@article{22929,
  abstract     = {The circle method has been successfully used over the last century to study rational points on hypersurfaces. More recently, a version of the method over function fields, combined with spreading out techniques, has led to a range of results about moduli spaces of rational curves on hypersurfaces. In this paper a version of the circle method is implemented in the setting of the Grothendieck ring of varieties. This allows us to approximate the classes of these moduli spaces directly, without relying on point counting, and leads to a deeper understanding of their geometry.},
  author       = {Bilu, Margaret and Browning, Timothy D},
  issn         = {1873-2151},
  journal      = {Annales Scientifiques de l’École Normale Supérieure},
  keywords     = {Circle method, moduli spaces of curves, hypersurfaces, Grothendieck ring of varieties, motivic integration},
  number       = {5},
  pages        = {1179--1242},
  publisher    = {Société Mathématique de France},
  title        = {{A motivic circle method}},
  doi          = {10.24033/asens.2628},
  volume       = {58},
  year         = {2025},
}

@article{8539,
  abstract     = {Cohomological and K-theoretic stable bases originated from the study of quantum cohomology and quantum K-theory. Restriction formula for cohomological stable bases played an important role in computing the quantum connection of cotangent bundle of partial flag varieties. In this paper we study the K-theoretic stable bases of cotangent bundles of flag varieties. We describe these bases in terms of the action of the affine Hecke algebra and the twisted group algebra of KostantKumar. Using this algebraic description and the method of root polynomials, we give a restriction formula of the stable bases. We apply it to obtain the restriction formula for partial flag varieties. We also build a relation between the stable basis and the Casselman basis in the principal series representations of the Langlands dual group. As an application, we give a closed formula for the transition matrix between Casselman basis and the characteristic functions.},
  author       = {Su, C. and Zhao, Gufang and Zhong, C.},
  issn         = {0012-9593},
  journal      = {Annales Scientifiques de l'Ecole Normale Superieure},
  number       = {3},
  pages        = {663--671},
  publisher    = {Societe Mathematique de France},
  title        = {{On the K-theory stable bases of the springer resolution}},
  doi          = {10.24033/asens.2431},
  volume       = {53},
  year         = {2020},
}