Comprehensive-List

Subject Key:

  • {F} formal and computer-assisted proof,
  • {D} discrete geometry,
  • {M} motivic integration,
  • {L} Langlands program,
  • {O} Other

Type Key:

  • {B} book,
  • {E} expository,
  • {R} recent,
  • {T} top-10,

Publication List:

  1. Unipotent classes induced from endoscopic groups, M.S.R.I. preprint series #08220-87, September 1987 –not-online–. {L}
  2. Shalika germs on GSp(4). Orbites unipotentes et représentations, II. Astérisque 171-172 (1989), 195–256 pdf-link. {L}
  3. Orbital integrals on U(3). The zeta functions of Picard modular surfaces, 303–333, Univ. Montréal, Montreal, QC, 1992 pdf-link. {L}
  4. The Subregular germ of orbital integrals Mem. AMS 99, 1992, no. 476, pdf-link. {L}{B}
  5. The sphere packing problem. J. Comput. Appl. Math. 44 (1992), no. 1, 41–76, pdf-link. {D}
  6. A simple definition of transfer factors for unramified groups. Representation theory of groups and algebras, 109–134, Contemp. Math., 145, Amer. Math. Soc., Providence, RI, 1993, pdf-link. {L}
  7. Remarks on the density of sphere packings in three dimensions. Combinatorica 13 (1993), no. 2, 181–197 pdf-link. {D}
  8. Unipotent representations and unipotent classes in SL(n). Amer. J. Math. 115 (1993), no. 6, 1347–1383, behind JSTOR wall. {L}
  9. The status of the Kepler conjecture. Math. Intelligencer 16 (1994), no. 3, 47–58, springer-link. {D}{E}
  10. The twisted endoscopy of GL(4) and GL(5): transfer of Shalika germs. Duke Math. J. 76 (1994), no. 2, 595–632, pdf-link. {L}
  11. Hyperelliptic curves and harmonic analysis (why harmonic analysis on reductive p-adic groups is not elementary). Representation theory and analysis on homogeneous spaces, 137–169, Contemp. Math., 177, Amer. Math. Soc., Providence, RI, 1994, pdf-link. {L}
  12. On the fundamental lemma for standard endoscopy: reduction to unit elements. Canad. J. Math. 47 (1995), no. 5, 974–994, pdf-link. {L}{T}
  13. The fundamental lemma for Sp(4). Proc. Amer. Math. Soc. 125 (1997), no. 1, 301–308, ams-pdf. {L}
  14. Sphere packings I. Discrete Comput. Geom. 17 (1997), no. 1, 1–51, arXiv:math/9811073. {D}
  15. Sphere packings II. Discrete Comput. Geom. 18 (1997), no. 2, 135–149, arXiv:math/9811074. {D}
  16. Cannonballs and honeycombs. Notices Amer. Math. Soc. 47 (2000), no. 4, 440–449, AMS-link. {D}{E}{T}
  17. (with P. Sarnak and M. C. Pugh) Advances in random matrix theory, zeta functions, and sphere packing. Proc. Natl. Acad. Sci. USA 97 (2000), no. 24, 12963–12964, pdf-link. {D}
  18. Sphere packings in 3 dimensions, Arbeitstagung proceedings, June 2001, arXiv:math/0205208. {D}
  19. The honeycomb conjecture. Discrete Comput. Geom. 25 (2001), no. 1, 1–22, arXiv:math/9906042. {D}{T}
  20. A computer verification of the Kepler conjecture. Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002), 795–804, Higher Ed. Press, Beijing, 2002, arXiv:math/0305012. {D}
  21. The honeycomb problem on the sphere, preprint 2002, arXiv:math/0211234. {D}
  22. (with J. Gordon) Virtual transfer factors. Represent. Theory 7 (2003), 81–100, arXiv:math/0209001. {M}{L}
  23. Some algorithms arising in the proof of the Kepler conjecture. Discrete Comput. Geom., 489–507, Algorithms Combin., 25, Springer, Berlin, 2003, arXiv:math/0205209. {D}
  24. Can p-adic integrals be computed? Contributions to automorphic forms, geometry, and number theory, 313–329, Johns Hopkins Univ. Press, Baltimore, MD, 2004, arXiv:math/0205207. {M}{L}
  25. (with C. Cunningham) Good orbital integrals. Represent. Theory 8 (2004), 414–457, arXiv:math/0311353. {M}{L}
  26. Orbital integrals are motivic. Proc. Amer. Math. Soc. 133 (2005), no. 5, 1515–1525, arXiv:math/0212236. {M}{L}
  27. What is motivic measure? Bull. Amer. Math. Soc. 42 (2005), 119-135, arxiv-link. {M}{E}{T}
  28. A proof of the Kepler conjecture. Ann. of Math. 162 (2005), no. 3, 1065–1185, Annals-link. {D}{T}
  29. Introduction to the Flyspeck project. Mathematics, Algorithms, Proofs, 05021, Dagstuhl Seminar Proceedings, Internationales Begegnungs- und Forschungszentrum (IBFI), Schloss Dagstuhl, Germany, 2006, pdf-link. {F}{D}
  30. (with S. P. Ferguson) A formulation of the Kepler conjecture. Discrete Comput. Geom., 36 (2006), 21–70, arXiv:math/9811072. {D}
  31. Historical overview of the Kepler conjecture. Discrete Comput. Geom., 36 (2006), 5–20, arXiv:math/9811071. {D}{E}
  32. Sphere packings III: extremal cases. Discrete Comput. Geom., 36 (2006), 71–110, arXiv:math/9811076. {D}
  33. Sphere packings IV: detailed bounds. Discrete Comput. Geom., 36 (2006), 111–166, arXiv:math/9811076. {D}
  34. Sphere packings VI: tame graphs and linear programs. Discrete Comput. Geom., 36 (2006), 205–266, arXiv:math/9811078. {D}
  35. A statement of the fundamental lemma. Harmonic Analysis, The Trace Formula, and Shimura Varieties, 643–658, Clay Math. Proc., 4, Amer. Math. Soc., Providence, RI, 2006, arXiv:math/0312227. {L}{E}
  36. The Jordan curve theorem, formally and informally. Amer. Math. Monthly 114 (2007), no. 10, 882–894, MAA-link. {D}{T}
  37. Jordan’s proof of the Jordan curve theorem. From Insight to Proof: Festscrift in Honour of Andrzej Trybulec, Studies in Logic, Grammar and Rhetoric 10 (23) 2007, 45–60, pdf-link. {D}
  38. Equidecomposable quadratic regions. Automated Deduction in Geometry, Lecture Notes in Computer Science 4869, Springer, 2007, pdf-link. {D}
  39. Some methods of problem solving in elementary geometry. LICS ’07: Proceedings of the 22nd Annual IEEE Symposium on Logic in Computer Science, IEEE Society Press, (2007), 35–40, –not-online–. {D}
  40. Formal proof. Notices Amer. Math. Soc. 55 (2008), no. 11, 1370–1380, AMS-link. {F}{E}{T}
  41. (with J. Harrison, S. McLaughlin, T. Nipkow, S. Obua, R. Zumkeller) A revision of the proof of the Kepler conjecture. Discrete Comput. Geom., (2009), arXiv:0902.0350. {D}
  42. (with S. McLaughlin) A proof of the dodecahedral conjecture. J. Amer. Math. Soc, 23 (2010), 299–344, arxiv-link. {D}
  43. My teacher Paul J. Cohen. Notices Amer. Math. Soc., 57, no. 7, August 2010, 833–834, notices-link. {O}{E}
  44. (with R. Cluckers and F. Loeser) Transfer principle for the fundamental lemma. Stabilization of the trace formula, Shimura varieties, and arithmetic applications ed. M. Harris, arXiv:0712.0708. {M}{L}{T}
  45. The Mathematical Work of the 2010 Fields Medalists: The Work of Ngô Bao Châu, Notices of the AMS, 58, no. 3, March 2011, 453–458, arXiv:1012.0382. {L}{E}
  46. Computational Discrete Gemetry, extended abstract in Mathematical Software — ICMS 2010, Proc. Third International Congress on Mathematical Software, 2010, LNCS 6327, pp. 1-3, Springer, 2010, pdf-link. {D}{F}
  47. Linear Programs for the Kepler Conjecture, extended abstract in Mathematical Software — ICMS 2010, Proc. Third International Congress on Mathematical Software, 2010, LNCS 6327, pp. 149–151, Springer, 2010, pdf-link. {D}{F}
  48. (with A. Solovyev) Efficient formal verification of bounds of linear programs, LNCS 6824, 2011, pdf-link. {F}
  49. The fundamental lemma and the Hitchin fibration (after Ngô Bao Châu), Bourbaki seminar 2010-2011, no. 1035, April 2011, arXiv:1103.4066K. {L}{E}
  50. (with J. Lagarias and S. Ferguson) The Kepler Conjecture: the Hales-Ferguson ProofSpringer, 2011. {B}{D}
  51. Dense Sphere Packings: a blueprint for formal proofs, Cambridge University Press, LMS volume 400, 2012, pdf-link. {F}{D}{B}{R}{T}
  52. On the Reinhardt Conjecture, Vietnam Journal of Mathematics, 39(3), 2012, arxiv:1103.4518. {D}{R}
  53. The Strong Dodecahedral Conjecture and Fejes Toth’s Contact Conjecture, in Discrete Geometry and Optimization Series: Fields Institute Communications, Vol. 69 Bezdek, Karoly; Deza, Antoine; Ye, Yinyu (Eds.) 2013, arxiv:1110.0402. {D}{R}
  54. (with A. Solovyev) Formal Verification of Nonlinear Inequalities with Taylor Interval Approximations, proceedings of the fifth NASA Formal Methods Symposium (NFM) 2013, arxiv:1301.1702. {F}{R}
  55. A Proof of Fejes Toth’s Conjecture on Sphere Packings with Kissing Number Twelve, preprint 2012, arxiv:1209.6043. {D}
  56. Mathematics in the Age of the Turing Machine, in Turing’s Legacy, Lecture Notes in Logic, 42, Cambridge, 2014, arxiv:1302.2898. {F}{E}{R}
  57. The NSA back door to NIST, Notices of the AMS, 61(2), February 2014, pdf-link. {O}{E}{R}
  58. Developments in Formal Proofs, Bourbaki, year 66, number 1086, June 2014, arxiv:1408.6474. {F}{E}{R}
  59. (with 21 other coauthors including A. Solovyev and Hoang Le Truong) A Formal proof of the Kepler conjecture, preprint 2014, arxiv:1501.02155. {D}{F}{R}{T}
  60. (with J. Gordon) Endoscopic transfer of orbital integrals in large residual characteristic, Amer. J. Math. 138(1), February 2016, pp. 109–148, arxiv:1502.07368. {M}{L}{R}
  61. (with W. Kusner) Packings of Regular Pentagons in the Plane, preprint 2016, arxiv:1602.07220. {D}{R}
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