Research
Research
Research
Research
6,427+ open-access research outputs.
We establish an It\^o-type formula for finite $p$-variation paths with jumps for arbitrary $p\geq 1$. The formula is stated in a fully pathwise form and separates the reduced rough integral from expli…
We extend Atiyah's holomorphic jet bundle formalism to holomorphic vector bundles over noncommutative algebras endowed with a bigraded differential calculus truncated at bidegree $(1,1)$; we refer to …
This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in …
We study some interesting hypersurfaces that naturally arise when studying the period map on the moduli space of hypersurfaces, in the context of Sung Gi Park's recent work on studying the GIT moduli …
A convex polyhedron is Rupert if a hole can be cut into it (making its genus $1$) such that an identical copy of the polyhedron can pass through the hole. Resolving a conjecture of Jerrard-Wetzel-Yuan…
We give a simple description of the coordinate ring of the universal centralizer associated to a simply connected semisimple group. To this end, we prove a general result on Weil restriction of affine…
Let $G=PSL(n,\mathbb{C})$. Let $T$ be a maximal torus of $G$. Let $\omega_{r}$ denote the $r^{th}$ fundamental weight. Let $\mathcal{L}(n\omega_{r})$ denote the line bundle on the Grassmannian $G_{r,n…
In this article, we introduce a time-independent version of the L\'evy colored noise considered in Balan (2015) and Balan and Jim\'enez (2026). We study the existence of the solution of a linear stoch…
We study a fixed-core absorption problem for regular induced subgraphs. A set is q-modular if all induced degrees are congruent modulo q. Given a q-modular witness A and a retained core U subset A, we…
The Pareto distribution plays a crucial role in various disciplines, necessitating robust goodness-of-fit tests for its validation. This article introduces a novel tests based on Stein's characterizat…
Schatten class properties of commutators $[b,T]$ of pointwise multipliers $b$ and singular integral operators $T$ have been characterised in a variety of settings. An abstract framework, covering many…
We describe the Bandicoot GPU linear algebra toolkit, a C++ based library that prioritises ease of use without compromising efficiency. Bandicoot's API is compatible with the popular Armadillo CPU lin…
We develop tools which use common fusion systems building techniques in order to compute higher limits over the centric orbit category. We apply these tools in order to study both the Diaz-Park sharpn…
In this paper, we study the following quasi-linear elliptic inequality $\Delta_m u +u^p |\nabla u|^q \leqslant 0$ on weighted graphs, where $(m,p,q)\in (1,\infty)\times\mathbb{R}\times\mathbb{R}$. Acc…
For a graph $G$, let $f_o(G)$ denote the maximum order of an induced subgraph of $G$ all of whose vertices have odd degree, and let $\chi(G)$ denote the chromatic number of $G$. Scott (CPC, 1992) prov…
This is a remastered and expanded version of a an earlier preprint of the author, in which we give a fully algebraic proof of an important theorem of Demailly, stating the existence of many Green-Grif…
Let $K$ be a complete discrete valuation field of characteristic $0$ with perfect residue field of characteristic $p>0$. Let $\mathbb{A}_K$ denote the imperfect coefficient ring of $(\varphi,\Gamma)$-…
We show that jets of initial data can be approximated up to arbitrary order by finite-gap solutions for classes of so-called BKM systems of PDEs introduced by Bolsinov--Konyaev--Matveev, which include…
We prove a lower bound on the Calabi functional for degenerations of polarized varieties, involving the difference of CM degrees between generically isomorphic families. This may be viewed as a discre…
Path-planning for autonomous vehicles in threat-laden environments is a fundamental challenge. While traditional optimal control methods can find ideal paths, the computational time is often too slow …
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