Related papers: Free Boundary Problems: The Forefront of Current a…
We study the free boundary regularity of the traveling wave solutions to a degenerate advection-diffusion problem of Porous Medium type, whose existence was proved in \cite{MonsaingonNovikovRoquejoffre}. We set up a finite difference scheme…
Artificial intelligence is transforming mathematics at a speed and scale that demand active engagement from the mathematical community. We examine five areas where this transformation is particularly pressing: values, practice, teaching,…
In our previous paper [GSV2020], we proved that the complementary components of a ring domain in $\mathbb{R}^n$ with large enough modulus may be separated by an annular ring domain and applied this result to boundary correspondence problems…
We consider equations of the form $\Delta u +\lambda^2 V(x)e^{\,u}=\rho$ in various two dimensional settings. We assume that $V>0$ is a given function, $\lambda>0$ is a small parameter and $\rho=\mathcal O(1)$ or $\rho\to +\infty$ as…
Academic challenges comprise effective means for (i) advancing the state of the art, (ii) putting in the spotlight of a scientific community specific topics and problems, as well as (iii) closing the gap for under represented communities in…
We introduce PHYSICS, a comprehensive benchmark for university-level physics problem solving. It contains 1297 expert-annotated problems covering six core areas: classical mechanics, quantum mechanics, thermodynamics and statistical…
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the workshop Linear Systems and Eigenvalue Problems, which was…
Boundary value problems on the unit sphere arise naturally in geophysics and oceanography when scientists model a physical quantity on large scales. Robust numerical methods play an important role in solving these problems. In this article,…
This document covers five broad topics from theory of small bodies: planetesimal formation, cosmochemistry, thermal evolution, collisions and dynamics. Each of these topics is described in a separate section, where we prioritize selected…
Robot navigation in crowded public spaces is a complex task that requires addressing a variety of engineering and human factors challenges. These challenges have motivated a great amount of research resulting in important developments for…
We summarize progress made in theoretical astrophysics and cosmology over the past decade and areas of interest for the coming decade. This Report is prepared as the TF09 "Astrophysics and Cosmology" topical group summary for the Theory…
We examine boundary regularity for a fully nonlinear free transmission problem. We argue using approximation methods, comparing the operators driving the problem with a limiting profile. Working natural conditions on the data of the…
Round table discussions are in the tradition of ACAT. This year's plenary round table discussion was devoted to questions related to the use of scientific software in High Energy Physics and beyond. The 90 minutes of discussion were lively,…
In connection to the development of the field of Combinatorics on Words, we present a list of open problems and conjectures that were stated during the ten last meetings WORDS. We wish to continually update the present document by adding…
The topic of the glass transition gives rise to a a wide diversity of views. It is, accordingly, characterized by a lack of agreement on which would be the most profitable theoretical perspective. In this chapter, I provide some elements…
In this paper we are concerned with a two-penalty boundary obstacle problem of interest in thermics, fluid dynamics and electricity. Specifically, we prove existence, uniqueness and optimal regularity of the solutions, and we establish…
This is a review of topics which haunted me for the last 40 years, starting with spontaneous symmetry breaking and ending with gauge/string/space-time correspondence. While the first part of this article is mostly historical, the second…
Advances in science and engineering often reveal the limitations of classical approaches initially used to understand, predict, and control phenomena. With progress, conceptual categories must often be re-evaluated to better track recently…
Inclusion and accessibility in visualization research have gained increasing attention in recent years. However, many challenges still remain to be solved on the road toward a more inclusive, shared-experience-driven visualization design…
After a brief review of integrability, first in the absence and then in the presence of a boundary, I outline the construction of actions for the N=1 and N=2 boundary sine-Gordon models. The key point is to introduce Fermionic boundary…