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This https://arxiv.org/abs/2204.03754 has been replaced.
link: https://scholar.google.com/scholar?q=a

Higher uniformity of arithmetic functions in short intervals I. All intervals
We study higher uniformity properties of the Möbius function $μ$, the von Mangoldt function $Λ$, and the divisor functions $d_k$ on short intervals $(X,X+H]$ with $X^{θ+\varepsilon} \leq H \leq X^{1-\varepsilon}$ for a fixed constant $0 \leq θ< 1$ and any $\varepsilon>0$. More precisely, letting $Λ^\sharp$ and $d_k^\sharp$ be suitable approximants of $Λ$ and $d_k$ and $μ^\sharp = 0$, we show for instance that, for any nilsequence $F(g(n)Γ)$, we have \[ \sum_{X < n \leq X+H} (f(n)-f^\…

Duality solutions to the hard-congestion model for the dissipative Aw-Rascle system
Nilasis ChaudhuriUW, Muhammed Ali MehmoodI2M, Charlotte PerrinI2M, Ewelina Zatorska
https://arxiv.org/abs/2402.08295

Duality solutions to the hard-congestion model for the dissipative Aw-Rascle system
We introduce the notion of duality solution for the hard-congestion model on the real line, and additionally prove an existence result for this class of solutions. Our study revolves around the analysis of a generalised Aw-Rascle system, where the offset function is replaced by the gradient of a singular function, such as $ρ$ $γ$ n , where $γ$ $\rightarrow$ $\infty$. We prove that under suitable assumptions on the initial data, solutions to the Aw-Rascle system converge towards the so-called…

This https://arxiv.org/abs/2312.16666 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An atomic Coxeter presentation
We study parabolic double cosets in a Coxeter system by decomposing them into atom(ic coset)s, a generalization of simple reflections introduced in a joint work with Elias, Libedinsky, Patimo. We define and classify braid relations between compositions of atoms and prove a Matsumoto theorem. Together with a quadratic relation, our braid relations give a presentation of nilCoxeter algebroids similar to Demazure's presentation of nilCoxeter algebras. Our consideration of reduced compositions of a…

Existence of weak solutions and long-time asymptotics for hydrodynamic model of swarming
Nilasis Chaudhuri, Young-Pil Choi, Oliver Tse, Ewelina Zatorska
https://arxiv.org/abs/2402.07130

Existence of weak solutions and long-time asymptotics for hydrodynamic model of swarming
We consider a one-dimensional hydrodynamic model featuring nonlocal attraction-repulsion interactions and singular velocity alignment. We introduce a two-velocity reformulation and the corresponding energy-type inequality, in the spirit of the Bresch-Desjardins estimate. We identify a dependence between the communication weight and interaction kernel and between the pressure and viscosity term allowing for this inequality to be uniform in time. It is then used to study long-time asymptotics of …