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 (1-199)
Gowers: Why this particular problem?
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 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: c0 = 1, c1 = 2, c2 = 6,
Tao.40: c3 = 18
|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?
|Feb 4||Gowers: Quick question|| Tao.100: Use density incrementation?
Tao.118: Szemeredi's proof of Roth looks inapplicable
|Jakobsen.90: c4 = 52|
|Feb 5||Tea time: Introspection|| Tao.130: 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 Dn
|Feb 7||Gowers.335: DHJ(j,k) introduced|| Jakobsen.207: ,
Peake.218: Lower bounds up to c15
|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?
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: ; xyz notation|
|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: , ,|
|Feb 12||Wiki set up|| O'Donnell.476: Fourier-analytic Sperner computations
McCutcheon.480: Strong Roth theorem proposed
Peake.262: Extremisers for c4
|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: n should already provide enough randomness
Tao.510: Finitary analogue of stationarity
|Sauvaget: A proof that c5 = 154?|
|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 cn
Markström.706: Integer program, c5 = 150
Cantwell.708: c6 = 450
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: c5 extremisers
Tao.731: Human proof that ;
|Feb 17|| Tao.536: Fourier-analytic proof of DHJ(2.6)
McCutcheon.541: "Cave-man" proof of DHJ(2.6)
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: c6 extremiser unique|
|Feb 19|| Markström.742: 43-point Moser sets in 4 listed
Peake.743: 43-point sets analysed
Tao.745: 50+ point line-free sets in 4 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: 42-point Moser sets listed
Peake.751: Human proof of
|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 c5 = 150, c6 = 450
Tao.753: Sequences submitted to OEIS
|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
Chua.766: 3D Moser sets with 222 have points
Tao.767: 4D Moser sets with 2222 have points
|Feb 24|| Tao.809.2: Low-influence implies Sperner-positivity
Gowers.812: Fourier vs physical positivity
O'Donnell.814: , 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 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|
|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:|
|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
Cantwell.787 125-sets have at most 41 points in middle slices
|Mar 4||Markstrom.788: for n = 2,3,4,5
Tao.793: "score" introduced
Tao.901: 125-sets have D=0
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
Cantwell.921 125-sets have C=78 or 79
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
Tao.941 Seeding GA?
Cantwell.942 (6,40,79,0,0) eliminated
Tao.943 Linear programming proof of c'4 = 43
|Mar 9|| Gowers.885 Sketch of DHJ(3)
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: c'5 = 124
Tao.950 submitted to OEIS
|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
|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
Cantwell.976: Partial recovery of 4D stats by hand
|Mar 13|| Nielsen: Biweekly links for 03/13/2009
Galdino: Links seminais
| Elsholtz.980: Use e=1, f=1, etc. refinements
Peake.982: xxyyzz inequalities
Cantwell.985: Human proof of begins
Peake.989: xxyyz inequalities
Peake.991: xxxyz, xxxxyz, xxxyyz inequalities
Seva.994: Kakeya in ^n?
|Mar 14||Hariss: Polymath||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...|
|Mar 16||Gowers: DHJ(3) and related results: 1050-1099|
|Mar 18||Polymath hits front page of Slashdot with this article|
|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?||
|Mar 25||Nielsen: On scaling up the polymath project||