arXiv preprints from January 1, 2026 through September 21, 2026 — 21:18:57 EST
Suppose we are given an arbitrary line bundle $\mathcal{L}$ on a complex algebraic variety $X$, not necessarily smooth. For a positive integer $N$, suppose there exists a global section $s \in Γ(X, \mathcal{L}^{N})$ that defines an effective Cartier divisor $D$. If we denote $π: Y \rightarrow X$ to be the $N$-fold cyclic covering of...
$X$ is a Nakajima quiver variety. In this note we report the observation that the space parameterizing quasimaps from $\mathbb{P}^1$ to $X$, sending infinity to a given point, may be presented globally as the critical locus of an explicit function.
The Turing jump has no fixed point on the Turing degrees: $\mathbf a <_T \mathbf a'$ for every degree $\mathbf a$. After passing to the ideal completion, however, a natural fixed-point phenomenon appears. We study the Scott-continuous lifting $Γ:\operatorname{Idl}(\mathbf D_T)\to\operatorname{Idl}(\mathbf D_T)$, given by...
Spatial patterns, such as those in dryland vegetation models, have historically been studied in systems of reaction-diffusion systems with pattern onset via a Turing bifurcation from a spatially uniform state. More recently, spatial patterns have been considered in models that incorporate spatially extended interactions via nonlocal...
The embedding dimension of categorical predictors is usually selected through heuristic tuning, although it directly affects model complexity, approximation quality, and finite-sample generalization. This paper formulates embedding dimension selection as a constrained allocation problem. The main contribution is to show that embedding...
Many time series are not stable over their full observation horizon, but may contain scientifically meaningful periods during which a signal remains stable up to a prescribed tolerance. We formulate this as an existence test for stable intervals in a non-stationary regression model with dependent, locally stationary errors. For a...
Linear programming (LP) formulations offer a conceptually elegant approach to infinite-horizon, model-free nonlinear optimal control in continuous spaces. However, in addition to the curse of dimensionality, their practical use is limited by the difficulty of consistently obtaining bounded solutions. In this work, we use...
This paper describes the electricity markets and operational processes in the Irish power system and translates them into a Mixed Integer Linear Programming (MILP) model. The model is designed to estimate renewable generation Curtailment and Constraint. A full mathematical formulation is presented and tested on both a simple example...
For a hyper-Kähler fourfold $X$ of generalized Kummer type, we construct an infinitesimal deformation of the tangent bundle $T_X$ with non-zero Yoneda square. This is the first example of a stable hyperholomorphic bundle with obstructed deformations.
We present a quaternionic proof that the quadratic form $t^2+2x^2+5y^2+10z^2$ represents all positive integers, and that the form $t^2+x^2+7y^2+7z^2$ represents all natural numbers which are neither equal to $3 \cdot 7^\ell$ nor equal to $6 \cdot 7^\ell$, for any $\ell \in \mathbb{N}_0$. To do this we introduce a technique that may be...
We prove that the connected sum of a possibly noncompact area enlargeable manifold $M_1$ with an arbitrary spin manifold $M_2$ of the same dimension admits no complete Riemannian metric of uniformly positive scalar curvature. This extends a theorem of Wang--Zhang, where $M_1$ is assumed closed, to noncompact enlargeable summands; in...
We prove that the bracket width of the Lie algebra of vector fields on any smooth affine algebraic variety of dimension $n$ is at most $(n+1)^2$. We give improved bounds for some families of $\mathbb{C}^*$-varieties, in particular for $\mathrm{SL}_n(\mathbb{C})$ and for the Koras--Russell cubic threefold.
We study the fundamental problem of estimating the dependence structure of a centered stationary Gaussian process under local differential privacy (LDP). In this setting, the spectral density characterizes the dependence structure of the data and is the quantity to be estimated. Our main contribution is to close the open...
We show that the higher Legendrian homology of any Legendrian link given by the rainbow closure of a positive braid must necessarily vanish. The result is proven in the most general setting: for any number of strands and crossings, integrally and with one basepoint per component of the Legendrian link.
We study the long-time dynamics near Couette flow for the 2D Euler equations in unbounded geometries. We identify a mechanism of nonlinear inviscid damping at Yudovich regularity, distinct from classical phase mixing: velocity decay driven by spatial evacuation of vorticity. The mechanism leads to a geometry-sign classification of...
Two competitors choose starting vertices for independent, constant-speed random walks, and each site is acquired by its first visitor. We study the spatial geometry of the resulting first-passage location game. On every finite path the optimal strategies are exactly the distributions supported on the central vertices. The proof...
Let $G$ be a quasi-split reductive group over a finite field and let $Ĝ$ be the Langlands dual group. Assuming the derived subgroup of $G$ is almost simple, we use techniques from the geometric Langlands program to relate special values of Bessel functions for generic principal series representations of $G$ to the trace of Frobenius...
A result of Cembranos states that a non-trivial injective tensor product of a $C$-space contains a complemented copy of $c_{0}$, and in particular fails the Grothendieck property. We establish a positive analogue of the Cembranos theorem for tensor products of Banach lattices. If $E$ and $F$ are infinite dimensional Banach lattices,...
Rapid data assimilation is required for real-time prediction and control in digital twins. For many physical systems, the data assimilation task requires the solution of a physics-constrained inverse problem, which is often computationally intractable in real time using traditional physics solvers. This work presents a reduced-basis...
We study pointwise convergence of polynomial ergodic averages over short intervals whose left endpoints tend to infinity. For a polynomial orbit of degree $d\geq2$ and doubly lacunary starting times, we prove $L^p$ variational estimates, and hence almost-everywhere convergence, for $1<p<\infty$ in the range $c>(d-1)/d$. This gives the...
We consider the SIS contact process on a Poisson system of independent Brownian motions in $\mathbb{R}^d$ of intensity $η$. Two particles are in contact when their distance is at most $2r$. An infected particle transmits the infection to a susceptible particle in contact with it at rate $λ\in(0,\infty]$, and recovers at rate...
Let $\mathbb{H}=\{z\in\mathbb{C}:\operatorname{Im}z>0\}$, and let $N(\mathbb{H})$ denote the Nevanlinna class in $\mathbb{H}$, consisting of meromorphic functions representable as quotients of two bounded analytic functions in $\mathbb{H}$. We construct a nonconstant meromorphic function $F$ on $\mathbb{C}$ such that...
Weil's criterion equates the Riemann Hypothesis with the positivity of an explicit quadratic form $Q(f)$. For test functions supported in a window $[-L,L]$ we study the profile $λ^*(L)=\inf Q(f)/\|f\|_2^2$ from both sides. A one-stroke reduction converts window positivity into positive semidefiniteness of a finite matrix; executing it...
We show that the operadic structure on the cohomology of the poset of noncrossing 2-partitions is isomorphic to the Brace operad.
Jungin Lee in 2018 proved a necessary and sufficient condition that an integral quadratic form $\sum_{i=1}^{m} a_iX_i^2$ is universal over $M_2(\mathbb{Z})$. For a positive integer $n \geq 2$, Lee defined $f(n)$ to be the smallest positive integer $m$ such that for every pairwise coprime $a_1, a_2, \ldots a_m \in \mathbb{Z}$,...