@article{10765,
  abstract     = {We establish the Hardy-Littlewood property (à la Borovoi-Rudnick) for Zariski open subsets in affine quadrics of the form q(x1,...,xn)=m, where q is a non-degenerate integral quadratic form in  n>3 variables and m is a non-zero integer. This gives asymptotic formulas for the density of integral points taking coprime polynomial values, which is a quantitative version of the arithmetic purity of strong approximation property off infinity for affine quadrics.},
  author       = {Cao, Yang and Huang, Zhizhong},
  issn         = {1090-2082},
  journal      = {Advances in Mathematics},
  number       = {3},
  publisher    = {Elsevier},
  title        = {{Arithmetic purity of the Hardy-Littlewood property and geometric sieve for affine quadrics}},
  doi          = {10.1016/j.aim.2022.108236},
  volume       = {398},
  year         = {2022},
}

@article{10033,
  abstract     = {The ⊗*-monoidal structure on the category of sheaves on the Ran space is not pro-nilpotent in the sense of [3]. However, under some connectivity assumptions, we prove that Koszul duality induces an equivalence of categories and that this equivalence behaves nicely with respect to Verdier duality on the Ran space and integrating along the Ran space, i.e. taking factorization homology. Based on ideas sketched in [4], we show that these results also offer a simpler alternative to one of the two main steps in the proof of the Atiyah-Bott formula given in [7] and [5].},
  author       = {Ho, Quoc P},
  issn         = {1090-2082},
  journal      = {Advances in Mathematics},
  keywords     = {Chiral algebras, Chiral homology, Factorization algebras, Koszul duality, Ran space},
  publisher    = {Elsevier},
  title        = {{The Atiyah-Bott formula and connectivity in chiral Koszul duality}},
  doi          = {10.1016/j.aim.2021.107992},
  volume       = {392},
  year         = {2021},
}