arXiv preprints from January 1, 2026 through September 19, 2026 — 00:23:26 EST
Let $\overline{Z}$ be a smooth projective variety with an simple normal crossing divisor $D$ such that $Ω_{\overline{Z}}^1(\log D)$ is nef. We prove that if $Y\subset Z:=\overline Z\setminus D$ is a smooth closed subvariety with nonzero Euler characteristic, and $P$ is a perverse sheaf on $Y$ with full support, then $χ(Y,P)>0$. This...
Becker et al. produced a striking trace formula for the sum of fourth powers of generalized magic angles, $ θ$, for the chiral model of twisted bilayer graphene (TBG) with the exact Bistritzer--MacDonald potential: $\sum θ^{4} = 8 π/ \sqrt 3 $. The purpose of this note is to generalize this formula to a larger class of potentials...
In this paper, we give a negative answer to Wang's conjecture. For every $n\geq 3$, there exist $\varepsilon>0$ and $δ\in (0,1)$ such that, for all $q$ and $λ$ satisfying \[ \frac{n}{n-2}-\varepsilon<q\le \frac{n}{n-2}, \qquad \frac{1}{q-1}\cdot δ<λ\le \frac{1}{q-1}, \] there exists a bounded Euclidean domain \(Ω\subset\mathbb{R}^n\)...
We prove optimal trace-norm relaxation for the one-dimensional Lindbladian associated with the Witten differential $a=h\partial_x+V'$ which annihilates the classical Gibbs density: if $λ_1(h)$ is the first positive eigenvalue of $H=a^*a$, then the relaxation rate is $γ_h=λ_1(h)/(2h)$. It applies to initial operators whose Schwartz...
Given a graph $F$, a family $\mathcal F$ of graphs on $[n]$ is \emph{$F$-intersecting} if $G\cap H$ contains a copy of $F$ for every $G,H\in\mathcal F$. We prove that there exists an absolute constant $\varepsilon>0$ such that every $P_4$-intersecting family $\mathcal F$ satisfies $|\mathcal...
We solve Serre's problem on the specialisation of Brauer group elements in all cases where the number of variables is sufficiently large.
Let $2\leq k<n/2$ and let $(M^n,[g_0])$ be a closed, connected, and locally conformally flat Riemannian manifold with a $k$-admissible metric in the conformal class $[g_0]$. We prove a stability result of the $σ_k$-curvature inequality on $M$, in the sense that if equality is almost satisfied for some conformal metric, then this...
In 2021, Chern and Tang introduced two families of two-parameter modular functions associated with the Rogers-Ramanujan continued fraction. They established recurrence relations that express the members of these families in terms of eta quotients, and used these expressions to obtain dissection formulas. Motivated by their work, we...
Let $d,K,N\in \mathbb{N}$ with $K\geq 3$ and $d\geq 4K+4$. Let $Δ\subset \mathbb{Z}^d$ be the vertex set of a nondegenerate $(K-1)$-simplex, and let $A\subseteq[N]^d$ contain no nontrivial similar copy of $Δ$. We prove that \[ |A|\ll_{Δ,d} N^d\exp\!\left(-c_{Δ,d}\sqrt{\log N}\right) \] improving upon a polylogarithmic bound...
Let $g(n)$ denote the minimum number of peeling sequences among all $n$-point sets in general position in the plane. Dumitrescu and Tóth proved an exponential upper bound with base $12.29$, and Simon subsequently lowered the base to $9.78$. Using the same recursive construction, we prove \begin{equation*} g(n) \le (8+o(1))^n. \end{equation*}
We investigate mean-variance portfolio selection with an $\ell_0$-penalty to promote sparsity in asset allocations. Uncertainty in the mean return vector is incorporated through an ellipsoidal uncertainty set, yielding a robust sparse optimization framework. We characterize the structure of both local and global minimizers and exploit...
We prove that the skew stickiness ratio converges to two at short maturity under local volatility models. This appears to be the first rigorous proof of this limit for a general time-dependent local volatility function. As a by-product, we strengthen the one-half rule of the implied volatility skew by removing uniform ellipticity and...
Constructing a confidence interval for the difference between two independent binomial proportions involves a nuisance direction that is not identified by the estimand. The one-sample Wilson score interval inverts a scalar score test, but has no direct bivariate analogue isolating the difference: inverting the joint normal...
In this paper, we establish a new version of one dimensional generalized discrete dual $p$-Hardy inequality with a shift. Using this generalized discrete dual p-Hardy inequality, we obtain improvements of two discrete dual $p$-Hardy inequalities. To be specific, for $p>1$ and $A\in C_c(\mathbb{N}_{0})$ satisfying $A_{0}=A_{1}=0$, we...
We prove the expected asymptotic in Waring's problem over $\mathbb F_q[T]$, with a power-saving error, whenever $n>2d$, the characteristic is greater than $(d-1)^2$, and $q$ satisfies an explicit lower bound. This range is sharp in general for the expected asymptotic uniformly in the target polynomial. Our main new input is an...
Let $π:Z\rightarrow Y$ be a smooth projective morphism of complex manifolds with connected rationally connected fibers. We prove holomorphic approximation on arbitrary compact sets and finite-jet interpolation on arbitrary closed discrete sets for continuous liftings defined on open Riemann surfaces and holomorphic near those sets....
We describe all functions $\mathbb{N}\rightarrow \mathbb{N}$ that can be realized, up to the standard equivalence, as conjugator length functions of finitely generated groups. Furthermore, we show that any two increasing functions $f,g\colon \mathbb N\to \mathbb N$ can be simultaneously realized as conjugator length functions of...
We provide a proof, free of ultrafilters and almost reduction, that every subset of a topological Ramsey space is Ramsey in the Solovay model.
We show that the adjacency operator of the $1$-skeleton of any regular tiling of the hyperbolic plane has no nonzero square-integrable eigenfunctions. As a consequence, the same holds for every infinite connected regular graph admitting a proper planar embedding with regular dual.
Let $q \equiv 1 \bmod 8$ be a prime power. We prove that $L\left(\tfrac{1}{2}, χ\right) \neq 0$ for 100% of the imaginary quadratic Dirichlet characters of $\mathbb{F}_q(T)$.
Berger and Coburn showed that boundedness of a Toeplitz operator $T_g$ on the Fock space controls the heat transform $g^{(t)}$ for $1/4<t<1$, and conjectured the endpoint $g^{(1/4)}$ characterizes boundedness. Looi recently disproved this by constructing a bounded $T_g$ with unbounded $g^{(1/4)}$. We show that $p=1$ is the exact...
For a vector of positive integers $\mathbf{b} = (b_1,\ldots,b_h)$ with $\gcd(b_1,\ldots,b_h) = 1$, we study sets $A \subseteq \mathbb{N}$ for which every sufficiently large integer has a bounded positive number of representations \[ n = b_1 x_1 + \cdots + b_h x_h \qquad (x_1,\ldots,x_h\in A). \] We prove that such a set exists for...
Let $G$ be a graph and $w_k(G)$ denote the number of walks in $G$ of length $k$. For sequences $a_1, \cdots, a_n$ and $b_1, \cdots, b_n$ of non-negative integers such that $a_1 + \cdots + a_n = b_1 + \cdots + b_n$, we determine a simple necessary and sufficient condition on $a_1, \cdots, a_n, b_1, \cdots, b_n$ for the inequality \[...
The Free $\mathbf{w}$-Maximal Spanning Forest (FMaxSF) is a weighted generalization of the classical Free Minimal Spanning Forest (FMSF) that is able to detect nonhyperfiniteness in percolation on nonunimodular graphs. We introduce a parameterized family of invariant random spanning forests that interpolates between these models. For...
We prove the Chen--Yang volume conjecture for all sufficiently long integral Dehn fillings of any fixed marked fundamental shadow-link exterior. For each fixed filling, the exponential growth of its $SO(3)$ Turaev--Viro invariants recovers its hyperbolic volume along the full sequence of odd levels. The filling coefficients may have...