@article{18483,
  abstract     = {In this paper we prove a perturbative version of a remarkable Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) result. They prove non perturbative Birkhoff conjecture for centrally-symmetric convex domains, namely, a centrally-symmetric convex domain with integrable billiard is ellipse. We combine techniques from Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) with a local result by Kaloshin–Sorrentino (Ann. Math. 188(1):315–380, 2018) and show that a domain close enough to a centrally symmetric one with integrable billiard is ellipse. To combine these results we derive a slight extension of Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) by proving that a notion of rational integrability is equivalent to the C0-integrability condition used in their paper.},
  author       = {Kaloshin, Vadim and Koudjinan, Edmond and Zhang, Ke},
  issn         = {1420-8970},
  journal      = {Geometric and Functional Analysis},
  pages        = {1973--2007},
  publisher    = {Springer Nature},
  title        = {{Birkhoff conjecture for nearly centrally symmetric domains}},
  doi          = {10.1007/s00039-024-00695-6},
  volume       = {34},
  year         = {2024},
}

@article{20616,
  abstract     = {We establish two WDVV-style relations for the disk invariants of real symplectic fourfolds by implementing Georgieva’s suggestion to lift homology relations from the Deligne–Mumford moduli spaces of stable real curves. This is accomplished by lifting judiciously chosen cobordisms realizing these relations. The resulting lifted relations lead to the recursions for Welschinger invariants announced by Solomon in 2007 and have the same structure as his WDVV-style relations, but differ by signs from the latter. Our topological approach provides a general framework for lifting relations via morphisms between not necessarily orientable spaces.},
  author       = {Chen, Xujia},
  issn         = {1420-8970},
  journal      = {Geometric and Functional Analysis},
  number       = {3},
  pages        = {490--567},
  publisher    = {Springer Nature},
  title        = {{Steenrod pseudocycles, lifted cobordisms, and Solomon’s relations for Welschinger invariants}},
  doi          = {10.1007/s00039-022-00596-6},
  volume       = {32},
  year         = {2022},
}

@article{22055,
  abstract     = {We present a general method for obtaining conservation laws for integrable PDE at negative regularity and exhibit its application to KdV, NLS, and mKdV. Our method works uniformly for these problems posed both on the line and on the circle.},
  author       = {Killip, Rowan and Visan, Monica and Zhang, Xiaoyi},
  issn         = {1420-8970},
  journal      = {Geometric and Functional Analysis},
  number       = {4},
  pages        = {1062--1090},
  publisher    = {Springer Nature},
  title        = {{Low regularity conservation laws for integrable PDE}},
  doi          = {10.1007/s00039-018-0444-0},
  volume       = {28},
  year         = {2018},
}

@article{259,
  abstract     = {The Hasse principle and weak approximation is established for
non-singular cubic hypersurfaces X over the function field Fq(t), provided that
char(Fq) > 3 and X has dimension at least 6.},
  author       = {Browning, Timothy D and Vishe, Pankaj},
  issn         = {1420-8970},
  journal      = {Geometric and Functional Analysis},
  number       = {3},
  pages        = {671 -- 732},
  publisher    = {Springer Nature},
  title        = {{Rational points on cubic hypersurfaces over F_q(t) }},
  doi          = {10.1007/s00039-015-0328-5},
  volume       = {25},
  year         = {2015},
}