Mathematics

We establish an anisotropic analogue of the celebrated theorem of Meeks-Simon-Yau: every minimizing sequence of surfaces within a fixed isotopy class converges to a smooth stable anisotropic minimal surface, with genus lower semicontinuity.…

Recent advances in biomedicine generate high-dimensional single-cell data that describe cellular heterogeneity with unprecedented detail, but their geometric complexity and non-linear structure often limit the effectiveness of conventional…

Let $R$ be a commutative Noetherian ring in which $2$ is invertible. We prove that a conjugate of Petrov's odd elementary unitary group is contained in the DSER elementary orthogonal group defined over projective modules. We also show a…

We consider the reflected stochastic reaction-diffusion equation on $[0,1]$: \begin{align*} \left\{ \begin{aligned} d u(t,x) &=\frac{1}{2}\partial_{xx} u(t,x)dt +b(u(t,x))dt + \sigma(u(t,x)) W(dt,dx)+L(dt,dx),\\ u(t,x)&\geq 0, \quad t\geq…

We prove a version of Heisenberg's uncertainty principle for a rather general class of locally compact abelian groups. We compare the lower bound provided by our approach with the optimal lower bound in the Euclidean case, and formulate the…

Settling a problem raised by Eccles in 2015, Narayanan in 2026 considers a two-player game in which two captains alternately select players while the opponent decides to which team each selected player is assigned. Moreover, the two teams…

We first rewrite the Chmutov and Vignes-Tourneret's three-permutation formula as an explicit hyperedge-partial-duality formula in the two-permutation model, and show that in this model partial duality acts exactly by preserving the support…

Let $k\ge4$ and $j\ge2$ be integers with $j$ even, and let $f$ be a primitive elliptic cusp form of weight $2k+j-2$ for $\mathrm{SL}_2(\mathbb{Z})$. We study congruences between a Hermitian Klingen--Eisenstein lift associated with $f$ and…

We prove Springer's Odd Degree Theorem for quadratic forms over LG rings, and Scharlau's and Knebusch's norm principles for quadratic forms over semilocal rings. We present applications to the flat cohomology of spin groups and {\'e}tale…

Let $G$ be a compact Lie group, $M$ be a smooth manifold with a $G$ action, then all the data of this model is contained in the action groupoid $G\ltimes M$. If $U_y$ is a small enough neighbourhood of $y\in M/G$, the slice theorem says…

We prove~\cite[Conjecture 2.12]{BGS20} on the signature tail asymptotics of pure rough paths and extend it to arbitrary reasonable tensor norms. In more details, let \[ \mathbf X_t=\exp(tl) \,\text{ with }\, l=l_1+\cdots+l_m\,\text{ and }\,…

We propose two novel first-order methods for minimizing nonconvex functions with Lipschitz-continuous gradients and Hessians. These algorithms attain an $\varepsilon$-approximate first-order stationary point in…

Axial algebras are non-associative algebras generated by idempotents, called axes, whose adjoint action satisfies a fusion law. When this fusion law is graded, axes naturally lead to automorphisms of the algebra, and so such axial algebras…

In this note, we prove that the transcendental basepoint-free conjecture for Calabi-Yau manifolds holds if it holds for its hyperk{\"a}hler factors in its Beauville-Bogomolov decomposition. Based on a contraction theorem due to Bakker and…

We determine the exact attainable region of the pair $(\xi(C),\beta(C))$ formed by Chatterjee's rank correlation $\xi$ and Blomqvist's $\beta$ over the class of all bivariate copulas and show that it is given by…

The recently introduced formalism of chiral cluster seeds replaces quantum cluster variables with deformed vertex operators. In this framework, a decorated quiver associated with a seed encodes the operator product expansions of the…

In this paper, we study a particular family of solutions of the Vlasov-Navier-Stokes system posed on $\mathbb{R}^d$ (with $d\geq 2$), and show their convergence to the unique solution of the pressureless Euler-Navier-Stokes system. A global…

We investigate adaptive increasingly rare Markov chain Monte Carlo algorithms and the associated time-average estimator for approximating expectations. Under a simultaneous Wasserstein contraction assumption on the underlying family of…

The Kohayakawa--Nagle--R\"odl--Schacht conjecture predicts that locally dense graphs contain, asymptotically, at least as many homomorphic copies of any fixed graph as the random graph of the same edge density. We prove that every graph…

We say that a hypersurface $\Sigma \subset\mathbb{R}^{n+1}$ is $\alpha$-stationary if it is a critical point of the Euler-Dierkes-Huisken functional $\mathcal{E}_\alpha(\Sigma)=\int_\Sigma|X|^\alpha\, d\mathcal{H}^n$, introduced by Dierkes…