Research
Research
Research
Research
1,360+ open-access research outputs.
We obtain a complete classification of components of strata of holomorphic and meromorphic k-differentials. We show that, when genus is at least two and outside of explicit exceptions when k < 4, ther…
The cross-ratio degree problem is about counting rational curves with $n$ marked points satisfying $n-3$ cross-ratio conditions. This problem has a tropical analogue which provides the same number, as…
``Behind every limit theorem, there is an inequality'' said Kolmogorov. We say ``for every inequality, there is an approximate inequality under approximate regularity conditions.'' Suppose $X, X'$ are…
We show for $\kappa \in (4,8)$ that the canonical conformally covariant measure on the conformal loop ensemble (CLE$_\kappa$) gasket, previously constructed indirectly by the first co-author and Schou…
Many engineering failures thermal hotspot concentration, Hertz contact fatigue localization, boundary-layer loss, mixing dead zones are geometric failure modes: changing the material delays the failur…
Let $(V, G)$ be an orthogonal representation of a compact Lie group $G$ with nontrivial copolarity, and $\Sigma$ a fat section of $(V, G)$. If $E$ is a $G$-invariant compact convex set in $V$, then $P…
We prove that two half-space models in the KPZ universality class, exponential last-passage percolation and a family of Poisson-avoiding metrics generalizing colored TASEP, converge to a common scalin…
This work is inspired by a remark of de Gennes about polyelectrolytes, which are charged polymers. A common model for a polymer is a self-avoiding or self-repelling random walk or Brownian motion. For…
We prove that every ordinal $\alpha<\omega_2$ is the order type of a certain system of uniform Borel sets in the sense of a well-ordering relation defined by Petr Novikov. This result gives a positive…
We prove central limit theorems (CLTs) for topological functionals of Bernoulli bond percolation on infinite graphs beyond the Euclidean lattice $\mathbb{Z}^{d}$. For quasi-transitive graphs of subexp…
We study pathwise $p$-th variation of continuous paths on a compact interval along a fixed partition sequence. Although the class of continuous paths with finite $p$-th variation is generally not line…
This paper presents a systematic observer design methodology for a class of port-Hamiltonian (pH) systems with state-dependent input matrices. Such systems can model a wide range of electromechanical …
We investigate the martingale Schr\"odinger bridge, recently introduced by Nutz and Wiesel as a distinguished martingale transport plan between two probability measures in convex order. We show that t…
We obtain bivariate asymptotics for one part monotone Hurwitz numbers in high genus (i.e. as both the size and the genus go to infinity). To do so, we start with a linear recurrence for these numbers …
This paper introduces a biharmonic interpolatory subdivision framework on Riemannian manifolds. In the Euclidean setting, the six-point Deslauriers-Dubuc stencil is characterised as the unique minimis…
This work presents a bilevel coordination model that captures the hierarchical interaction between the transmission and distribution layers under a Distribution System Operator(DSO)-led configuration.…
Assume $\kappa = \kappa^{< \kappa}$ (usually $\aleph_0$ or an inaccessible). We shall deal with iterated forcings preserving ${}^{\kappa>}{\rm Ord}$ and not collapsing cardinals along a linear order…
This survey-style note reviews constructive versions of the Peter--Weyl theorem in the Bishop--Coquand--Spitters line. Its main purpose is to clarify which parts of the classical Peter--Weyl package a…
We consider decentralized stochastic convex optimization on connected network, in which gradients of agents are unavailable and each agent can query only noisy function values of its own local objecti…
We study the fixed-time spatial covariance of the KPZ equation with flat initial profile. Using Malliavin calculus and a Clark-Ocone representation, we show that as $|x|\to\infty$, $\mathrm{Cov}[h(t,x…
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