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References

918 bibliography records ground the catalog in original papers, established surveys and monographs, institutional problem lists, and formal-proof archives.

Complete bibliography

918 records

  1. Tao2026KakeyaBourbaki

    The Kakeya conjecture, after Wang and Zahl

    2026 · misc

    Terence Tao, “The Kakeya conjecture, after Wang and Zahl,” Séminaire Bourbaki, 2026, arXiv: 2604.03416.

    Open source ↗
  2. Tasaki2025HeisenbergTopology

    The ground state of the antiferromagnetic Heisenberg chain is topologically nontrivial

    2025 · misc

    Hal Tasaki, “The ground state of the antiferromagnetic Heisenberg chain is topologically nontrivial,” 2025, arXiv: 2411.06789.

    Open source ↗
  3. Taubes2007Weinstein3D

    The Seiberg–Witten equations and the Weinstein conjecture

    2007 · misc

    Clifford H. Taubes, “The Seiberg–Witten equations and the Weinstein conjecture,” Geom. Topol. 11 (2007), 2117–2202, DOI 10.2140/gt.2007.11.2117.

    Open source ↗
  4. VanDeMoortel2026SCCSurvey

    The strong cosmic censorship conjecture

    2026 · misc

    Maxime Van de Moortel, “The strong cosmic censorship conjecture,” revised 2026, arXiv: 2501.13180. number number Dynamical systems

    Open source ↗
  5. Wang2026CylindricalVlasov

    Large data global solution of the 3D RVM system with cylindrical symmetry

    2026 · misc

    Xuecheng Wang, “Large data global solution of the 3D RVM system with cylindrical symmetry,” Princeton Analysis Seminar, 2026, abstract.

    Open source ↗
  6. WangZahl2025Kakeya3D

    Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions

    2025 · misc

    Hong Wang and Joshua Zahl, “Volume estimates for unions of convex sets, and the Kakeya set conjecture in three dimensions,” 2025, arXiv: 2502.17655.

    Open source ↗
  7. Weinberger2024HigherSignatures

    Higher -invariants and the surgery structure set

    2049 · misc

    Shmuel Weinberger, “Higher -invariants and the surgery structure set,” in contemporary surveys of the Novikov conjecture; for a stable source see the open survey DOI 10.5802/aif.2049.

    Open source ↗
  8. Weinreich2025AlgebraicBilliards

    Algebraic billiards in the Fermat hyperbola

    2025 · misc

    Max Weinreich, “Algebraic billiards in the Fermat hyperbola,” Adv. Math. (2025), arXiv: 2406.16172.

    Open source ↗
  9. Weinstein1979PeriodicOrbits

    On the hypotheses of Rabinowitz's periodic orbit theorems

    1979 · misc

    Alan Weinstein, “On the hypotheses of Rabinowitz's periodic orbit theorems,” J. Differential Equations 33 (1979), 353–358, DOI 10.1016/0022-0396(79)90070-690070-6).

    Open source ↗
  10. Wigner1934InteractionElectrons

    On the interaction of electrons in metals

    1934 · misc

    Eugene Wigner, “On the interaction of electrons in metals,” Phys. Rev. 46 (1934), 1002–1011, DOI 10.1103/PhysRev.46.1002.

    Open source ↗
  11. Wolff1999KakeyaSurvey

    Recent work connected with the Kakeya problem

    1999 · misc

    Thomas Wolff, “Recent work connected with the Kakeya problem,” in Prospects in Mathematics, AMS, 1999, 129–162.

  12. Wu2025BoussinesqSurvey

    Global regularity problem for the 2D Boussinesq equations with partial or fractional dissipation

    2025 · misc

    Jiahong Wu, “Global regularity problem for the 2D Boussinesq equations with partial or fractional dissipation,” invited survey lecture, 2025, event page.

    Open source ↗
  13. Xia1992NoncollisionSingularities

    The existence of noncollision singularities in Newtonian systems

    1992 · misc

    Zhihong Xia, “The existence of noncollision singularities in Newtonian systems,” Ann. of Math. 135 (1992), 411–468, DOI 10.2307/2946572.

    Open source ↗
  14. Yakovenko2001QuantitativeHilbert

    Quantitative theory of ordinary differential equations and the tangential Hilbert 16th problem

    2005 · misc

    Sergei Yakovenko, “Quantitative theory of ordinary differential equations and the tangential Hilbert 16th problem,” in On Finiteness in Differential Equations and Diophantine Geometry, CRM Monograph Series 24, AMS, 2005, 41–109, arXiv: math/0104140.

    Open source ↗
  15. YangMills1954IsotopicSpin

    Conservation of isotopic spin and isotopic gauge invariance

    1954 · misc

    Chen Ning Yang and Robert L. Mills, “Conservation of isotopic spin and isotopic gauge invariance,” Phys. Rev. 96 (1954), 191–195, DOI 10.1103/PhysRev.96.191.

    Open source ↗
  16. Yau1982OpenProblemsGeometry

    Seminar on Differential Geometry

    1982 · misc

    Shing-Tung Yau (ed.), Seminar on Differential Geometry, Annals of Mathematics Studies 102, Princeton Univ. Press, 1982.

  17. Yau1982ProblemNodalSets

    Problem section

    1982 · misc

    Shing-Tung Yau, “Problem section,” in Seminar on Differential Geometry, Annals of Mathematics Studies 102, Princeton Univ. Press, 1982, 669–706.

  18. Yoccoz1995PetitsDiviseurs

    Petits diviseurs en dimension 1

    1995 · misc

    Jean-Christophe Yoccoz, “Petits diviseurs en dimension 1,” Astérisque 231 (1995).

  19. Zahl2025KakeyaSurvey

    A survey of the Kakeya conjecture, 2000–2025

    2025 · misc

    Joshua Zahl, “A survey of the Kakeya conjecture, 2000–2025,” 2025, arXiv: 2512.09397.

    Open source ↗
  20. Ziller2007ExamplesNonnegative

    Examples of Riemannian manifolds with non-negative sectional curvature

    2006 · misc

    Wolfgang Ziller, “Examples of Riemannian manifolds with non-negative sectional curvature,” in Surveys in Differential Geometry XI, 2007, 63–102, DOI 10.4310/SDG.2006.v11.n1.a3.

    Open source ↗
  21. BrownSchreiberTaylor1973Pompeiu

    Spectral synthesis and the Pompeiu problem

    1973 · misc

    Leon Brown, Bertram M. Schreiber and B. Alan Taylor, “Spectral synthesis and the Pompeiu problem,” Ann. Inst. Fourier 23 (1973), no. 3, 125–154.

    Open source ↗
  22. Williams1976Pompeiu

    A partial solution of the Pompeiu problem

    1976 · misc

    Stephen A. Williams, “A partial solution of the Pompeiu problem,” Math. Ann. 223 (1976), 183–190.

    Open source ↗
  23. Zalcman1992PompeiuSurvey

    A bibliographic survey of the Pompeiu problem

    1992 · misc

    Lawrence Zalcman, “A bibliographic survey of the Pompeiu problem,” in Approximation by Solutions of Partial Differential Equations, NATO ASI Series C 365, Kluwer, 1992, 185–194.

    Open source ↗
  24. Dai2025SchifferWithdrawn

    Confirmed answer to the Schiffer conjecture and the Berenstein conjecture

    2025 · misc

    Guowei Dai, arXiv:2501.02724 (2025), withdrawn by the author because the constant-breadth proof was insufficient.

    Open source ↗
  25. Logunov2018NodalLowerBound

    Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture

    2018 · misc

    Alexander Logunov, “Nodal sets of Laplace eigenfunctions: proof of Nadirashvili's conjecture and of the lower bound in Yau's conjecture,” Ann. of Math. 187 (2018), 241–262.

    Open source ↗
  26. Stovall2020ParaboloidExtremizersOpen source ↗
  27. RiosSawyer2026ParaboloidCharacterization

    A smooth Alpert testing characterization of convolution type for the Fourier extension conjecture on paraboloids

    Cristian Rios and Eric T. Sawyer · 2026 · misc

    Current version v9, July 31, 2026; v8 explicitly retracts the earlier proof claim because of an uncontrolled error term

    Open source ↗
  28. Penrose1973NakedSingularities

    Naked singularities

    Roger Penrose · 1973 · article

    Open source ↗
  29. Mars2009PenroseStatus

    Present status of the Penrose inequality

    Marc Mars · 2009 · article

    Open source ↗
  30. AllenBrydenKazarasKhuri2025SuboptimalPenroseOpen source ↗
  31. Xu2025ConditionalSpacetimePenrose

    The Spacetime Penrose Inequality: Conditional Results for Stable MOTS and General Trapped Surfaces

    Da Xu · 2025 · misc

    Current version v5; the unconditional claim in v1 is superseded

    Open source ↗
  32. AmbrosioCabre2000DeGiorgi

    Entire solutions of semilinear elliptic equations in R3 and a conjecture of De Giorgi

    2000 · misc

    Luigi Ambrosio and Xavier Cabré, “Entire solutions of semilinear elliptic equations in R3 and a conjecture of De Giorgi,” J. Amer. Math. Soc. 13 (2000), 725–739, DOI 10.1090/S0894-0347-00-00345-3.

    Open source ↗
  33. BaumConnesHigson1994Classifying

    Classifying space for proper actions and K-theory of group C*-algebras

    1994 · misc

    Paul Baum, Alain Connes and Nigel Higson, “Classifying space for proper actions and K-theory of group C*-algebras,” in C*-Algebras: 1943–1993, Contemp. Math. 167 (1994), 241–291, DOI 10.1090/conm/167/1292018.

    Open source ↗
  34. BourgainSarnakZiegler2013Mobius

    Disjointness of Möbius from horocycle flows

    2013 · misc

    Jean Bourgain, Peter Sarnak and Tamar Ziegler, “Disjointness of Möbius from horocycle flows,” in From Fourier Analysis and Number Theory to Radon Transforms and Geometry, Dev. Math. 28, Springer, 2013, 67–83, DOI 10.1007/978-1-4614-4075-8_5.

    Open source ↗
  35. DeGiorgi1979ConvergenceProblems

    Convergence problems for functionals and operators

    1979 · misc

    Ennio De Giorgi, “Convergence problems for functionals and operators,” Proceedings of the International Meeting on Recent Methods in Nonlinear Analysis (Rome, 1978), Pitagora, Bologna, 1979, 131–188.

  36. DelPinoKowalczykWei2011DeGiorgi

    On De Giorgi's conjecture in dimension N greater than or equal to 9

    2011 · misc

    Manuel del Pino, Michał Kowalczyk and Juncheng Wei, “On De Giorgi's conjecture in dimension N greater than or equal to 9,” Ann. of Math. 174 (2011), 1485–1569, DOI 10.4007/annals.2011.174.3.3.

    Open source ↗
  37. DuminilCopin2022CriticalIsing

    100 years of the (critical) Ising model on the hypercubic lattice

    2022 · misc

    Hugo Duminil-Copin, “100 years of the (critical) Ising model on the hypercubic lattice,” Proc. Int. Cong. Math. 2022, Vol. 1, 164–210, DOI 10.4171/ICM2022/204.

    Open source ↗
  38. Dykema1994InterpolatedFreeGroupFactors

    Interpolated free group factors

    1994 · misc

    Kenneth J. Dykema, “Interpolated free group factors,” Pacific J. Math. 163 (1994), 123–135, DOI 10.2140/pjm.1994.163.123.

    Open source ↗
  39. ElShowkEtAl2012ThreeDimensionalIsing

    Solving the 3D Ising model with the conformal bootstrap

    2012 · misc

    Sheer El-Showk, Miguel F. Paulos, David Poland, Slava Rychkov, David Simmons-Duffin and Alessandro Vichi, “Solving the 3D Ising model with the conformal bootstrap,” Phys. Rev. D 86 (2012), 025022, DOI 10.1103/PhysRevD.86.025022.

    Open source ↗
  40. FerencziKulagaPrzymusLemanczyk2018Sarnak

    Sarnak's conjecture: what's new

    2018 · misc

    Sébastien Ferenczi, Joanna Kułaga-Przymus and Mariusz Lemańczyk, “Sarnak's conjecture: what's new,” in Ergodic Theory and Dynamical Systems in their Interactions with Arithmetics and Combinatorics, Lecture Notes in Math. 2213, Springer, 2018, 163–235, DOI 10.1007/978-3-319-74908-2_11.

    Open source ↗
  41. FrantzikinakisHost2018LogarithmicSarnak

    The logarithmic Sarnak conjecture for ergodic weights

    2018 · misc

    Nikos Frantzikinakis and Bernard Host, “The logarithmic Sarnak conjecture for ergodic weights,” Ann. of Math. 187 (2018), 869–931, DOI 10.4007/annals.2018.187.3.6.

    Open source ↗
  42. GoldbringPi2025FirstOrderFreeGroupFactors

    On the first-order free group factor elementary equivalence

    2025 · misc

    Isaac Goldbring and Jennifer Pi, “On the first-order free group factor elementary equivalence,” J. Operator Theory 94 (2025), 129–150, DOI 10.7900/jot.2023sep11.246.

    Open source ↗
  43. GomezAparicioJulgValette2019BaumConnesSurvey

    The Baum–Connes conjecture: an extended survey

    2019 · misc

    María Paula Gómez Aparicio, Pierre Julg and Alain Valette, “The Baum–Connes conjecture: an extended survey,” in Advances in Noncommutative Geometry, Springer, 2019, 127–244, DOI 10.1007/978-3-030-29597-4_3.

    Open source ↗
  44. HigsonKasparov2001ETheory

    E-theory and KK-theory for groups which act properly and isometrically on Hilbert space

    2001 · misc

    Nigel Higson and Gennadi Kasparov, “E-theory and KK-theory for groups which act properly and isometrically on Hilbert space,” Invent. Math. 144 (2001), 23–74, DOI 10.1007/s002220000118.

    Open source ↗
  45. HigsonLafforgueSkandalis2002Counterexamples

    Counterexamples to the Baum–Connes conjecture

    2002 · misc

    Nigel Higson, Vincent Lafforgue and Georges Skandalis, “Counterexamples to the Baum–Connes conjecture,” Geom. Funct. Anal. 12 (2002), 330–354, DOI 10.1007/s00039-002-8249-5.

    Open source ↗
  46. Kulske2025IsingHighlights

    The Ising model: highlights and perspectives

    2025 · misc

    Christof Külske, “The Ising model: highlights and perspectives,” Math. Phys. Anal. Geom. 28 (2025), article 20, DOI 10.1007/s11040-025-09515-1.

    Open source ↗
  47. PolandSimmonsDuffin2016ConformalBootstrap

    The conformal bootstrap

    2016 · misc

    David Poland and David Simmons-Duffin, “The conformal bootstrap,” Nature Phys. 12 (2016), 535–539, DOI 10.1038/nphys3761.

    Open source ↗
  48. Radulescu1994RandomMatricesFreeFactors

    Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index

    1994 · misc

    Florin Rădulescu, “Random matrices, amalgamated free products and subfactors of the von Neumann algebra of a free group, of noninteger index,” Invent. Math. 115 (1994), 347–390.

    Open source ↗