Research
Research
Research
Research
146+ open-access research outputs.
We develop a family-based route to unicyclic graphs whose independence polynomials are unimodal but not log-concave. The paper is organized around one flagship statement: for the explicit KL-closure f…
A Somos sequence of order $n$ is defined by a quadratic recurrence of width $n + 1$. Some of the remarkable properties of these sequences for small $n$ are tied to certain matrices built out of them b…
We prove an $L^2$-stability estimate for the variance Brascamp-Lieb inequality [J. Funct. Anal. 22 (4), 366-389 (1976)] by bootstrapping the recent $L^1$-stability theorem of Machado and Ramos [arXiv:…
Recently, Ramos and Whiting showed that any generalized cluster algebra of geometric type is isomorphic to a quotient of a subalgebra of a certain cluster algebra. Based on their idea and method, we s…
In this article we give an elementary introduction to the representation theory of finite magnetic groups from a purely mathematical point of view. -- En este art\'iculo damos una introducci\'on e…
We investigate the special fibers associated with certain coordinate sections of Hankel determinantal ideals. We provide explicit descriptions of their defining equations, showing that these equations…
We present a generalization of the classical Nicomachus' identity for the sum of the first $n$ cubes. Unlike previous generalizations, it has three rather than two terms, and involves not just one, bu…
We prove sharp spectral gap estimates on compact manifolds with integral curvature bounds. We generalize the results of Kr\"oger (Kr\"oger '92) as well as of Bakry and Qian (Bakry-Qian '00) to the cas…
This work investigates transmission conditions for the domain decomposition-based coupling of subdomain-local models using the non-overlapping Schwarz alternating method (NO-SAM). Building on prior ef…
We introduce classes of restricted walks, surfaces and their generalisations. For example, self-osculating walks (SOWs) are supersets of self-avoiding walks (SAWs) where edges are still not allowed to…
We prove stability results in hypercontractivity estimates for the Hopf--Lax semigroup in $\mathbb R^n$ and apply them to deduce stability results for the Euclidean $L^p$-logarithmic Sobolev inequalit…
We consider a nodal curve $C$ in the complex projective plane whose irreducible components $C_i$ are smooth. A minimal set of generators $G$ for the first and second syzygy modules of the Jacobian ide…
We recall a higher dimension analog of the classic plane de Jonqui\`eres transformations, as given by Hassanzadeh and Simis. Such a parameterization defines a birational map from $\mathbb{P}^{n-1}$ to…
In this note, we show that to each elliptic curve of the form $$y^2-axy-y=x^3-bx^2-cx,$$ we can associate a family of lattice paths whose step set is determined by the parameters of the elliptic curve…
Stavskaya's process, a discrete-time version of the contact process on $\Z$, is known to exhibit a phase transition at a critical parameter $\alpc$ whose exact value remains an open problem. Recent wo…
In this paper, we construct singular Lagrangian fibrations on some examples of disk cotangent bundles in dimensions 4 and 6. As an application, we show how this construction can be used to obtain tori…
We propose a novel parametrization of Cumulative Prospect Theory (CPT), as developed by Daniel Kahneman and Amos Tversky, that yields an explicit gamble valuation formula for Gaussian reward distribut…
Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study circuit varieties of m…
In this paper we present a proof of sharp boundedness of the discrete 1-dimensional Hardy-Littlewood nontangential maximal operator, when the parameter is in the range $[\frac{1}{3},+\infty)$. This ge…
We give an exposition of some connections between Fourier optimization problems and problems in number theory. In particular, we present some recent conditional bounds under the generalized Riemann hy…
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