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Jonathan Toledo

Publications and source records attributed to Jonathan Toledo.

12 recordsLinked to original sources
arXiv2026

Strong persistence index and fluctuations in colon powers of monomial ideals

Let $I$ be an ideal in a commutative Noetherian ring $R$. We say that a positive integer $\ell_0$ is the strong persistence index of $I$ if $\ell_0$ is the smallest integer such that $(I^{\ell+1} :_R I) = I^{\ell}$ for all $\ell \geq \ell_0$. The first aim of this paper is to study this notion for monomial ideals. We also introduce the notion of fluctuation in colon powers if there exist positive integers $a < b < c$ such that at least one of the following cases occurs: (i) $(I^{a} : I) = I^{a-1}$, $(I^{b} : I) \neq I^{b-1}$, but $(I^{c} : I) = I^{c-1}$. (ii) $(I^{a} : I) \neq I^{a-1}$, $(I^{b} : I) = I^{b-1}$, but $(I^{c} : I) \neq I^{c-1}$. The second purpose of this work is to study this phenomenon for monomial ideals.

math.AC↗
arXiv2026

Asymptotic Properties of Filtrations of Ideals

We introduce a unified framework for studying persistence phenomena in commutative algebra via filtrations of ideals. For a filtration $\mathcal{F} = \{I_i\}_{i \in \mathbb{N}}$, we define $\mathcal{F}$-persistence and $\mathcal{F}$-strong persistence, extending the classical notions for ordinary and symbolic powers of ideals. We show that if $\mathcal{F}$ is strongly persistent, then $\mathcal{F}_{\mathrm{sym}}$ is strongly persistent, where $\mathcal{F}_{\mathrm{sym}}$ denotes the symbolic filtration associated with the filtration $\mathcal{F}$. In addition, we prove that if $\mathcal{F}$ is strongly persistent, then $\mathcal{F}$ is persistent.

math.AC↗
arXiv2025

Demotions of ideals in commutative rings with applications to normally torsion-freeness

Let J \subseteq I be ideals in a commutative Noetherian ring R, and r,s \geq 0. We say that J is a demotion of I if I^r J^s = I^{r+s} \cap J^s for all r,s \geq 0. In this paper, we mainly aim to explore this notion in polynomial rings. In particular, we investigate the relation between the demotion property and normal torsion-freeness. Furthermore, we compare the reductions of ideals and demotions of ideals.

math.AC↗
arXiv2025

Criteria for the presence of the maximal ideal in the set of associated primes

In this paper, we establish some criteria to detect the presence of the maximal ideal $(x_1, \ldots, x_n)$ in the set of associated primes of powers of monomial ideals in the polynomial ring $K[x_1, \ldots, x_n]$. Furthermore, for each of these criteria, we illustrate its applicability with corresponding examples.

math.AC↗
arXiv2024

On the strong persistence property and normally torsion-freeness of square-free monomial ideals

In this paper, we first show that any square-free monomial ideal in $K[x_1, x_2, x_3, x_4, x_5]$ has the strong persistence property. Next we will provide a criterion for a minimal counterexample to the Conforti-Cornuejols conjecture. Finally we give a necessary and sufficient condition to determine the normally torsion-freeness of a linear combination of two normally torsion-free square-free monomial ideals.

math.AC↗
arXiv2021

Gorenstein homogeneous subrings of graphs

Let $G=(V,E)$ be a connected simple graph, with $n$ vertices such that $S$ is its homogeneous monomial subring. We prove that if $S$ is normal and Gorenstein, then $G$ is unmixed with cover number $\lceil\frac{n}{2}\rceil$ and $G$ has a strong $\lceil\frac{n}{2}\rceil$-$τ$-reduction. Furthermore, if $n$ is even, then we show that $G$ is bipartite. Finally, if $S$ is normal and $G$ is unmixed whose cover number is $\lceil\frac{n}{2}\rceil$, we give sufficient conditions for $S$ to be Gorenstein.

math.CO↗
arXiv2019

The S-matrix Bootstrap IV: Multiple Amplitudes

We explore the space of consistent three-particle couplings in $\mathbb Z_2$-symmetric two-dimensional QFTs using two first-principles approaches. Our first approach relies solely on unitarity, analyticity and crossing symmetry of the two-to-two scattering amplitudes and extends the techniques of [arXiv:1607.06110] to a multi-amplitude setup. Our second approach is based on placing QFTs in AdS to get upper bounds on couplings with the numerical conformal bootstrap, and is a multi-correlator version of [arXiv:1607.06109]. The space of allowed couplings that we carve out is rich in features, some of which we can link to amplitudes in integrable theories with a $\mathbb Z_2$ symmetry, e.g., the three-state Potts and tricritical Ising field theories. Along a specific line our maximal coupling agrees with that of a new exact S-matrix that corresponds to an elliptic deformation of the supersymmetric Sine-Gordon model which preserves unitarity and solves the Yang-Baxter equation.

hep-th↗
arXiv2017

Monomial ideals of weighted oriented graphs

Let I=I(D) be the edge ideal of a weighted oriented graph D. We determine the irredundant irreducible decomposition of I. Also, we characterize the associated primes and the unmixed property of I. Furthermore, we give a combinatorial characterization for the unmixed property of I, when D is bipartite, D is a whisker or D is a cycle. Finally, we study the Cohen-Macaulay property of I.

math.AC↗
arXiv2017

The S-matrix Bootstrap III: Higher Dimensional Amplitudes

We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 3+1 dimensions due to crossing symmetry, analyticity and unitarity. We extremize cubic couplings, quartic couplings and scattering lengths relevant for the elastic scattering amplitude of two identical scalar particles. In the cases where our results can be compared with the older S-matrix literature they are in excellent agreement. We also extremize a cubic coupling in 2+1 dimensions which we can directly compare to a universal bound for a QFT in AdS. This paper generalizes our previous 1+1 dimensional results of arXiv:1607.06109 and arXiv:1607.06110.

hep-th↗
arXiv2017

The S-matrix Bootstrap I: QFT in AdS

We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solutions of the crossing equations in one lower dimension. By sending the curvature radius of the background hyperbolic space to infinity we expect to recover flat-space physics. We explain that this regime corresponds to large scaling dimensions of the boundary operators, and discuss how to obtain the flat-space scattering amplitudes from the corresponding limit of the boundary correlators. We implement this strategy to obtain universal bounds on the strength of cubic couplings in 2D flat-space QFTs using 1D conformal bootstrap techniques. Our numerical results match precisely the analytic bounds obtained in our companion paper using S-matrix bootstrap techniques.

hep-th↗
arXiv2017

The S-matrix Bootstrap II: Two Dimensional Amplitudes

We consider constraints on the S-matrix of any gapped, Lorentz invariant quantum field theory in 1 + 1 dimensions due to crossing symmetry and unitarity. In this way we establish rigorous bounds on the cubic couplings of a given theory with a fixed mass spectrum. In special cases we identify interesting integrable theories saturating these bounds. Our analytic bounds match precisely with numerical bounds obtained in a companion paper where we consider massive QFT in an AdS box and study boundary correlators using the technology of the conformal bootstrap.

hep-th↗