Timeline
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 | Gowers.9: Reweighting vertices needed for Varnavides?
Tao.17: Should use [math]\displaystyle{ 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]\displaystyle{ c_0=1 }[/math], [math]\displaystyle{ c_1=2 }[/math], [math]\displaystyle{ c_2=6 }[/math], [math]\displaystyle{ 3^{n-O(\sqrt{n}} \leq c_n \leq o(3^n) }[/math]
Kalai.15: [math]\displaystyle{ c_n \gg 3^n/\sqrt{n} }[/math] Tao.39: [math]\displaystyle{ c_n \geq 3^{n-O(\sqrt{\log n})} }[/math] Tao.40: [math]\displaystyle{ 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]\displaystyle{ c_4 \geq 49 }[/math]
Tao.78: [math]\displaystyle{ c_4 \leq 54 }[/math] Neylon.83: [math]\displaystyle{ 52 \leq c_4 \leq 54 }[/math], [math]\displaystyle{ 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]\displaystyle{ c_4=52 }[/math] | |
| Feb 5 | 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]\displaystyle{ D_n }[/math] | ||
| Feb 7 | Gowers.335: DHJ(j,k) introduced | Jakobsen.207: [math]\displaystyle{ c_5 \geq 150 }[/math], [math]\displaystyle{ c_6 \geq 450 }[/math]
Peake.217: [math]\displaystyle{ c_7 \geq 1308 }[/math], [math]\displaystyle{ c_8 \geq 3780 }[/math] Peake.218: Lower bounds up to [math]\displaystyle{ 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]\displaystyle{ 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]\displaystyle{ c_5 \leq 155 }[/math]; xyz notation
Peake.243: [math]\displaystyle{ c_5 \leq 154 }[/math] | ||
| Feb 11 | 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]\displaystyle{ \overline{c}^\mu_0 = 1 }[/math], [math]\displaystyle{ \overline{c}^\mu_1 = 2 }[/math], [math]\displaystyle{ \overline{c}^\mu_2 = 4 }[/math]
Dyer.254: [math]\displaystyle{ \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]\displaystyle{ \overline{c}^\mu_4 = 9 }[/math]
Jakobsen.258: [math]\displaystyle{ \overline{c}^\mu_5 = 12 }[/math] Peake.262: Extremisers for [math]\displaystyle{ 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]\displaystyle{ [3]^n }[/math] should already provide enough randomness Tao.510: Finitary analogue of stationarity |
Sauvaget: A proof that [math]\displaystyle{ 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]\displaystyle{ c_n }[/math]
Markström.706: Integer program, [math]\displaystyle{ c_5=150 }[/math] Cantwell.708: [math]\displaystyle{ 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]\displaystyle{ c_5 }[/math] extremisers
Tao.731: Human proof that [math]\displaystyle{ c_5 \leq 152 }[/math]; [math]\displaystyle{ 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]\displaystyle{ 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]\displaystyle{ c_6 }[/math] extremiser unique | ||
| Feb 19 | Markström.742: 43-point Moser sets in [math]\displaystyle{ [3]^4 }[/math] listed
Peake.743: 43-point sets analysed Cantwell.744: [math]\displaystyle{ c'_5 \leq 128 }[/math] Tao.745: 50+ point line-free sets in [math]\displaystyle{ [3]^4 }[/math] listed | |||
| Feb 20 | Vipulniak: [1] | 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]\displaystyle{ 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]\displaystyle{ c_5=150 }[/math], [math]\displaystyle{ 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]\displaystyle{ c'_5 \leq 127 }[/math] Chua.766: 3D Moser sets with 222 have [math]\displaystyle{ \leq 13 }[/math] points Tao.767: 4D Moser sets with 2222 have [math]\displaystyle{ \leq 39 }[/math] points | ||
| Feb 24 | Tao.809.2: Low-influence implies Sperner-positivity
Gowers.812: Fourier vs physical positivity O'Donnell.814: [math]\displaystyle{ \ell_1 }[/math], [math]\displaystyle{ \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]\displaystyle{ \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]\displaystyle{ 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]\displaystyle{ c'_5 \leq 125 }[/math] | |||
| Mar 2 | Gowers: DHJ 851-899 |
