# Difference between revisions of "Timeline"

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− | | | + | | Vipulnaik: [http://whatisresearch.wordpress.com/2009/02/02/on-new-modes-of-mathematical-collaboration/ On new modes of mathematical collaboration] |

| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1661 Gowers.9]: Reweighting vertices needed for Varnavides? | | [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1661 Gowers.9]: Reweighting vertices needed for Varnavides? |

## Revision as of 14:01, 16 March 2009

Some highlights of the polymath1 project to date.

Date | General | Uniformity | Ergodic theory | Small n |
---|---|---|---|---|

Jan 26 | Nielsen: Doing science online | |||

Jan 27 | Gowers: Is massively collaborative mathematics possible? | |||

Jan 28 | Kalai: Mathematics, science, and blogs | |||

Jan 30 | Gowers: Background to a polymath project | |||

Feb 1 | Gowers: Questions of procedure
Gowers: A combinatorial approach to DHJ (1-199) Gowers: Why this particular problem? Tao: A massively collaborative mathematical project Trevisan: A people's history of mathematics |
Solymosi.2: IP-corners problem proposed
Tao.4: Analytic proof of Sperner? Regularisation needed? Hoang.4: Naive Varnavides for DHJ fails |
Gowers.1: Carlson-Simpson theorem useful?
Tao.4: Stationarity useful? | |

Feb 2 | Vipulnaik: On new modes of mathematical collaboration | Gowers.9: Reweighting vertices needed for Varnavides?
Tao.17: Should use [math]O(\sqrt{n})[/math] wildcards Tao.18: Use rich slices? Gowers.19: Collect obstructions to uniformity! Kalai.29: Fourier-analytic proof of Sperner? O'Donnell.32: Use uniform distribution on slices Gowers.38: Can't fix # wildcards in advance Tao.39: Can take # wildcards to be O(1) Bukh.44: Obstructions to Kruskal-Katona? |
Tao.8: [math]c_0=1[/math], [math]c_1=2[/math], [math]c_2=6[/math], [math]3^{n-O(\sqrt{n}} \leq c_n \leq o(3^n)[/math]
Kalai.15: [math]c_n \gg 3^n/\sqrt{n}[/math] Tao.39: [math]c_n \geq 3^{n-O(\sqrt{\log n})}[/math] Tao.40: [math]c_3=18[/math] Elsholtz.43: Moser(3)? | |

Feb 3 | Nielsen: The polymath project | Gowers.64: Use local equal-slices measure?
Gowers.70: Collection of obstructions to uniformity begins Tao.86: Use Szemeredi's proof of Roth? |
Jakobsen.59: [math]c_4 \geq 49[/math]
Tao.78: [math]c_4 \leq 54[/math] Neylon.83: [math]52 \leq c_4 \leq 54[/math], [math]140 \leq c_5 \leq 162[/math] | |

Feb 4 | Gowers: Quick question | Tao.100: Use density incrementation?
Tao.118: Szemeredi's proof of Roth looks inapplicable |
Jakobsen.90: [math]c_4=52[/math] | |

Feb 5 | Tea time: Introspection | Tao.130: DHJ(2.5)?
Bukh.132, O'Donnell.133, Solymosi.135: Proof of DHJ(2.5) Tao.148: Obstructions to uniformity summarised |
Tao: Upper and lower bounds for DHJ (200-299) | |

Feb 6 | Solymosi.155: Pair removal for Kneser graphs
Gowers: The triangle removal approach (300-399) |
Neylon.201: Greedy algorithm
Tao.206: Use [math]D_n[/math] | ||

Feb 7 | Gowers.335: DHJ(j,k) introduced | Jakobsen.207: [math]c_5 \geq 150[/math], [math]c_6 \geq 450[/math]
Peake.217: [math]c_7 \geq 1308[/math], [math]c_8 \geq 3780[/math] Peake.218: Lower bounds up to [math]c_{15}[/math] | ||

Feb 8 | Gowers: Quasirandomness and obstructions to uniformity: (400-499)
Ajtai-Szemeredi approach proposed Tao.402: Standard obstruction to uniformity? Gowers.403: Complexity 1 sets are more fundamental obstructions Gowers.411: Are global complexity 1 sets the only obstructions? |
Peake.219: [math]c_{99} \geq 3^{98}[/math]
Tao.225: Spreadsheet set up | ||

Feb 9 | Nielsen: Update on the polymath project | Bukh.412: Negative answer to Gowers' question
Gowers.365: Equal slices measure introduced Tao.419: Use low-influence instead of complexity 1? Gowers.420: Need DHJ(0,2) Tao.431: Use local obstructions rather than global obstructions? |
Kalai.233: Higher k? | |

Feb 10 | Tao.439: Use hypergraph regularity? | Peake.241: [math]c_5 \leq 155[/math]; xyz notation
Peake.243: [math]c_5 \leq 154[/math] | ||

Feb 11 | le Bruyn: Yet another Math 2.0 proposal
Tao.470: Proto-wiki created |
Tao.451: 01-insensitive case OK
Kalai.455: Hyper-optimistic conjecture |
Tao.460: Connections with ergodic approach
Tao: A reading seminar on DHJ (600-699) |
Tao.249: [math]\overline{c}^\mu_0 = 1[/math], [math]\overline{c}^\mu_1 = 2[/math], [math]\overline{c}^\mu_2 = 4[/math]
Dyer.254: [math]\overline{c}^\mu_3 = 6[/math] |

Feb 12 | Wiki set up | O'Donnell.476: Fourier-analytic Sperner computations
McCutcheon.480: Strong Roth theorem proposed |
Jakobsen.257: [math]\overline{c}^\mu_4 = 9[/math]
Jakobsen.258: [math]\overline{c}^\mu_5 = 12[/math] Peake.262: Extremisers for [math]c_4[/math] | |

Feb 13 | Gowers: Possible proof strategies (500-599) | McCutcheon.505: IP uniformity norms?
Tao.614: Carlson-Simpson not needed for stationarity |
Tao: Bounds for first few DHJ numbers (700-799) | |

Feb 14 | Gowers.496: Equal slices implies uniform | McCutcheon.508: Ergodic proof strategy
Tao.618: More randomness needed to invert maps O'Donnell.622: [math][3]^n[/math] should already provide enough randomness Tao.510: Finitary analogue of stationarity |
Sauvaget: A proof that [math]c_5=154[/math]? | |

Feb 15 | Tao.498: Uniform implies equal slices
Tao.514: DHJ(2.6) proposed McCutcheon.518: Ramsey proof of DHJ(2.6) |
Sauvaget: A new strategy for computing [math]c_n[/math]
Markström.706: Integer program, [math]c_5=150[/math] Cantwell.708: [math]c_6=450[/math] Tao.715: Genetic algorithm? | ||

Feb 16 | Tao.524: Simplification of proof
O'Donnell 529: Ramsey-free proof of DHJ(2.6)? McCutcheon.533: Ramsey theory incompatible with symmetry |
Tao.626: Ramsey theorems summarised | Peake.730: [math]c_5[/math] extremisers
Tao.731: Human proof that [math]c_5 \leq 152[/math]; [math]c_7 \leq 1348[/math] | |

Feb 17 | Tao.536: Fourier-analytic proof of DHJ(2.6)
McCutcheon.541: "Cave-man" proof of DHJ(2.6) |
Chua.736: [math]c'_5 \geq 124[/math]
Peake.738: Connection between Moser(3) and sphere packing | ||

Feb 18 | Gowers.544: Corners(1,3)?
Gowers.545: Fourier computations on equal-slices measure begin |
Markström.739: [math]c_6[/math] extremiser unique | ||

Feb 19 | Markström.742: 43-point Moser sets in [math][3]^4[/math] listed
Peake.743: 43-point sets analysed Cantwell.744: [math]c'_5 \leq 128[/math] Tao.745: 50+ point line-free sets in [math][3]^4[/math] listed | |||

Feb 20 | Vipulniak: A quick review of the polymath project | Solymosi.563: Moser(6) implies DHJ(3) | Tao.630: IP convergence lemma | Markström.747: 42-point Moser sets listed
Peake.751: Human proof of [math]c_5 \leq 151[/math] |

Feb 21 | Gowers: To thread or not to thread | Gowers.580: Extreme localisation + density increment = DHJ(3)?
Gowers.581: Multidimensional Sperner Gowers.582: Use Ajtai-Szemeredi argument to get density increment? |
Tao.631: Informal combinatorial translation of ergodic DHJ(2)
Tao.578: Finitary ergodic proof of DHJ(2) proposed Tao.632: Special cases of DHJ(3) translated |
Peake.752: Human proof of [math]c_5=150[/math], [math]c_6=450[/math]
Tao.753: Sequences submitted to OEIS |

Feb 22 | ||||

Feb 23 | McCutcheon.593: DHJ(2.7)
O'Donnell.596: Fourier-analytic proof of DHJ(2) Gowers: Brief review of polymath1 (800-849) O'Donnell.800: Fourier-analytic + density increment proof of DHJ(2) |
Markström.463: 42-point Moser sets analysed
Tao.464: [math]c'_5 \leq 127[/math] Chua.766: 3D Moser sets with 222 have [math] \leq 13[/math] points Tao.767: 4D Moser sets with 2222 have [math] \leq 39[/math] points | ||

Feb 24 | Tao.809.2: Low-influence implies Sperner-positivity
Gowers.812: Fourier vs physical positivity O'Donnell.814: [math]\ell_1[/math], [math]\ell_2[/math] equivalence |
|||

Feb 25 | Gowers.820: Density increment on complexity 1 set | Tao.818: Finitary ergodic sketch of DHJ(3)
O'Donnell.821: Simplified Fourier proof of DHJ(2) structure theorem |
Cantwell.769: 5D Moser sets with 2222* have [math] \leq 124[/math] points
Peake.771: Exotic 43-point Moser sets described | |

Feb 26 | Gowers.824: Complexity 1 + Ajtai-Szemeredi DHJ(3) sketch | |||

Feb 27 | Tao.826: Non-Fourier proof of DHJ(2) structure theorem
Gowers.828: Does correlation with 1-set imply density increment? Tao.828.4: Energy increment proof for Gowers Q? |
McCutcheon.832.2: Use dense fibres to answer Gowers Q? | Elsholtz.775: Human proof of 2222* result
Cantwell.776: [math]c'_5 \leq 126[/math] | |

Feb 28 | Tao.834: Use pullbacks for Gowers Q?
Gowers.835: Pullbacks don't work O'Donnell 839: Increment-free Fourier proof of DHJ(2) |
Tao.837.2: Dense fibres argument for Gowers Q | Markström.779: 41-point Moser sets listed | |

Mar 1 | Cantwell.782, Peake.784: [math]c'_5 \leq 125[/math] | |||

Mar 2 | Gowers: DHJ 851-899
Tao.853 Mass increment; connection with Hahn decomposition Gowers.854 Higher-D Ajtai-Szemeredi? |
|||

Mar 3 | McCutcheon.864 Caution: 12-sets not sigma-algebra! | Dyer.786 [math] \overline{c}^\mu_6 \lt 18[/math]
Cantwell.787 125-sets have at most 41 points in middle slices | ||

Mar 4 | Markstrom.788: [math] c^\mu_n = 4,6,9,12[/math] for [math]n=2,3,4,5[/math]
Marc.791: [math]\overline{c}^\mu_{10} \geq 29[/math] Tao.793: "score" introduced Tao: DHJ3 (900-999) Density Hales-Jewett type numbers Tao.901: 125-sets have D=0 Dyer.902: [math]\overline{c}^\mu_6 \lt 17[/math] Carr.903: Genetic algorithm implemented | |||

Mar 5 | Peake.904 Scores for 6D Moser?
Tao.908 Find Pareto-optimal and extremal statistics? Dyer.909 Wildcard variants of Moser Cantwell.912 125-sets have at most 40 points in middle slices Cantwell.913 125-sets have D=0 (alternate proof) Peake.914 Pareto-optimal 3D statistics | |||

Mar 6 | Gowers.873 12-set density increment difficulty identified | Dyer.917 [math]\overline{c}^\mu_7 \leq 22[/math]
Cantwell.920 [math]c'_6 \leq 373[/math] Cantwell.921 125-sets have C=78 or 79 Markstrom.923 [math]\overline{c}^\mu_n = 6,9,12,15,18,22,26,31,35,40[/math] for [math]n=3,\ldots,12[/math] Guest.930 GA without crossover? | ||

Mar 7 | Solymosi.880 Shelah-type flip-flop spaces? | Peake.931 3D extremals and inequalities
Cantwell.932 125-sets have a middle slice of at most 39 points Cantwell.933 125-sets have A=6,7,8 Cantwell.934 If C=78 then A=7,8 Tao.935 125-sets have stats (6,40,79,0,0,0), (7,40,78,0,0) or (8,39,78,0,0) | ||

Mar 8 | Gowers.881 Iterative partitioning of 12-sets?
Gowers.882 New proof of Ajtai-Szemeredi O'Donnell.884 Multidimensional Sperner written up |
Peake.939 [math]c'_6 \leq 365[/math]
Carr.940 [math]c'_6 \geq 353; c'_7 \geq 978[/math] Tao.941 Seeding GA? Cantwell.942 (6,40,79,0,0) eliminated Tao.943 Linear programming proof of [math]c'_4 =43[/math] Tao.944 [math]c'_6 \leq 364[/math] | ||

Mar 9 | Gowers.885 Sketch of DHJ(3)
Gowers.886 DHJ(4)? Gowers.897 Writing of DHJ(k) begins |
Austin.894 New ergodic proof of DHJ(k) | Cantwell.945 (7,40,78,0,0) eliminated
Cantwell.949 (8,39,87,0,0) eliminated: [math]c'_5 = 124[/math] Tao.950 [math]\overline{c}^\mu_n[/math] submitted to OEIS Carr.954 [math]c'_7 \geq 988[/math] | |

Mar 10 | Gowers: Polymath1 and open collaborative mathematics
OU Math club: Problem solved (probably) |
Gowers: Problem solved (probably) (1000-1049)
Gowers.1005.1 Tower-type bounds |
Tao.1003 1-sets, 2-sets locally independent | |

Mar 11 | Kalai: Polymath1: probable success | Gowers.1007 Correlation component of DHJ(k) proof complete
Solymosi.1011 Shelah-type argument? |
Markstrom.961 Partial confirmation of HOC for n=6,7
Elsholtz.962 Analysis of GA solutions Tao.969 Integer programming for Behrend sphere statistics Tao.970 [math]c'_7 \leq 1086[/math] | |

Mar 12 | O'Donnell.1021 DHJ(k) => Varnavides completed
Gowers.1020 No apparent obstacles to proving DHJ(k) O'Donnell.1025 Work exclusively with equal (non-degenerate) slices measure? |
Tao.1024 Informal combinatorial translation of Austin's proof | Markstrom.972, Dyer.973, Tao.974, Markstrom.977: Integer programming problem discovered, isolated, fixed
Tao.974: [math]c'_6 \leq 361[/math], [math]c'_7 \leq 1078[/math] Cantwell.976: Partial recovery of 4D stats by hand | |

Mar 13 | Nielsen: Biweekly links for 03/13/2009
Galdino: Links seminais Flaxman: Gowers' polymath experiment: problem probably solved |
Elsholtz.980: Use e=1, f=1, etc. refinements
Peake.982: xxyyzz inequalities O'Bryant.984, O'Bryant.993: [math]c_n \gg 3^{n - 4\sqrt{\log 2}\sqrt{\log n}+\frac 12 \log \log n}[/math] Cantwell.985: Human proof of [math]c^\mu_3=6[/math] begins Peake.989: xxyyz inequalities Tao.990: [math]c'_7 \leq 1071[/math] Peake.991: xxxyz, xxxxyz, xxxyyz inequalities Seva.994: Kakeya in [3]^n? | ||

Mar 14 | Hariss: Polymath | Gowers.1036 Density Graham-Rothschild? | Tao.1035 Ramsey-free translation of Austin's proof | Tao: DHJ(3) 1100-1199 |

Mar 15 | Neylon: There are crowds, and then there are crowds... |