Difference between revisions of "Timeline"
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−    +   Vipulnaik: [http://whatisresearch.wordpress.com/2009/02/20/aquickreviewofthepolymathproject/ A quick review of the polymath project] 
 [http://gowers.wordpress.com/2009/02/13/dhjpossibleproofstrategies/#comment2296 Solymosi.563]: Moser(6) implies DHJ(3)   [http://gowers.wordpress.com/2009/02/13/dhjpossibleproofstrategies/#comment2296 Solymosi.563]: Moser(6) implies DHJ(3)  
 [http://terrytao.wordpress.com/2009/02/11/areadingseminarondensityhalesjewett/#comment36041 Tao.630]: IP convergence lemma   [http://terrytao.wordpress.com/2009/02/11/areadingseminarondensityhalesjewett/#comment36041 Tao.630]: IP convergence lemma  
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[http://terrytao.wordpress.com/2009/02/13/boundsforthefirstfewdensityhalesjewettnumbersandrelatedquantities/#comment36059 Tao.753]: Sequences submitted to OEIS  [http://terrytao.wordpress.com/2009/02/13/boundsforthefirstfewdensityhalesjewettnumbersandrelatedquantities/#comment36059 Tao.753]: Sequences submitted to OEIS  
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 Neylon: [http://blog.openwetware.org/scienceintheopen/2009/03/15/therearecrowdsandthentherearecrowds/ There are crowds, and then there are crowds...]   Neylon: [http://blog.openwetware.org/scienceintheopen/2009/03/15/therearecrowdsandthentherearecrowds/ There are crowds, and then there are crowds...]  
    
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+   Gowers: [http://gowers.wordpress.com/2009/03/16/dhj3andrelatedresults10501099/ DHJ(3) and related results: 10501099]  
    
    
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 Gowers: [http://gowers.wordpress.com/2009/03/24/canpolymathbescaledup/#comments Can Polymath be scaled up?]   Gowers: [http://gowers.wordpress.com/2009/03/24/canpolymathbescaledup/#comments Can Polymath be scaled up?]  
−  +  Vipulnaik: [http://whatisresearch.wordpress.com/2009/03/24/concludingnotesonthepolymathprojectandachallenge/ Concluding notes on the polymath project  and a challenge]  
    
   
Latest revision as of 16:47, 5 April 2009
A partial list of events occurring during 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 (1199) Gowers: Why this particular problem? Tao: A massively collaborative mathematical project Trevisan: A people's history of mathematics 
Solymosi.2: IPcorners problem proposed
Tao.4: Analytic proof of Sperner? Regularisation needed? Hoang.4: Naive Varnavides for DHJ fails 
Gowers.1: CarlsonSimpson 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: Fourieranalytic 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 KruskalKatona? 
Tao.8: [math]c_0=1[/math], [math]c_1=2[/math], [math]c_2=6[/math], [math]3^{nO(\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^{nO(\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 equalslices 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 (200299)  
Feb 6  Solymosi.155: Pair removal for Kneser graphs
Gowers: The triangle removal approach (300399) 
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: (400499)
AjtaiSzemeredi 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 lowinfluence 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: Protowiki created 
Tao.451: 01insensitive case OK
Kalai.455: Hyperoptimistic conjecture 
Tao.460: Connections with ergodic approach
Tao: A reading seminar on DHJ (600699) 
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: Fourieranalytic 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 (500599)  McCutcheon.505: IP uniformity norms?
Tao.614: CarlsonSimpson not needed for stationarity 
Tao: Bounds for first few DHJ numbers (700799)  
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: Ramseyfree 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: Fourieranalytic proof of DHJ(2.6)
McCutcheon.541: "Caveman" 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 equalslices measure begin 
Markström.739: [math]c_6[/math] extremiser unique  
Feb 19  Markström.742: 43point Moser sets in [math][3]^4[/math] listed
Peake.743: 43point sets analysed Cantwell.744: [math]c'_5 \leq 128[/math] Tao.745: 50+ point linefree sets in [math][3]^4[/math] listed  
Feb 20  Vipulnaik: A quick review of the polymath project  Solymosi.563: Moser(6) implies DHJ(3)  Tao.630: IP convergence lemma  Markström.747: 42point 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 AjtaiSzemeredi 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 23  McCutcheon.593: DHJ(2.7)
O'Donnell.596: Fourieranalytic proof of DHJ(2) Gowers: Brief review of polymath1 (800849) O'Donnell.800: Fourieranalytic + density increment proof of DHJ(2) 
Markström.463: 42point 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: Lowinfluence implies Spernerpositivity
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 43point Moser sets described  
Feb 26  Gowers.824: Complexity 1 + AjtaiSzemeredi DHJ(3) sketch  
Feb 27  Tao.826: NonFourier proof of DHJ(2) structure theorem
Gowers.828: Does correlation with 1set 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: Incrementfree Fourier proof of DHJ(2) 
Tao.837.2: Dense fibres argument for Gowers Q  Markström.779: 41point Moser sets listed  
Mar 1  Cantwell.782, Peake.784: [math]c'_5 \leq 125[/math]  
Mar 2  Gowers: DHJ 851899
Tao.853 Mass increment; connection with Hahn decomposition Gowers.854 HigherD AjtaiSzemeredi? 

Mar 3  McCutcheon.864 Caution: 12sets not sigmaalgebra!  Dyer.786 [math] \overline{c}^\mu_6 \lt 18[/math]
Cantwell.787 125sets 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 (900999) Density HalesJewett type numbers Tao.901: 125sets 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 Paretooptimal and extremal statistics? Dyer.909 Wildcard variants of Moser Cantwell.912 125sets have at most 40 points in middle slices Cantwell.913 125sets have D=0 (alternate proof) Peake.914 Paretooptimal 3D statistics  
Mar 6  Gowers.873 12set density increment difficulty identified  Dyer.917 [math]\overline{c}^\mu_7 \leq 22[/math]
Cantwell.920 [math]c'_6 \leq 373[/math] Cantwell.921 125sets 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 Shelahtype flipflop spaces?  Peake.931 3D extremals and inequalities
Cantwell.932 125sets have a middle slice of at most 39 points Cantwell.933 125sets have A=6,7,8 Cantwell.934 If C=78 then A=7,8 Tao.935 125sets 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 12sets?
Gowers.882 New proof of AjtaiSzemeredi 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) (10001049)
Gowers.1005.1 Towertype bounds 
Tao.1003 1sets, 2sets locally independent  
Mar 11  Kalai: Polymath1: probable success  Gowers.1007 Correlation component of DHJ(k) proof complete
Solymosi.1011 Shelahtype 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 (nondegenerate) 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  Tao.1035 Ramseyfree translation of Austin's proof  Tao: DHJ(3) 11001199  
Mar 15  Neylon: There are crowds, and then there are crowds...  
Mar 16  Gowers: DHJ(3) and related results: 10501099  
Mar 18  Polymath hits front page of Slashdot with this article
Nielsen: How changing the technology of collaboration can change the nature of collaboration 

Mar 20  Nielsen: The Polymath project: scope of participation  
Mar 21  Gans: Something interesting is going on in Maths  
Mar 24  Gowers: Can Polymath be scaled up?
Vipulnaik: Concluding notes on the polymath project  and a challenge 
 
Mar 25  Nielsen: On scaling up the polymath project 
