint reduction vectors for a fa…