Mathematics

Let $M$ be a closed, connected, smooth $n$-dimensional manifold. We prove that $M$ is dominated by the underlying space of the $n$-skeleton of a finite simplicial complex. Furthermore, the total number of simplices in the $n$-skeleton is…

Motivated by the correspondence between ideal cotorsion pairs in Frobenius exact categories and those in their stable categories, we introduce the notion of an ideal $n$-cotorsion pair in an extriangulated category. We study the…

Let $(\Omega,\mu)$ be a finite measure space with $M=\mu(\Omega)>0$. We investigate the integral form, stability, and metric geometry associated with a square-root complex. After proving the inequality and determining all equality cases, we…

Of concern is a class of non-autonomous evolution equations of second order in Hilbert spaces, with a nonnegative self-adjoint operator $A$, time-varying damping and nonlinear source term. We give an upper decay rate of the energy, valid…

We prove that the heat semigroup on the free orthogonal quantum group $O_F^+$ of Kac type satisfies hypercontractivity with the optimal time.

Let $F$ be a number field. Given finitely many $F$-valued points on a commutative algebraic group defined over $F$, a question of interest to number theorists is the determination of the group of their linear relations. In this article, we…

We prove a scaling limit theorem for a double sequence of probability measures involving additive free convolution $\boxplus$ and additive Boolean convolution $\uplus$. Let $\mu$ be a probability measure on $\mathbb{R}$ with mean zero and…

Let $T$ be a positive $\ddc$-closed current of bidimension $(1,1)$ on a projective manifold $X$ of dimension $n.$ We show that for every $c > 0$ the set of points of $X$ where the Lelong number of $T$ is larger or equal to $c$ is an…

We develop a Fourier--Hankel moment framework for extracting topological counting information from full-aperture acoustic far-field data. The method is based on the observation that separated localized components generate distinct phase…

An integer palindrome is a self-reciprocal polynomial evaluated at its base, so its roots are symmetric about the unit circle -- where the coordinate is angle, in turns of $\tau$. Read this way, the date $\texttt{6/28/26}\to 62826$ secretly…

We give a thorough analysis of the time complexity of computing Reshetikhin--Turaev knot polynomials via tensor contractions on the associated tensor networks, showing that the computation is fixed-parameter tractable with respect to a…

Characterizing fade duration in wireless channels is fundamental for designing robust communication systems. Classical approaches -- Rice's level-crossing theory and Monte Carlo simulation -- lack precision for tail events and are…

We prove that if $f\in \mathbb Z[x]$ is a monic polynomial of degree $k\geq 2$, then there exists a constant $c>0$, depending only on $f$, and finite sets $A\subset \mathbb R$ of arbitrarily large size such that \[ |f(A)|\leq |A|^{k-c}, \]…

We produce a formula, analogous to the Gauss-Codazzi equation, which relates the geometry of a $G_2$-structure and its Hodge Laplacian to the geometry of the induced $SU(3)$-structure on an embedded hypersurface. As an application, we…

In this expository article, we present on state-of-the art results regarding three closely related invariants of moduli spaces of curves: their Chow rings, cohomology rings, and point counts over finite fields. We study the moduli space…

This paper investigates the persistence of maximum likelihood paths in degenerate stochastic differential systems and quantifies how small periodic perturbations modulate the metastable transition rate. Within the Freidlin--Wentzell large…

The solutions of algebraic differential equations in certain valued differential fields, including the differential field of transseries, can be analyzed using a Newton diagram method. In this paper, we show that (eventual) equalizers, a…

We classify all skew left braces with additive group isomorphic to the infinite dihedral group. There are ten isomorphism classes.

We study the siblings version of the coupon collector problem. A main collector stops when every coupon type has appeared at least once, duplicates are passed successively to later siblings, and $U_j^N$ denotes the number of empty spaces in…

We establish an infinite-dimensional affine transform theory for the time-augmented Brownian signature. Our first main result shows that, for a suitable class of linear functions of the signature, the conditional Fourier-Laplace transform…