@article{21343,
  abstract     = {The large sieve is used to estimate the density of quadratic polynomials Q ∈ Z[x],
such that there exists an odd degree polynomial defined over Z which has resultant ±1 with Q.
Given a monic polynomial R ∈ Z[x] of odd degree, this is used to show that for almost all
quadratic polynomials Q ∈ Z[x], there exists a prime p such that Q and R share a common
root in Fp. Using recent work of Landesman, an application to the average size of the odd part
of the class group of quadratic number fields is also given},
  author       = {Browning, Timothy D and Chan, Yik Tung},
  issn         = {2270-518X},
  journal      = {Journal de l'ecole polytechnique mathematiques},
  pages        = {1677--1691},
  publisher    = {Ecole polytechnique},
  title        = {{Solubility of a resultant equation and applications}},
  doi          = {10.5802/jep.320},
  volume       = {12},
  year         = {2025},
}

@article{18158,
  abstract     = {We study the geometry of Poisson point processes from the point of view of optimal transport and Ricci lower bounds. We construct a Riemannian structure on the space of point processes and the associated distance W that corresponds to the Benamou–Brenier variational formula. Our main tool is a non-local continuity equation formulated with the difference operator. The closure of the domain of the relative entropy is a complete geodesic space, when endowed with 
W. The geometry of this non-local infinite-dimensional space is analogous to that of spaces with positive Ricci curvature. Among others: (a) the Ornstein–Uhlenbeck semi-group is the gradient flow of the relative entropy; (b) the Poisson space has an entropic Ricci curvature bounded from below by 1; (c) W satisfies an HWI inequality.},
  author       = {Dello Schiavo, Lorenzo and Herry, Ronan and Suzuki, Kohei},
  issn         = {2270-518X},
  journal      = {Journal de l'Ecole Polytechnique - Mathematiques},
  pages        = {957--1010},
  publisher    = {Ecole Polytechnique},
  title        = {{Wasserstein geometry and Ricci curvature bounds for Poisson spaces}},
  doi          = {10.5802/jep.270},
  volume       = {11},
  year         = {2024},
}

@article{180,
  abstract     = {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. We prove that the UEG arises in Density Functional Theory in the limit of a slowly varying density, minimizing the indirect Coulomb energy. We also construct the quantum UEG and compare it to the classical UEG at low density.},
  author       = {Lewi, Mathieu and Lieb, Élliott and Seiringer, Robert},
  issn         = {2270-518X},
  journal      = {Journal de l'Ecole Polytechnique - Mathematiques},
  pages        = {79 -- 116},
  publisher    = {Ecole Polytechnique},
  title        = {{Statistical mechanics of the uniform electron gas}},
  doi          = {10.5802/jep.64},
  volume       = {5},
  year         = {2018},
}