作者：Mathieu Lewin , Elliott H. Lieb , Robert Seiringer 来源：[J].CEDRAM 摘要：In this paper we define and study the classical Uniform Electron Gas (UEG), a system of infinitely many electrons whose density is constant everywhere in space. The UEG is defined differently from Jellium, which has a positive constant background but no constraint on the density....
 作者：Stéphane Druel , Henri Guenancia 来源：[J].CEDRAM 摘要：In this paper we show that any smoothable complex projective variety, smooth in codimension two, with klt singularities and numerically trivial canonical class admits a finite cover, étale in codimension one, that decomposes as a product of an abelian variety, and singular a...
 作者：Nikolay Nikolov , Jakob Schneider , Andreas Thom 来源：[J].Journal de l'École polytechnique — Mathématiques, 2018, pp.239-258CEDRAM 摘要：The concept of a $\mathcal{C}$-approximable group, for a class of finite groups $\mathcal{C}$, is a common generalization of the concepts of a sofic, weakly sofic, and linear sofic group. Glebsky raised the question whether all groups are approximable by finite solvable groups wi...
 作者：Anne de Roton 来源：[J].Journal de l'École polytechnique — Mathématiques, 2018, pp.177-196CEDRAM 摘要：We prove a full continuous Freiman’s $3k-4$ theorem for small sumsets in $\mathbb{R}$ by using some ideas from Ruzsa’s work on measure of sumsets in $\mathbb{R}$ as well as some graphic representation of density functions of sets. We thereby get some structural properties of...
 作者：Houssam Abdoul-Anziz , Pierre Seppecher 来源：[J].Journal de l'École polytechnique — Mathématiques, 2018, pp.259-288CEDRAM 摘要：In the framework of $\Gamma$-convergence and periodic homogenization of highly contrasted materials, we study cylindrical structures made of one material and voids. Interest in high contrast homogenization is growing rapidly but assumptions are generally made in order to remain ...
 作者：Hoel Queffelec , Alistair Savage , Oded Yacobi 来源：[J].Journal de l'École polytechnique — Mathématiques, 2018, pp.197-238CEDRAM 摘要：We introduce a simple diagrammatic 2-category $\mathscr{A}$ that categorifies the image of the Fock space representation of the Heisenberg algebra and the basic representation of $\mathfrak{sl}_\infty$. We show that $\mathscr{A}$ is equivalent to a truncation of the Khovano...
 作者：Karine Beauchard , Karel Pravda-Starov 来源：[J].Journal de l'École polytechnique — Mathématiques, 2018, pp.1-43CEDRAM 摘要：We study the null-controllability of parabolic equations associated with a general class of hypoelliptic quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols. We consider in this work...
 作者：Raf Cluckers , Immanuel Halupczok 来源：[J].Journal de l'École polytechnique — Mathématiques, 2018, pp.45-78CEDRAM 摘要：Through a cascade of generalizations, we develop a theory of motivic integration which works uniformly in all non-archimedean local fields of characteristic zero, overcoming some of the difficulties related to ramification and small residue field characteristics. We define a clas...
 作者：Guido Carlet , Reinier Kramer , Sergey Shadrin 来源：[J].Journal de l'École polytechnique — Mathématiques, 2018, pp.149-175CEDRAM 摘要：We use refined spectral sequence arguments to calculate known and previously unknown bi-Hamiltonian cohomology groups, which govern the deformation theory of semi-simple bi-Hamiltonian pencils of hydrodynamic type with one independent and $N$ dependent variables. In particular, w...
 作者：Yiwen Ding 来源：[J].Annales de l'institut Fourier(IF 0.527), 2017, Vol.67 (4), pp.1457-1519CEDRAM 摘要：Let $F_{\wp }$ be a finite extension of $\mathbb{Q}_p$. By considering partially de Rham families, we establish a Colmez–Greenberg–Stevens formula (on Fontaine–Mazur $\mathcal{L}$-invariants) for (general) $2$-dimensional semi-stable non-crystalline representations of t...