@incollection{Carleson1980,
  author = {Carleson, Lennart},
  title = {Some analytic problems related to statistical mechanics},
  booktitle = {Euclidean Harmonic Analysis},
  editor = {Benedetto, John J.},
  series = {Lecture Notes in Mathematics},
  volume = {779},
  pages = {5--45},
  publisher = {Springer},
  address = {Berlin--Heidelberg},
  year = {1980},
  doi = {10.1007/BFb0087666},
  url = {https://doi.org/10.1007/BFb0087666}
}

@incollection{DahlbergKenig1982,
  author = {Dahlberg, Bj{\"o}rn E. J. and Kenig, Carlos E.},
  title = {A note on the almost everywhere behavior of solutions to the {Schr{\"o}dinger} equation},
  booktitle = {Harmonic Analysis},
  editor = {Ricci, Fulvio and Weiss, Guido},
  series = {Lecture Notes in Mathematics},
  volume = {908},
  pages = {205--209},
  publisher = {Springer},
  address = {Berlin--Heidelberg},
  year = {1982},
  doi = {10.1007/BFb0093289},
  url = {https://doi.org/10.1007/BFb0093289}
}

@article{Bourgain2016,
  author = {Bourgain, Jean},
  title = {A note on the {Schr{\"o}dinger} maximal function},
  journal = {Journal d'Analyse Math{\'e}matique},
  volume = {130},
  pages = {393--396},
  year = {2016},
  doi = {10.1007/s11854-016-0042-8},
  url = {https://arxiv.org/abs/1609.05744}
}

@article{DuGuthLi2017,
  author = {Du, Xiumin and Guth, Larry and Li, Xiaochun},
  title = {A sharp {Schr{\"o}dinger} maximal estimate in {$\mathbb{R}^2$}},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {186},
  number = {2},
  pages = {607--640},
  year = {2017},
  doi = {10.4007/annals.2017.186.2.5},
  url = {https://annals.math.princeton.edu/2017/186-2/p05}
}

@article{DuZhang2019,
  author = {Du, Xiumin and Zhang, Ruixiang},
  title = {Sharp {$L^2$} estimates of the {Schr{\"o}dinger} maximal function in higher dimensions},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {189},
  number = {3},
  pages = {837--861},
  year = {2019},
  doi = {10.4007/annals.2019.189.3.4},
  url = {https://arxiv.org/abs/1805.02775v3},
  note = {Theorem locators refer to arXiv:1805.02775v3}
}

@article{BD2015,
  author = {Bourgain, Jean and Demeter, Ciprian},
  title = {The proof of the {$l^2$} {Decoupling Conjecture}},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {182},
  number = {1},
  pages = {351--389},
  year = {2015},
  doi = {10.4007/annals.2015.182.1.9},
  url = {https://annals.math.princeton.edu/2015/182-1/p09}
}

@article{GIOW2020,
  author = {Guth, Larry and Iosevich, Alex and Ou, Yumeng and Wang, Hong},
  title = {On {Falconer's} distance set problem in the plane},
  journal = {Inventiones Mathematicae},
  volume = {219},
  pages = {779--830},
  year = {2020},
  doi = {10.1007/s00222-019-00917-x},
  url = {https://arxiv.org/abs/1808.09346v1},
  note = {Theorem locators refer to arXiv:1808.09346v1}
}

@article{DIOWZ2021,
  author = {Du, Xiumin and Iosevich, Alex and Ou, Yumeng and Wang, Hong and Zhang, Ruixiang},
  title = {An improved result for {Falconer's} distance set problem in even dimensions},
  journal = {Mathematische Annalen},
  volume = {380},
  pages = {1215--1231},
  year = {2021},
  doi = {10.1007/s00208-021-02170-1},
  url = {https://arxiv.org/abs/2006.06833v2},
  note = {Theorem locators refer to arXiv:2006.06833v2}
}

@article{BCT2006,
  author = {Bennett, Jonathan and Carbery, Anthony and Tao, Terence},
  title = {On the multilinear restriction and {Kakeya} conjectures},
  journal = {Acta Mathematica},
  volume = {196},
  number = {2},
  pages = {261--302},
  year = {2006},
  doi = {10.1007/s11511-006-0006-4},
  url = {https://webhomes.maths.ed.ac.uk/~carbery/analysis/papers/Carbery/MRKbct_revised7.pdf},
  note = {Theorem locators refer to the author manuscript dated April 2006}
}

@article{Guth2010,
  author = {Guth, Larry},
  title = {The endpoint case of the {Bennett--Carbery--Tao} multilinear {Kakeya} conjecture},
  journal = {Acta Mathematica},
  volume = {205},
  number = {2},
  pages = {263--286},
  year = {2010},
  doi = {10.1007/s11511-010-0055-6},
  url = {https://arxiv.org/abs/0811.2251v2},
  note = {Theorem locators refer to arXiv:0811.2251v2}
}

@article{Tao2020,
  author = {Tao, Terence},
  title = {Sharp bounds for multilinear curved {Kakeya}, restriction and oscillatory integral estimates away from the endpoint},
  journal = {Mathematika},
  volume = {66},
  number = {2},
  pages = {517--576},
  year = {2020},
  doi = {10.1112/mtk.12029},
  url = {https://arxiv.org/abs/1907.11342v2},
  note = {Theorem locators refer to arXiv:1907.11342v2}
}

@article{He2020,
  author = {He, Weikun},
  title = {Orthogonal projections of discretized sets},
  journal = {Journal of Fractal Geometry},
  volume = {7},
  number = {3},
  pages = {271--317},
  year = {2020},
  doi = {10.4171/JFG/92},
  url = {https://arxiv.org/abs/1710.00795v2},
  note = {Theorem locators refer to arXiv:1710.00795v2}
}

@article{BourgainProjection2010,
  author = {Bourgain, Jean},
  title = {The discretized sum-product and projection theorems},
  journal = {Journal d'Analyse Math\'{e}matique},
  volume = {112},
  pages = {193--236},
  year = {2010},
  doi = {10.1007/s11854-010-0028-x}
}

@article{Wongkew1993,
  author = {Wongkew, Richard Alexander},
  title = {Volumes of tubular neighbourhoods of real algebraic varieties},
  journal = {Pacific Journal of Mathematics},
  volume = {159},
  number = {1},
  pages = {177--184},
  year = {1993},
  doi = {10.2140/pjm.1993.159.177},
  url = {https://msp.org/pjm/1993/159-1/pjm-v159-n1-p10-s.pdf}
}

@misc{Basu2014,
  author = {Basu, Saugata},
  title = {Algorithms in real algebraic geometry: a survey},
  year = {2014},
  howpublished = {arXiv:1409.1534v1},
  url = {https://arxiv.org/abs/1409.1534v1},
  note = {Theorem 2.4 on p.~6 and the connecting-path discussion on p.~37 of this version}
}

@article{GuthKatz2015,
  author = {Guth, Larry and Katz, Nets Hawk},
  title = {On the {Erd{\H{o}}s} distinct distances problem in the plane},
  journal = {Annals of Mathematics},
  series = {2},
  volume = {181},
  number = {1},
  pages = {155--190},
  year = {2015},
  doi = {10.4007/annals.2015.181.1.2},
  url = {https://annals.math.princeton.edu/2015/181-1/p02}
}

@article{Guth2016Restriction,
  author = {Guth, Larry},
  title = {A restriction estimate using polynomial partitioning},
  journal = {Journal of the American Mathematical Society},
  volume = {29},
  number = {2},
  pages = {371--413},
  year = {2016},
  doi = {10.1090/jams827},
  url = {https://arxiv.org/abs/1407.1916v3},
  note = {Theorem locators refer to arXiv:1407.1916v3}
}

@article{GuthKatz2010Algebraic,
  author = {Guth, Larry and Katz, Nets Hawk},
  title = {Algebraic methods in discrete analogs of the {Kakeya} problem},
  journal = {Advances in Mathematics},
  volume = {225},
  pages = {2828--2839},
  year = {2010},
  doi = {10.1016/j.aim.2010.05.015},
  url = {https://arxiv.org/abs/0812.1043v1},
  note = {Theorem locators refer to arXiv:0812.1043v1}
}

@article{BourgainGuth2011,
  author = {Bourgain, Jean and Guth, Larry},
  title = {Bounds on oscillatory integral operators based on multilinear estimates},
  journal = {Geometric and Functional Analysis},
  volume = {21},
  number = {6},
  pages = {1239--1295},
  year = {2011},
  doi = {10.1007/s00039-011-0140-9},
  url = {https://arxiv.org/abs/1012.3760v3},
  note = {Section locators refer to arXiv:1012.3760v3}
}

@article{Sjolin1987,
  author = {Sj{\"o}lin, Per},
  title = {Regularity of solutions to the {Schr{\"o}dinger} equation},
  journal = {Duke Mathematical Journal},
  volume = {55},
  number = {3},
  pages = {699--715},
  year = {1987},
  doi = {10.1215/S0012-7094-87-05535-9}
}

@article{Vega1988,
  author = {Vega, Luis},
  title = {{Schr{\"o}dinger} equations: pointwise convergence to the initial data},
  journal = {Proceedings of the American Mathematical Society},
  volume = {102},
  number = {4},
  pages = {874--878},
  year = {1988},
  doi = {10.1090/S0002-9939-1988-0934859-0}
}

@article{SjogrenSjolin1989,
  author = {Sj{\"o}gren, Peter and Sj{\"o}lin, Per},
  title = {Convergence properties for the time-dependent {Schr{\"o}dinger} equation},
  journal = {Annales Academiae Scientiarum Fennicae, Series A I Mathematica},
  volume = {14},
  pages = {13--25},
  year = {1989},
  url = {https://www.acadsci.fi/mathematica/Vol14/vol14pp013-025.pdf}
}

@incollection{Bourgain1995,
  author = {Bourgain, Jean},
  title = {Some new estimates on oscillatory integrals},
  booktitle = {Essays on Fourier Analysis in Honor of Elias M. Stein},
  editor = {Fefferman, Charles and Fefferman, Robert and Wainger, Stephen},
  series = {Princeton Mathematical Series},
  volume = {42},
  pages = {83--112},
  publisher = {Princeton University Press},
  year = {1995},
  url = {https://omeka.ihes.fr/document/M_91_60.pdf}
}

@article{MoyuaVargasVega1996,
  author = {Moyua, A. and Vargas, Ana and Vega, Luis},
  title = {{Schr{\"o}dinger} maximal function and restriction properties of the Fourier transform},
  journal = {International Mathematics Research Notices},
  volume = {1996},
  number = {16},
  pages = {793--815},
  year = {1996},
  doi = {10.1155/S1073792896000499}
}

@article{TaoVargas2000,
  author = {Tao, Terence and Vargas, Ana},
  title = {A bilinear approach to cone multipliers. {II}. Applications},
  journal = {Geometric and Functional Analysis},
  volume = {10},
  number = {1},
  pages = {216--258},
  year = {2000},
  doi = {10.1007/s000390050007}
}

@article{Tao2003,
  author = {Tao, Terence},
  title = {A sharp bilinear restriction estimate for paraboloids},
  journal = {Geometric and Functional Analysis},
  volume = {13},
  number = {6},
  pages = {1359--1384},
  year = {2003},
  doi = {10.1007/s00039-003-0449-0},
  url = {https://arxiv.org/abs/math/0210084}
}

@article{Lee2006,
  author = {Lee, Sanghyuk},
  title = {On pointwise convergence of the solutions to {Schr{\"o}dinger} equations in {$\mathbb R^2$}},
  journal = {International Mathematics Research Notices},
  volume = {2006},
  pages = {1--21},
  year = {2006},
  doi = {10.1155/IMRN/2006/32597},
  note = {Article ID 32597}
}

@article{Bourgain2013,
  author = {Bourgain, Jean},
  title = {On the {Schr{\"o}dinger} maximal function in higher dimension},
  journal = {Proceedings of the Steklov Institute of Mathematics},
  volume = {280},
  number = {1},
  pages = {46--60},
  year = {2013},
  doi = {10.1134/S0081543813010045},
  url = {https://arxiv.org/abs/1201.3342}
}

@article{DuGuthLiZhang2018,
  author = {Du, Xiumin and Guth, Larry and Li, Xiaochun and Zhang, Ruixiang},
  title = {Pointwise convergence of {Schr{\"o}dinger} solutions and multilinear refined {Strichartz} estimates},
  journal = {Forum of Mathematics, Sigma},
  volume = {6},
  pages = {1--18},
  year = {2018},
  doi = {10.1017/fms.2018.11},
  url = {https://arxiv.org/abs/1803.01720v2},
  note = {Article e14; theorem locators refer to arXiv:1803.01720v2}
}

@article{DuLi2024,
  author = {Du, Xiumin and Li, Jianhui},
  title = {{$L^p$} estimates of the maximal {Schr{\"o}dinger} operator in {$\mathbb R^n$}},
  journal = {Journal of Functional Analysis},
  volume = {288},
  number = {3},
  pages = {110737},
  year = {2025},
  doi = {10.1016/j.jfa.2024.110737},
  url = {https://arxiv.org/abs/2404.10958v2},
  note = {Theorem locators refer to arXiv:2404.10958v2}
}

@misc{SinghSinghParmar2026,
  author = {Singh, Shalender and Singh Parmar, Vishnu Priya},
  title = {Repairing the refined-decoupling proof of the {5/4} planar pinned {Falconer} theorem},
  year = {2026},
  howpublished = {arXiv:2608.28711v1},
  url = {https://arxiv.org/abs/2608.28711v1},
  note = {Theorems 1.1--1.2, Proposition 2.1, and Appendix A; planar ambient dimension}
}

@misc{PSE2026,
  author = {{OpenAI}},
  title = {{Endpoint convergence for the planar Schr\"odinger equation}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Endpoint-convergence-for-the-planar-Schrodinger-equation-September-24-2026/paper.pdf}{OAI:Endpoint-convergence-for-the-planar-Schrodinger-equation-September-24-2026}},
  year = {2026}
}

@misc{PanSunTan2026,
  author = {Pan, Yucheng and Sun, Wenchang and Tan, Jiheng},
  title = {Pointwise convergence of {Schr{\"o}dinger} operators in {Bessel} potential spaces},
  year = {2026},
  howpublished = {arXiv:2605.25833v2},
  url = {https://arxiv.org/abs/2605.25833v2},
  note = {Version dated 26 May 2026}
}

@misc{Chu2026,
  author = {Chu, Rena},
  title = {Counterexamples for generalizations of the non-elliptic {Schr{\"o}dinger} maximal operator},
  year = {2026},
  howpublished = {arXiv:2608.30048v1},
  url = {https://arxiv.org/abs/2608.30048v1},
  note = {Version dated 30 August 2026}
}