arXiv preprints from January 1, 2026 through September 22, 2026 — 09:33:22 EST
We consider here several aspects of the following challenging question: is it possible to use a passive cloak to make invisible a dielectric inclusion on a finite frequency interval in the quasistatic regime of Maxwell's equations for an observer close to the object? In this work, by considering the Dirichlet-to-Neumann (DtN) map, we...
In this work, we investigate a modified version of the classical SIS model that incorporates hospitalization for treatment and disease-induced mortality, aiming to more accurately capture the dynamics relevant to health insurance pricing models. More precisely, we introduce a new framework, referred to as the SISHD model, which...
Let $(\mathbf{U}, \mathbf{U}^\imath)$ be a quasi-split affine quantum symmetric pair of type $\mathsf{AIII}$. This case is of particular interest thanks to the existence of geometric realizations and Schur--Weyl dualities. We establish factorization and coproduct formulae for the Drinfeld--Cartan series $\boldsymbolΘ_i(z)$ in the...
This survey provides a practical and algorithmic perspective on Drinfeld modules over $\mathbb F_q[T]$. Starting with the construction of the Carlitz module, we present Drinfeld modules in any rank and some of their arithmetic properties. We emphasise the analogies with elliptic curves, and in the meantime, we also highlight key...
The study of projectively equivalent metrics, i.e., metrics sharing the same unparametrized geodesics, is a classical and well-established area of investigation. In the Kaehler context, such branch of research goes by the name of c-projective geometry: it mainly studies c-projectively equivalent metrics, i.e., Kaehler metrics sharing...
These are the notes for a mini-course on the problem of determining knots by means of their cyclic branched coverings given at the Workshop on Branched Covers held at IMUS in Seville from November 17 to 21, 2025.
We are interested in how regular a transport velocity field must be in order to control Riesz-type commutators. Estimates for these commutators play a central role in the analysis of the mean-field limit and fluctuations for systems of particles with pairwise Riesz interactions, which we start by reviewing. Our first new result shows...
These notes are designed for those who either plan to work in differential geometry, or at least want to have a good reason not to do it. We discuss smooth curves and surfaces -- the main gate to differential geometry. We focus on the techniques that are absolutely essential for further study, keeping it problem-centered, elementary,...
We study the crossing matrix of a braid and introduce a polynomial invariant for braid systems that is invariant under Hurwitz equivalence. As an application to the study of surface braids and surface links, we also define an invariant that can be used as an indicator of the necessity of Euler fusion or fission between braid systems.
Statistical inference for spatial processes from partially realized or scattered data has seen voluminous developments in diverse areas ranging from environmental sciences to business and economics. Inference on the associated rates of change has seen some recent developments. The literature has been restricted to Euclidean domains,...
Coxeter and Dynkin diagrams classify a wide variety of structures, most notably finite reflection groups, lattices having such groups as symmetries, compact simple Lie groups and complex simple Lie algebras. The simply laced or "ADE" Dynkin diagrams also classify finite subgroups of SU(2) and quivers with finitely many indecomposable...
In this article, we present several different ways to define hyperconvexity in partial metric spaces. In particular, we show that the analogue of the Aronszajn--Panitchpakdi notion of hyperconvexity fails to exhibit certain key properties present in the classical metric setting.
This paper investigates the localization properties of solutions to the semi-classical Schrödinger equation on closed Riemann surfaces. Unlike classical studies that assume a smooth potential, our work addresses the challenges arising from irregular potentials, specifically those that are merely bounded. We employ a regularization...
Is the specific structure of Western tonal harmony a physical inevitability derived from acoustics, or is it merely one solution among many in a purely algebraic landscape? In this paper, we strip away the physics of vibrating strings and treat harmony as the solution to a simple linear system within the cyclic group...
There exist Lakes of Wada in $\mathbb S^n, n\ge 3,$ which are quasiconformally equivalent to a Euclidean ball and are John domains.
We formulate the normalized period conjecture proposed by Ben-Zvi, Sakellaridis and Venkatesh in the framework of the categorical local Langlands correspondence and study its relation to distinction problems. Motivated by the work of Feng and Wang in the geometric setting, we verify the conjecture for the Iwasawa-Tate and Hecke...
We investigate convergence of the expectation maximization algorithm by representing it as a generalized proximal method. Convergence of iterates and not just in value is investigated under natural hypotheses such as definability of the incomplete data log-likelihood in the sense of o-minimal structure theory.
We establish a loop space decomposition for certain $CW$-complexes with a single top cell in the presence of a spherical pair, thereby generalizing several known decompositions of Poincaré duality complexes in which a loop of a product of spheres appears as a direct summand. This decomposition is further applied to derive results on...
We study a hybrid computational model for integer factorization in which the only non-classical resource is access to an \emph{iterated diffusion process} on a finite graph. Concretely, a \emph{diffusion step} is defined to be one application of a symmetric stochastic matrix (the half-lazy walk operator) to an $\ell^{1}$--normalized...
We derive and analyze well-posed, energy- and entropy-stable boundary conditions (BCs) for the two-dimensional linear and nonlinear rotating shallow water equations (RSWE) in vector invariant form. The focus of the study is on subcritical flows, which are commonly observed in atmospheric, oceanic, and geostrophic flow applications. We...
We introduce and analyze a class of interacting particle systems on the real line that combine features of the stochastic rat race and (deterministic) follow-the-leader models. The particle system evolves as a continuous-time pure jump process: the leading particle moves independently, at Exponential jump times, with constant jump...
We introduce variational spectral learning (VSL), a machine learning framework for solving partial differential equations (PDEs) that operates directly in the coefficient space of spectral expansions. VSL offers a principled bridge between variational PDE theory, spectral discretization, and contemporary machine learning practice. The...
According to the well-known Heyde theorem, the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of $n$ independent random variables given another. In the article, we prove an analogue of this theorem for two independent random variables taking values in a...
In this paper, we investigate left invariant Riemannian metrics on Lie groups with one and two-dimensional commutator subgroups. We explicitly provide the Levi-Civita connection, sectional curvature, and Ricci curvature, and we give computable necessary and sufficient conditions for these Riemannian manifolds to be Ricci solitons....
For any code loop $L$, we prove that the half-automorphism group of $L$ is the product of the automorphism group of $L$ by an elementary abelian $2-$group consisting of all half-automorphisms that acts as the identity on a fixed basis. Also, we prove that elementary mappings only can be a half-automorphism on code loops of rank at most $3$.