Mathematics

In this paper, we establish three finiteness and boundedness theorems for compact positive monotone symplectic manifolds endowed with special actions, called GKM$_3$, which generalize smooth toric varieties. Specifically, we prove that, for…

We construct infinite-time singularities with vanishing mean curvature for Lagrangian mean curvature flow in Gibbons--Hawking spaces. We consider circle-invariant Lagrangian $2$-spheres whose quotient curves are concave and are $C^2$-close…

Let $p_1,p_2\in(1,\infty)$ and $M=M_1\times M_2$ be the product of two geodesically complete Riemannian manifolds. In this paper, the authors first develop an anisotropic potential-theoretic framework adapted to the Green operator $G^M$ and…

We develop a quantum algorithm for the regularized Wasserstein proximal operator, which is a fundamental tool in optimal transport and mean-field games. The regularization introduces a small diffusive term into the continuity equation of…

We study the mean first capture time of isotropic L\'evy flights on Zoll surfaces, namely the expected time for a geodesic L\'evy process to reach a shrinking geodesic ball. While the leading-order asymptotics are universal, we prove that…

We give applications of the properties $\mathrm{NSOP}_{r}$ for non-integer values of $r$ to problems on the original hierarchy $\mathrm{NSOP}_{n}$ for integer values of $n$. We first show that the properties $\mathrm{NSOP}_{r}$, previously…

We analyse the space of points of the canonical extension of a coherent doctrine. We first give a full characterisation of doctrine morphisms that are extensible, and relate it to the existing notion of p-model of a coherent category.…

The central unsolved problem in the modular representation theory of symmetric groups is to find the decomposition matrices, which describe how irreducible representations in characteristic zero decompose upon reduction modulo a prime…

The theory of full conformal prediction uses deterministic non-conformity measure, but modern usage of full conformal prediction often relies on machine learning training, making stochasticity inevitable. A simple sufficient condition of…

A graph $G$ is said to be $F$-semi-saturated if the addition of any nonedge $e \not \in E(G)$ would create a new copy of $F$ in $G+e$. The semi-saturation number $ssat(n,F)$ is the minimum number of edges in an $F$-semi-saturated graph of…

For a strict partition $\lambda$, let $\mathcal Q_\lambda(X;t)=Q_\lambda[X-tX]$ be the shifted $t$-Schur function arising from the modified Greaves--Jing--Zhu operator on the odd power-sum ring. We study transition matrices between the…

Let $T(x)=\prod_{k=0}^{\infty}(1-x^{2^k})$ be the generating function of the Thue--Morse sequence, and write $T(x)^m=\sum_{n\geq 0}t_m(n)x^n$. We prove exact formulas for the $2$-adic valuations of the coefficients $t_5(n)$ and $t_9(n)$: \[…

The dynamical stability of laminates or planar phase boundaries for hyperelastic materials of Hadamard type in two space dimensions is studied. For that purpose, the stability function, known as the Lopatinskii determinant, is computed for…

We study exterior Dirichlet problems for \(k\)-Hessian equations with prescribed quadratic asymptotics, allowing the asymptotic matrix to be merely \(k\)-admissible and not necessarily positive definite. The key point is that the correct…

We develop a reduced interface formulation for elliptic interface problems with highly conducting interfaces. The interface condition consists of continuity of the primal variable together with a jump in the normal flux proportional to the…

We extend the notion of discrete homotopy groups of graphs to arbitrary cubical sets, and show that the discrete homotopy groups of quasisymmetric cubical sets are naturally isomorphic to the homotopy groups of their geometric realizations.…

We introduce a general framework for studying natural contravariant adjunctions that refine the adjunction between frames and spaces so that the fixpoints are $T_0$-spaces. Our objects of study are \textit{spatializable…

The gravitational field of a distant, isolated system is manifested by the conformally invariant Weyl tensor. Thus the conformal structure far from the system encodes the system's gravitational mass. It also encodes the causal structure,…

This paper is devoted to the study of Bowen's dimensional entropy on subsets for actions of amenable groups. We prove three main results. (1) First, topological conditional entropy is characterized by the dimensional entropy of stable sets…

We investigate the realizations of Coxeter permutahedra which are also Coxeter matroid polytopes; these are polytopes of the form $\mathrm{conv}(W \cdot \mathbf{a})$ where $W$ is a finite Coxeter group acting on $\mathbb{R}^n$ and…