Research
Research
Research
Research
1,246+ open-access research outputs.
Understanding the evolution of connectivity in spatiotemporal systems requires mathematical frameworks capable of encoding not only instantaneous interactions but also their cumulative causal structur…
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 establish an observability inequality from space-time measurable sets for a class of strongly coupled parabolic systems consisting of two equations, where the observation acts on a single-component…
We study weighted composition operators on quasi-Banach spaces of holomorphic functions via their induced action on jets along periodic orbits. Under a natural graded nondegeneracy condition, boundedn…
The general construction of lattice (co)homology assigns to a lattice $\mathbb{Z}^r$ and a weight function $w:\mathbb{Z}^r \to \mathbb{Z}$ a bigraded $\mathbb{Z}[U]$-module $\mathbb{H}_*$. The weight …
In this paper we consider a one-dimensional reaction-diffusion model with piecewise continuous reaction term that describes propagation of autoignition fronts in reactive co-flow jets in a certain par…
This paper extends the theoretical framework introduced in Liquidity Pools as Mean Field Games: A New Framework, where the interactions among traders in a constant product market-making protocol were …
We generalize well-known bijections between alternative tableaux and permutations to bijections between rhombic alternative tableaux (RAT) and assembl\'ees of permutations. We show how these various b…
We study closed subschemes $X$ in ${\mathbb P}^n$ of dimension one, locally defined at any point by at most $n$ equations such that the analytic spread of $I_{\mathfrak{m}}$ is at most $n$, where $I \…
Let $R$ be a $d$-dimensional Noetherian local ring with maximal ideal $m_R$. In this article, we give a generalization of the multiplicity $e(I)$ of an $m_R$-primary ideal $I$ of $R$ to a multiplicity…
We consider a two-dimensional, pure capillary drop of nearly-circular shape, having constant vorticity. We write the Craig-Sulem equations on the unit circle, then on the flat torus. We show their Ham…
An edge-coloring of a hypergraph is {\em spanning} if every vertex sees every color used in the coloring. In this paper, we prove that for $k \geq 2r \geq 6$, in any spanning $k$-coloring of the edges…
Rosenbloom and Tsfasman, in their foundational work on the $m$-metric, introduced algebraic-geometric codes defined by multiple points on a smooth projective curve $X$. This construction involves a di…
We study the optimal routing problem in decentralized exchanges built on Constant Function Market Makers when trades can be split across multiple heterogeneous pools and execution incurs fixed on-chai…
This paper is intended as a companion to the author's talk "Commutator estimates and mean-field limits for Coulomb/Riesz gases" at the 2025 Journ\'ees \'equations aux d\'eriv\'ees partielles in Aussoi…
We construct an explicit flat one-parameter family of 22-dimensional Artinian $k$-algebras whose special fibre is the spider algebra $k[x,y,z]/(x^8, y^8, z^8, xy, xz, yz)$ and whose generic fibre is t…
We develop a unified algebraic and valuative theory of Lojasiewicz exponents for pairs of graded families and filtrations of ideals. Within this framework, local Lojasiewicz exponents, gradient expone…
Given a semigroup $S$, a diagonal subsemigroup $\rho$ is defined to be a reflexive and compatible relation on $S$, i.e. a subsemigroup of the direct square $S\times S$ containing the diagonal $\{ (s,s…
Kruse and Wu [Math. Comp. 88 (2019) 2793--2825] proposed a fully discrete randomized Galerkin finite element method for semilinear stochastic evolution equations (SEEs) driven by additive noise and sh…
Nous d\'emontrons l'invariance Galoisienne de la propri\'et\'e d'annulation en $1/2$ des fonctions L standard ou de Rankin-Selberg pour certaines repr\'esentations automorphes cuspidales alg\'ebriques…
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