Difference between revisions of "Timeline"

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Some highlights of the polymath1 project to date.
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| Feb 6
 
| Feb 6
 
|  
 
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| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1895 Solymosi.155] Pair removal for Kneser graphs
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| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1895 Solymosi.155]: Pair removal for Kneser graphs
  
 
Gowers: [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/ The triangle removal approach] (300-399)
 
Gowers: [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/ The triangle removal approach] (300-399)
 
|  
 
|  
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35495 Neylon.201] Greedy algorithm
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| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35495 Neylon.201]: Greedy algorithm
  
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35528 Tao.206] Use <math>D_n</math>
+
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35528 Tao.206]: Use <math>D_n</math>
 
|-
 
|-
 
| Feb 7
 
| Feb 7
 
|  
 
|  
| [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/#comment-1945 Gowers.335] DHJ(j,k) introduced
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| [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/#comment-1945 Gowers.335]: DHJ(j,k) introduced
 
|  
 
|  
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35537 Jakobsen.207] <math>c_5 \geq 150</math>, <math>c_6 \geq 450</math>
+
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35537 Jakobsen.207]: <math>c_5 \geq 150</math>, <math>c_6 \geq 450</math>
  
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35585 Peake.217] <math>c_7 \geq 1308</math>, <math>c_8 \geq 3780</math>
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[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35585 Peake.217]: <math>c_7 \geq 1308</math>, <math>c_8 \geq 3780</math>
  
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35593 Peake.218] Lower bounds up to <math>c_{15}</math>
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[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35593 Peake.218]: Lower bounds up to <math>c_{15}</math>
 
|-
 
|-
 
| Feb 8
 
| Feb 8
 
|  
 
|  
| Gowers: [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/ Quasirandomness and obstructions to uniformity] (400-499)
+
| Gowers: [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/ Quasirandomness and obstructions to uniformity]: (400-499)
  
 
Ajtai-Szemeredi approach proposed
 
Ajtai-Szemeredi approach proposed
  
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2001 Tao.402] Standard obstruction to uniformity?
+
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2001 Tao.402]: Standard obstruction to uniformity?
  
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2002 Gowers.403] Complexity 1 sets are more fundamental obstructions
+
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2002 Gowers.403]: Complexity 1 sets are more fundamental obstructions
  
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2019 Gowers.411] Are global complexity 1 sets the only obstructions?
+
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2019 Gowers.411]: Are global complexity 1 sets the only obstructions?
  
 
|  
 
|  
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35597 Peake.219] <math>c_{99} \geq 3^{98}</math>
+
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35597 Peake.219]: <math>c_{99} \geq 3^{98}</math>
  
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35608 Tao.225] Spreadsheet set up
+
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35608 Tao.225]: Spreadsheet set up
 
|-
 
|-
 
| Feb 9
 
| Feb 9
 
| Nielsen: [http://michaelnielsen.org/blog/?p=555 Update on the polymath project]
 
| Nielsen: [http://michaelnielsen.org/blog/?p=555 Update on the polymath project]
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2029 Bukh.412] Negative answer to Gowers' question
+
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2029 Bukh.412]: Negative answer to Gowers' question
  
[http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/#comment-2047 Gowers.365] Equal slices measure introduced
+
[http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/#comment-2047 Gowers.365]: Equal slices measure introduced
  
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2056 Tao.419]  Use low-influence instead of complexity 1?
+
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2056 Tao.419]: Use low-influence instead of complexity 1?
  
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2057 Gowers.420] Need DHJ(0,2)
+
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2057 Gowers.420]: Need DHJ(0,2)
  
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2072 Tao.431] Use local obstructions rather than global obstructions?
+
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2072 Tao.431]: Use local obstructions rather than global obstructions?
  
 
|  
 
|  
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35631 Kalai.233] Higher k?
+
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35631 Kalai.233]: Higher k?
 
|-
 
|-
 
| Feb 10
 
| Feb 10
 
|  
 
|  
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2086 Tao.439] Use hypergraph regularity?
+
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2086 Tao.439]: Use hypergraph regularity?
 
|  
 
|  
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35662 Peake.241] <math>c_5 \leq 155</math>; xyz notation
+
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35662 Peake.241]: <math>c_5 \leq 155</math>; xyz notation
  
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35672 Peake.243] <math>c_5 \leq 154</math>
+
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35672 Peake.243]: <math>c_5 \leq 154</math>
 
|-
 
|-
 
| Feb 11
 
| Feb 11
 
| [http://docs.google.com/Doc?id=dhs78pth_15dfw8jhz4 Tao.470]: Proto-wiki created
 
| [http://docs.google.com/Doc?id=dhs78pth_15dfw8jhz4 Tao.470]: Proto-wiki created
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2086 Tao.451] 01-insensitive case OK
+
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2086 Tao.451]: 01-insensitive case OK
  
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2114 Kalai.455] Hyper-optimistic conjecture
+
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2114 Kalai.455]: Hyper-optimistic conjecture
  
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2120 Tao.460] Connections with ergodic approach
+
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2120 Tao.460]: Connections with ergodic approach
  
 
Tao: [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/ A reading seminar on DHJ] (600-699)
 
Tao: [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/ A reading seminar on DHJ] (600-699)
 
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35691 Tao.249]: <math>\overline{c}^\mu_0 = 1</math>, <math>\overline{c}^\mu_1 = 2</math>, <math>\overline{c}^\mu_2 = 4</math>
 
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35691 Tao.249]: <math>\overline{c}^\mu_0 = 1</math>, <math>\overline{c}^\mu_1 = 2</math>, <math>\overline{c}^\mu_2 = 4</math>
  
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35709 Dyer.254] <math>\overline{c}^\mu_3 = 6</math>
+
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35709 Dyer.254]: <math>\overline{c}^\mu_3 = 6</math>
 
|-
 
|-
 
| Feb 12
 
| Feb 12
 
| [http://michaelnielsen.org/polymath1/index.php?title=Main_Page Wiki set up]
 
| [http://michaelnielsen.org/polymath1/index.php?title=Main_Page Wiki set up]
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2143 O'Donnell.476] Fourier-analytic Sperner computations
+
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2143 O'Donnell.476]: Fourier-analytic Sperner computations
  
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2149 McCutcheon.480] Strong Roth theorem proposed
+
[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2149 McCutcheon.480]: Strong Roth theorem proposed
  
 
|  
 
|  
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35728 Jakobsen.257] <math>\overline{c}^\mu_4 = 9</math>
+
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35728 Jakobsen.257]: <math>\overline{c}^\mu_4 = 9</math>
  
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35733 Jakobsen.258] <math>\overline{c}^\mu_5 = 12</math>
+
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35733 Jakobsen.258]: <math>\overline{c}^\mu_5 = 12</math>
  
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35749 Peake.262] Extremisers for <math>c_4</math>
+
[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35749 Peake.262]: Extremisers for <math>c_4</math>
 
|-
 
|-
 
| Feb 13
 
| Feb 13
 
|  
 
|  
 
| Gowers: [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#more-441/ Possible proof strategies] (500-599)
 
| Gowers: [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#more-441/ Possible proof strategies] (500-599)
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2179 McCutcheon.505] IP uniformity norms?
+
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2179 McCutcheon.505]: IP uniformity norms?
  
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35801 Tao.614] Carlson-Simpson not needed for stationarity  
+
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35801 Tao.614]: Carlson-Simpson not needed for stationarity  
 
| Tao: [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/ Bounds for first few DHJ numbers] (700-799)
 
| Tao: [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/ Bounds for first few DHJ numbers] (700-799)
 
|-
 
|-
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|  
 
|  
 
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2183 Gowers.496]: Equal slices implies uniform
 
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2183 Gowers.496]: Equal slices implies uniform
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2185 McCutcheon.508] Ergodic proof strategy
+
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2185 McCutcheon.508]: Ergodic proof strategy
  
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35821 Tao.618] More randomness needed to invert maps
+
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35821 Tao.618]: More randomness needed to invert maps
  
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35837 O'Donnell.622] <math>[3]^n</math> should already provide enough randomness
+
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35837 O'Donnell.622]: <math>[3]^n</math> should already provide enough randomness
  
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2188 Tao.510] Finitary analogue of stationarity  
+
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2188 Tao.510]: Finitary analogue of stationarity  
  
 
| Sauvaget: [http://thomas1111.wordpress.com/2009/02/14/a-proof-that-c_5154/ A proof that <math>c_5=154</math>?]
 
| Sauvaget: [http://thomas1111.wordpress.com/2009/02/14/a-proof-that-c_5154/ A proof that <math>c_5=154</math>?]
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| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2195 Tao.498]: Uniform implies equal slices
 
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2195 Tao.498]: Uniform implies equal slices
  
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2196 Tao.514] DHJ(2.6) proposed
+
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2196 Tao.514]: DHJ(2.6) proposed
  
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2206 McCutcheon.518] Ramsey proof of DHJ(2.6)
+
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2206 McCutcheon.518]: Ramsey proof of DHJ(2.6)
 
|  
 
|  
 
| Sauvaget: [http://thomas1111.wordpress.com/2009/02/15/a-new-strategy-for-computing-c_n/ A new strategy for computing <math>c_n</math>]
 
| Sauvaget: [http://thomas1111.wordpress.com/2009/02/15/a-new-strategy-for-computing-c_n/ A new strategy for computing <math>c_n</math>]
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[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35865 Cantwell.708]: <math>c_6=450</math>
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35865 Cantwell.708]: <math>c_6=450</math>
 +
 +
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35877 Tao.715]: Genetic algorithm?
  
 
|-
 
|-
 
| Feb 16
 
| Feb 16
 
|  
 
|  
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2214 Tao.524] Simplification of proof
+
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2214 Tao.524]: Simplification of proof
  
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2222 O'Donnell 529] Ramsey-free proof of DHJ(2.6)?
+
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2222 O'Donnell 529]: Ramsey-free proof of DHJ(2.6)?
  
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2228 McCutcheon.533] Ramsey theory incompatible with symmetry
+
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2228 McCutcheon.533]: Ramsey theory incompatible with symmetry
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35921 Tao.626] Ramsey theorems summarised
+
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35921 Tao.626]: Ramsey theorems summarised
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35926 Peake.730] <math>c_5</math> extremisers
+
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35926 Peake.730]: <math>c_5</math> extremisers
  
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35927 Tao.731] Human proof that <math>c_5 \leq 152</math>; <math>c_7 \leq 1348</math>  
+
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35927 Tao.731]: Human proof that <math>c_5 \leq 152</math>; <math>c_7 \leq 1348</math>  
 
|-
 
|-
 
| Feb 17
 
| Feb 17
 
|  
 
|  
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2234 Tao.536] Fourier-analytic proof of DHJ(2.6)
+
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2234 Tao.536]: Fourier-analytic proof of DHJ(2.6)
  
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2242 McCutcheon.541] "Cave-man" proof of DHJ(2.6)
+
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2242 McCutcheon.541]: "Cave-man" proof of DHJ(2.6)
 
|  
 
|  
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35945 Chua.736] <math>c'_5 \geq 124</math>
+
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35945 Chua.736]: <math>c'_5 \geq 124</math>
  
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35951 Peake.738] Connection between Moser(3) and sphere packing
+
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35951 Peake.738]: Connection between Moser(3) and sphere packing
  
 
|-
 
|-
 
| Feb 18
 
| Feb 18
 
|  
 
|  
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2255 Gowers.544] Corners(1,3)?
+
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2255 Gowers.544]: Corners(1,3)?
  
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2260 Gowers.545] Fourier computations on equal-slices measure begin
+
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2260 Gowers.545]: Fourier computations on equal-slices measure begin
  
 
|  
 
|  
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35963 Markström.739] <math>c_6</math> extremiser unique
+
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35963 Markström.739]: <math>c_6</math> extremiser unique
 
|-
 
|-
 
| Feb 19
 
| Feb 19
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|  
 
|  
 
|  
 
|  
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36011 Markström.742] 43-point Moser sets in <math>[3]^4</math> listed
+
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36011 Markström.742]: 43-point Moser sets in <math>[3]^4</math> listed
  
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36017 Peake.743] 43-point sets analysed
+
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36017 Peake.743]: 43-point sets analysed
  
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36018 Cantwell.744] <math>c'_5 \leq 128</math>
+
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36018 Cantwell.744]: <math>c'_5 \leq 128</math>
  
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36024 Tao.745] 50+ point line-free sets in <math>[3]^4</math> listed
+
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36024 Tao.745]: 50+ point line-free sets in <math>[3]^4</math> listed
  
 
|-
 
|-
 
| Feb 20
 
| Feb 20
 
| Vipulniak: [http://whatisresearch.wordpress.com/2009/02/20/a-quick-review-of-the-polymath-project/]
 
| Vipulniak: [http://whatisresearch.wordpress.com/2009/02/20/a-quick-review-of-the-polymath-project/]
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2296 Solymosi.563] Moser(6) implies DHJ(3)
+
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2296 Solymosi.563]: Moser(6) implies DHJ(3)
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36041 Tao.630] IP convergence lemma
+
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36041 Tao.630]: IP convergence lemma
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36031 Markström.747] 42-point Moser sets listed
+
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36031 Markström.747]: 42-point Moser sets listed
  
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36045 Peake.751] Human proof of <math>c_5 \leq 151</math>
+
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36045 Peake.751]: Human proof of <math>c_5 \leq 151</math>
  
 
|-
 
|-
 
| Feb 21
 
| Feb 21
 
| Gowers: [http://gowers.wordpress.com/2009/02/21/to-thread-or-not-to-thread/ To thread or not to thread]
 
| Gowers: [http://gowers.wordpress.com/2009/02/21/to-thread-or-not-to-thread/ To thread or not to thread]
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2327 Gowers.580] Extreme localisation + density increment = DHJ(3)?
+
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2327 Gowers.580]: Extreme localisation + density increment = DHJ(3)?
  
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2329 Gowers.581] Multidimensional Sperner
+
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2329 Gowers.581]: Multidimensional Sperner
  
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2331 Gowers.582] Use Ajtai-Szemeredi argument to get density increment?
+
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2331 Gowers.582]: Use Ajtai-Szemeredi argument to get density increment?
  
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36084 Tao.631] Informal combinatorial translation of ergodic DHJ(2)
+
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36084 Tao.631]: Informal combinatorial translation of ergodic DHJ(2)
  
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2321 Tao.578] Finitary ergodic proof of DHJ(2) proposed
+
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2321 Tao.578]: Finitary ergodic proof of DHJ(2) proposed
  
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36085 Tao.632] Special cases of DHJ(3) translated
+
[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36085 Tao.632]: Special cases of DHJ(3) translated
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36051 Peake.752] Human proof of <math>c_5=150</math>, <math>c_6=450</math>
+
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36051 Peake.752]: Human proof of <math>c_5=150</math>, <math>c_6=450</math>
  
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36059 Tao.753] Sequences submitted to OEIS
+
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36059 Tao.753]: Sequences submitted to OEIS
 
|-
 
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| Feb 22
 
| Feb 22
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| Feb 23
 
| Feb 23
 
|  
 
|  
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2356 McCutcheon.593] DHJ(2.7)
+
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2356 McCutcheon.593]: DHJ(2.7)
  
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2370 O'Donnell.596] Fourier-analytic proof of DHJ(2)
+
[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2370 O'Donnell.596]: Fourier-analytic proof of DHJ(2)
  
 
Gowers: [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/ Brief review of polymath1] (800-849)
 
Gowers: [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/ Brief review of polymath1] (800-849)
  
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2372 O'Donnell.800] Fourier-analytic + density increment proof of DHJ(2)
+
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2372 O'Donnell.800]: Fourier-analytic + density increment proof of DHJ(2)
  
 
|  
 
|  
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36112 Markström.463] 42-point Moser sets analysed
+
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36112 Markström.463]: 42-point Moser sets analysed
  
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36115 Tao.464] <math>c'_5 \leq 127</math>
+
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36115 Tao.464]: <math>c'_5 \leq 127</math>
  
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36126 Chua.766] 3D Moser sets with 222 have <math> \leq 13</math> points
+
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36126 Chua.766]: 3D Moser sets with 222 have <math> \leq 13</math> points
  
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36127 Tao.767] 4D Moser sets with 2222 have <math> \leq 39</math> points
+
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36127 Tao.767]: 4D Moser sets with 2222 have <math> \leq 39</math> points
 
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| Feb 24
 
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| Feb 25
 
| Feb 25
 
|  
 
|  
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2431 Gowers.820] Density increment on complexity 1 set
+
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2431 Gowers.820]: Density increment on complexity 1 set
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2427 Tao.818] Finitary ergodic sketch of DHJ(3)
+
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2427 Tao.818]: Finitary ergodic sketch of DHJ(3)
  
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2435 O'Donnell.821] Simplified Fourier proof of DHJ(2) structure theorem
+
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2435 O'Donnell.821]: Simplified Fourier proof of DHJ(2) structure theorem
  
 
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36157 Cantwell.769]: 5D Moser sets with 2222* have <math> \leq 124</math> points
 
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36157 Cantwell.769]: 5D Moser sets with 2222* have <math> \leq 124</math> points
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| Feb 28
 
| Feb 28
 
|  
 
|  
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2476 Tao.834] Use pullbacks for Gowers Q?
+
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2476 Tao.834]: Use pullbacks for Gowers Q?
  
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2478 Gowers.835] Pullbacks don't work
+
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2478 Gowers.835]: Pullbacks don't work
  
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2496 O'Donnell 839] Increment-free Fourier proof of DHJ(2)
+
[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2496 O'Donnell 839]: Increment-free Fourier proof of DHJ(2)
  
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2490 Tao.837.2] Dense fibres argument for Gowers Q
+
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2490 Tao.837.2]: Dense fibres argument for Gowers Q
  
 
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36216 Markström.779]: 41-point Moser sets listed
 
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36216 Markström.779]: 41-point Moser sets listed

Revision as of 22:15, 1 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

Nielsen: Is massively collaborative mathematics possible?

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]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 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 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: [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]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