Mathematics

We study the trianguline variety for split connected reductive groups. We generalize a theorem of Breuil, Hellmann, and Schraen about its local structure, establishing smoothness over the loci determined by various regularity conditions on…

We give counterexamples to two well-known conjectures about matroids: White's conjecture on the generation of the toric ideal by symmetric exchange binomials, and a conjecture of Mason on the log-concavity of the counts of flats of a given…

This paper introduces relative versions of the inner automorphism group and the transvection group associated with surjective quandle homomorphisms.By using the relative inner automorphism group, we define a notion of \emph{connectedness}…

In \cite{Wang1954}, Wang proved (among other things) a sufficiency result for a compact homogeneous manifold $G/H$ to admit a $G$-invariant complex structure. In this note, we give a simple proof of Wang's theorem which relies on nothing…

We prove new $L^p$ boundedness results for Bochner-Riesz means associated with the spectral decomposition of the sub-Laplacian on the Heisenberg group $\mathbb H_n$. Our results hold for a range $1\le p\le p_n$ where $p_n\to 2$ as…

This paper concerns a three-dimensional inverse acoustic obstacle scattering problem from scattered field or phased/phaseless far-field data. Based on the boundary integral defined on a homothetic surface, we propose a highly efficient…

We propose and analyze a linearly implicit mass-lumped finite element method for the heat flow of harmonic maps into the unit sphere. The method consists of a linear predictor followed by a nodal projection and therefore preserves the…

For an arbitrary reduced root system, we give upper bounds for the Dunkl kernel with regular spectral parameter and its derivatives, which are uniform in the spatial variable. These estimates generalize well-known sharp upper bounds for…

We consider the Sherrington--Kirkpatrick spin glass model at the critical inverse temperature $\beta = 1$ with zero external field. We prove that the free energy $F_N = F_{N,\beta=1}$ of this model has variance \[ \mathrm{Var}(F_N) =…

Recent work by Gusakova et al. (Stochastic Process. Appl. 164 (2023) 357-382) has shown a central and a stable limit theorem for the logarithmic volume of random simplices and random convex bodies under an elliptical framework in the high…

Let $\mathcal{M}_{g,n}(\mathbf{L})$ be the moduli space of hyperbolic surfaces of genus $g$ with $n \geq 0$ hyperbolic ends of widths $\mathbf{L} \in \mathbb{R}_{\geq 0}^n$. We regard the total mass $|\mu_X^\kappa|$ of the Brownian loop…

We survey recent progress on the geometric Bombieri--Lang conjecture over function fields of characteristic zero. We discuss recent work of Xie--Yuan and Guoquan Gao, which together proves the conjecture for varieties admitting finite…

Mumford curves generalize the Tate uniformization of elliptic curves with split multiplicative reduction and provide p-adic analogues of the uniformization of Riemann surfaces. In this paper, we present several algorithms for hyperelliptic…

We show that, for every fixed graph $H$, every $n$-vertex graph $G$ that excludes $H$ as a minor is $3$-colourable with clustering $O_H(n^{4/9})$. That is, there exists a function $f$ such that for every graph $H$, every $n\ge 1$, every…

The Feigin-Semikhatov duality asserts that the Heisenberg cosets of the subregular $W$-algebra of $\mathfrak{sl}_n$ at level $k$ and the one of the principal $W$-superalgebra of $\mathfrak{sl}_{n|1}$ at level $\ell$ coincide when the levels…

This study establishes Liouville-type theorems for indefinite quasilinear elliptic equations in the upper half-space. Additionally, we demonstrate the existence of solutions for this class of problems using the fibering method. Our approach…

This paper investigates the relationship between tiles and weak tiles in the context of finite cyclic group $\mathbb{Z}_{pq}$. We prove that weak tiles and translational tiles are equivalent in this group. Our proof employs Fourier…

We study the growth spectrum of groups acting on hyperbolic spaces, i.e.\ the set of exponential growth rates achieved by subgroups. For a finitely generated free group or a surface group acting convex-cocompactly on a proper geodesic…

We note that homeomorphism groups of all pseudo-solenoids, including the pseudo-circle, have non-metrizable universal minimal flows.

Let $G$ be an abelian group, and let $\mathcal F (G)$ be the free commutative monoid with basis $G$, and $\mathcal A (G)$ the set consisting of all minimal zero-sum subsequences over $G$. For any subset $\Omega \subset \mathcal F (G)$, we…